pense-bête de bruno sanchiz

M87-6 L'ombre et la masse du trou noir central

bruno — 2019-04-15T02:46:39Z

The Shadow and Mass of the Central Black Hole

M87-5 Origine Physique de l'anneau asymétrique

bruno — 2019-04-15T02:46:36Z

Origine Physique de l'anneau asymétrique

Le télescope Event Horizon (EHT) a cartographié à 1,3 mm la source radio compacte au centre de la galaxie elliptique M87 avec une résolution angulaire sans précédent. Nous examinons ici les implications physiques de l'anneau asymétrique observé dans les données de l'EHT de 2017.
À cette fin, nous construisons une vaste bibliothèque de modèles basés sur des simulations magnétohydrodynamiques relativistes générales (GRMHD) et des images de synthèse produites par des lancés de rayons de relativité générale.
Nous comparons les visibilités observées avec cette bibliothèque et confirmons que l'anneau asymétrique est cohérent avec les prévisions antérieures de forte lentille gravitationnelle de l'émission synchrotron d'un plasma chaud en orbite autour de l'horizon des événements de trou noir.
Le rayon de l'anneau et l'asymétrie de l'anneau dépendent respectivement de la masse et du spin du trou noir, et les deux devraient donc être stables lorsqu'ils seront observés lors de futures campagnes EHT. Dans l'ensemble, l'image observée correspond aux prévisions concernant l'ombre d'un trou noir de Kerr en rotation, telles que prédites par la relativité générale. Si le spin du trou noir et le jet à grande échelle de M87 sont alignés, alors le vecteur de spin du trou noir est dirigé loin de la Terre. Les modèles de notre bibliothèque de trous noirs pas en rotation ne concordent pas avec les observations car ils ne produisent pas de jets suffisamment puissants. Dans le même temps, dans ces modèles qui produisent un jet suffisamment puissant, ce dernier est alimenté par extraction de l'énergie de spin du trou noir par le biais de mécanismes similaires au processus de Blandford-Znajek. Nous considérons brièvement des alternatives au trou noir pour l'objet compact central.
L'analyse des données de polarisation EHT existantes et des données prises simultanément à d'autres longueurs d'onde permettra bientôt de nouveaux tests des modèles GRMHD, de même que les futures campagnes EHT à 230 et 345 GHz.

introduction

En 1918, la galaxie Messier 87 (M87) fut observée par Curtis et fut trouvée avoir '''un curieux rayon droit… apparemment lié au noyau par une fine ligne de matière''' (Curtis 1918, p. 31). Le rayon de Curtis est maintenant connu pour être un jet, s'étendant de l'échelle sous-parsec à plusieurs kpc, et peut être observé à travers le spectre électromagnétique, de la radio jusqu'aux rayons γ. Les observations d'interférométrie à base très longues (VLBI) qui zooment sur le noyau, sondant des échelles angulaires progressivement plus petites à des fréquences progressivement plus élevées jusqu'à 86 GHz avec la matrice ?? Global mm-VLBI (GMVA ; par exemple, Hada et al. 2016 ; Boccardi et al. 2017 ; Kim et al. 2018 ; Walker et al 2018) ont révélé que le jet émerge d'un noyau central. Les modèles de la distribution de vitesse stellaire impliquent une masse pour le noyau central $M \ approx 6,2 \ times 10 ^ 9 \, M _ \ odot $$ à une distance de $16,9 \, \ mathrm Mpc $$ ( Gebhardt et al., 2011) ; les modèles de raies d'émission de gaz ionisé d'échelle d'une seconde d'arc impliquent une masse qui est inférieure d'un facteur deux environ (Walsh et al. 2013).

Le modèle conventionnel de l'objet central dans M87 est un trou noir entouré par un flux d'accrétion de disque optiquement fin et géométriquement épais (par exemple, Ichimaru 1977 ; Rees et al. 1982 ; Narayan & Yi 1994, 1995 ; Reynolds et al. 1996).
Le pouvoir radiatif du flux d'accrétion dérive finalement de l'énergie de liaison gravitationnelle du plasma entrant. Il n'existe pas de modèle consensuel pour le lancement de jets, mais les deux scénarios principaux sont que le jet est un flux dominé magnétiquement qui est finalement alimenté en exploitant l'énergie de rotation du trou noir (Blandford & Znajek 1977) et que le jet est un vent collimaté magnétiquement depuis le disque d'accrétion environnant (Blandford et Payne, 1982 ; Lynden-Bell, 2006).

Les observations VLBI de M87 aux fréquences $ \gtrsim 230 \, \mathrm GHz $$ avec le Télescope Horizon des Evénements (EHT) peuvent résoudre des échelles angulaires de dizaines de $ \ mu \ mathrm as$$, comparables à l'échelle de l'horizon des événements (Doeleman et al. 2012 ; Akiyama et al. 2015 ; EHT Collaboration et al. 2019a, 2019b, 2019c, ci-après désigné : documents I, II et III).
Ils ont donc le pouvoir de sonder la nature de l'objet central et de tester des modèles de lancement de jet. En outre, les observations EHT peuvent limiter les paramètres physiques clés du système, notamment la masse et le spin du trou noir, le taux d'accrétion et le flux magnétique piégé par l'accrétion de plasma dans le trou noir.

Dans cette lettre, nous adoptons l'hypothèse de travail selon laquelle l'objet central est un trou noir décrit par la métrique de Kerr, avec une masse M et un spin sans dimension $a_ * , -1 \ lt a _ * \ lt 1 $$.
Ici, $* \ equiv Jc / GM ^ 2 $$, où J, G et c sont respectivement le moment angulaire du trou noir, la constante de gravitation et la vitesse de la lumière. Dans notre convention, $* \ lt 0 $$ implique que le moment angulaire du flux d'accrétion et celui du trou noir sont antialignés. À l'aide de modèles magnétohydrodynamiques relativistes généraux (GRMHD) pour le flux d'accrétion et d'images synthétiques de ces simulations produites par des calculs de transfert radiatif relativiste général, nous vérifions si les résultats de la campagne d'observation EHT de 2017 (ci-après EHT2017) sont compatibles avec l'hypothèse du trou noir. .

Cette lettre est organisée comme suit. Dans la section 2, nous passons en revue les principales caractéristiques des observations et fournissons des estimations par ordre de grandeur des conditions physiques de la source. Dans la section 3, nous décrivons les modèles numériques. Dans la section 4, nous décrivons notre procédure de comparaison des modèles avec les données de manière à prendre en compte la variabilité du modèle. Dans la section 5, nous montrons qu'un grand nombre de modèles ne peuvent pas être rejetés sur la base des seules données EHT. Dans la section 6, nous combinons les données EHT avec d'autres contraintes sur l'efficacité radiative, la luminosité des rayons X et la puissance des jets, et montrons que cette dernière contrainte élimine tous les modèles $a_ * = 0 $$. Dans la section 7, nous discutons des limites de nos modèles et des solutions de rechange aux modèles de trou noir de Kerr. Dans la section 8, nous résumons nos résultats et expliquons comment une analyse plus poussée des données EHT existantes, des futures données EHT et des observations complémentaires sur plusieurs longueurs d'onde accentueront les contraintes sur les modèles.

Review and Estimates

Dans la Collaboration EHT et al. (2019d ; ci-après Paper IV), nous présentons des images générées à partir des données EHT2017 (pour plus de détails sur le tableau, la campagne d'observation de 2017, la corrélation et l'étalonnage, voir les documents II et III). Une image représentative est reproduite dans le panneau de gauche de la figure 1.

Figure 1. Left panel : an EHT2017 image of M87 from Paper IV of this series (see their Figure 15). Middle panel : a simulated image based on a GRMHD model. Right panel : the model image convolved with a $20\,\mu \mathrmas$ FWHM Gaussian beam. Although the most evident features of the model and data are similar, fine features in the model are not resolved by EHT.

Quatre caractéristiques de l'image sur le panneau de gauche de la figure 1 jouent un rôle important dans notre analyse : (1) la géométrie en anneau, (2) la température de brillance de pointe, (3) la densité de flux totale et (4) la asymétrie de la bague. Nous considérons maintenant chacun à son tour.

(1) La source compacte présente un anneau lumineux avec une zone sombre centrale sans composants étendus significatifs. Cela présente une similitude remarquable avec la structure longtemps prédite pour l'émission optiquement mince d'un plasma chaud entourant un trou noir (Falcke et al. 2000). Le trou central entouré d'un anneau brillant résulte d'une forte lentille gravitationnelle (par exemple, Hilbert 1917 ; von Laue 1921 ; Bardeen 1973 ; Luminet 1979). Le « cercle de photons » correspond aux lignes de vision qui passent près des orbites de photons (instables) (voir Teo 2003), s'attardent près de l'orbite des photons et ont donc un long trajet à travers le plasma émetteur. Ces lignes de visée apparaîtront relativement brillantes si le plasma émetteur est optiquement mince. La dépression du flux central est ce qu'on appelle le"trou noir"("trou noir") (Falcke et al. 2000) et correspond aux lignes de mire qui se terminent à l'horizon des événements. L'ombre pourrait être vue contrairement à l'émission environnante provenant du flux d'accrétion ou du contre-jet à lentilles dans M87 (Broderick & Loeb 2009).

L'anneau de photons est presque circulaire pour toutes les rotations des trous noirs et toutes les inclinaisons de l'axe de rotation des trous noirs par rapport à la ligne de mire (par exemple, Johannsen & Psaltis 2010). Pour un _ * = 0 $ trou noir de masse $ et de distance D, le rayon angulaire de l'anneau du photon dans le ciel est
Équation (1)

où nous avons réduit à la masse la plus probable de Gebhardt et al. (2011) et une distance de 6,9 \, \ mathrm Mpc $ (voir aussi EHT Collaboration et al. 2019e, (ci-après Article VI ; Blakeslee et al. 2009 ; Bird et al. 2010 ; Cantiello et al. 2018). Le rayon angulaire de l'anneau du photon pour les autres inclinaisons et les valeurs de _ * $ diffère d'au plus 13% de l'équation (1), et la majeure partie de cette variation se produit à - | a _ * | \ ll 1 $ ( par exemple, Takahashi 2004 ; Younsi et al 2016). À l'évidence, le rayon angulaire de l'anneau de photons observé est approximativement égal à $ \ sim 20 \, \ mu \ mathrm as $ (Figure 1 et papier IV), prédiction du modèle de trou noir donné dans l'équation (1).

(2) The observed peak brightness temperature of the ring in Figure 1 is $T_b,pk\sim 6\times 10^9\,\rmK$, which is consistent with past EHT mm-VLBI measurements at 230 GHz (Doeleman et al. 2012 ; Akiyama et al. 2015), and GMVA 3 mm-VLBI measurements of the core region (Kim et al. 2018). Expressed in electron rest-mass (me) units, $\rm\Theta

_b,pk\equiv k_\rmB
T_b,pk/(m_ec^2)\simeq 1$, where $k_\rmB

$ is Boltzmann's constant. The true peak brightness temperature of the source is higher if the ring is unresolved by EHT, as is the case for the model image in the center panel of Figure 1.

L'émission de 1,3 mm de M87 illustrée à la figure 1 devrait être générée par le processus synchrotron (voir Yuan & Narayan 2014 et les références qui y figurent) et dépend donc de la fonction de distribution d'électrons (eDF). Si le plasma émetteur a un eDF thermique, il est caractérisé par une température électronique
$T_e\geqslant T_b$, or $\rm\Theta

_e\equiv k_\rmB

T_e/(m_ec^2)\gt 1$, because $\rm\Theta

_e\gt \rm\Theta
_b,pk$ if the ring is unresolved or optically thin.

La température de luminosité observée est-elle conforme à ce que l'on pourrait attendre de modèles phénoménologiques de la source ? Les modèles d'écoulement d'accrétion inefficaces sur le plan radiatif de M87 (Reynolds et al. 1996 ; Di Matteo et al. 2003) produisent une émission en mm dans un beignet de plasma géométriquement épais autour du trou noir. Le plasma émetteur est sans collision : la diffusion de Coulomb est faible à ces faibles densités et hautes températures. Par conséquent, les températures des électrons et des ions ne doivent pas nécessairement être les mêmes (par exemple, Spitzer 1962). Dans les modèles de flux d'accrétion inefficaces par radiation, la température des ions est légèrement inférieure à la température viriale des ions,

Equation (2)

where $r_\rmg

\equiv GM/c^2$ is the gravitational radius, r is the Boyer–Lindquist or Kerr–Schild radius, and mp is the proton mass. Most models have an electron temperature $T_e\lt T_i$ because of electron cooling and preferential heating of the ions by turbulent dissipation (e.g., Yuan & Narayan 2014 ; Mościbrodzka et al. 2016). If the emission arises at $\sim 5\,r_\rmg

$, then $\rm\Theta

_e\simeq 37(T_e/T_i)$, which is then consistent with the observed $\rm\Theta
_b,pk$ if the source is unresolved or optically thin.

(3)La densité de flux totale dans l'image à.3 \, \ mathrm mm $ est $ \ simeq 0.5 $ Jy. Avec quelques hypothèses, nous pouvons utiliser ceci pour estimer la densité de nombre d'électrons et l'intensité du champ magnétique B dans la source. Nous adoptons un modèle simple, sphérique, à une zone pour la source avec rayon
$r\simeq 5\,r_\rmg

$, pressure $n_ikT_i+n_ekT_e=\beta _\rmp

B^2/(8\pi )$ with $\beta _\rmp

\equiv p_\mathrmgas/p_\mathrmmag\sim 1$, $T_i\simeq 3T_e$, and temperature $\theta _e\simeq 10\theta _b,pk$, ce qui est conforme à la discussion dans (2) ci-dessus. En fixant ne = ni (c'est-à-dire en supposant un plasma d'hydrogène totalement ionisé), les valeurs de B et ne nécessaires pour produire la densité de flux observée peuvent être trouvées en résolvant une équation non linéaire (en supposant un angle moyen entre le champ et la ligne de visée, 60 °). La solution peut être approchée comme une loi de puissance :

Equation (3)

Equation (4)

en supposant que = 6.2 \ times 10 ^ 9 \, M _ \ odot $ et = 16.9 \, \ mathrm Mpc $, et en utilisant l'émissivité thermique approximative de Leung et al. (2011). Ensuite, la profondeur optique du synchrotron à.3 \, \ mathrm mm $ est 0.2. On peut maintenant estimer un taux d'accrétion à partir de (3) en utilisant

Equation (5)

assuming spherical symmetry. The Eddington accretion rate is
Equation (6)

where $L_\mathrmEdd\equiv 4\pi GMcm_p/\sigma _T$ is the Eddington luminosity ($\sigma _T$ is the Thomson cross section). Setting the efficiency $\epsilon =0.1$ and $M=6.2\times 10^9\,M_\odot $, $\dotM_\mathrmEdd=137\,M_\odot \,\mathrmyr^-1$, and therefore $\dotM/\dotM_\mathrmEdd\,\sim 2.0\times 10^-5$.

Cette estimation est similaire mais légèrement supérieure à la limite supérieure déduite des propriétés de polarisation linéaire à 230 GHz de M87 (Kuo et al. 2014).

(4)L'anneau est plus brillant dans le sud que le nord. Cela peut s'expliquer par une combinaison de mouvement dans la source et de faisceau Doppler. Comme exemple simple, nous considérons un anneau lumineux optiquement mince tournant avec la vitesse v et un vecteur de moment angulaire incliné à un angle de vue i
> 0° to the line of sight.Ensuite, le côté approchant de l'anneau est dopé par Doppler et le côté reculant est atténué en Doppler, produisant un contraste de luminosité de surface d'un ordre égal à un si v est relativiste. L'approche du jet à grande échelle dans M87 est orientée ouest-nord-ouest (angle de position $ \ mathrm PA \ environ 288 ^ \ circ ; $ dans le papier VI, on l'appelle
$\mathrmPA_\mathrmFJ$), ou à droite et légèrement en haut dans l'image. Walker et al. (2018) ont estimé que l'angle entre le jet en approche et la ligne de mire était de 17 °. Si l'émission est produite par un anneau tournant avec un vecteur moment cinétique orienté le long de l'axe du jet, le plasma au sud s'approche de la Terre et le plasma au nord recule. Cela implique une circulation dans le sens des aiguilles d'une montre du plasma dans la source, tel que projeté sur le plan du ciel. Ce sens de rotation est cohérent avec le sens de rotation dans le gaz ionisé à des échelles d'arcsecondes (Harms et al. 1994 ; Walsh et al. 2013). Notez que l'asymétrie de l'anneau est compatible avec l'asymétrie déduite d'observations à 43 GHz du rapport de luminosité entre les côtés nord et sud du jet et du contre-jet (Walker et al. 2018).

Toutes ces estimations donnent une image de la source qui correspond remarquablement aux attentes du modèle de trou noir et aux modèles GRMHD existants (par exemple, Dexter et al. 2012 ; Mościbrodzka et al. 2016). Ils suggèrent même une sensation de rotation du gaz près du trou noir. Une comparaison quantitative avec les modèles GRMHD peut en révéler davantage.

models

Conformément à la discussion à la section 2, nous adoptons maintenant l'hypothèse de travail selon laquelle M87 contient un flux d'accrétion turbulent et magnétisé entourant un trou noir de Kerr. Pour tester quantitativement cette hypothèse par rapport aux données EHT2017, nous avons généré une bibliothèque de simulation de modèles GRMHD idéaux 3D dépendant du temps. Pour générer efficacement cette bibliothèque coûteuse en calculs et avec des contrôles indépendants des résultats, nous avons utilisé plusieurs codes différents qui ont évolué pour correspondre aux conditions initiales à l'aide des équations de GRMHD idéal. Les codes utilisés incluent BHAC (Porth et al. 2017), H-AMR (Liska et al. 2018 ; K. Chatterjee et al. 2019, en préparation), iharm (Gammie et al. 2003) et KORAL (Sa̧dowski et al. 2013b, 2014). On trouvera une comparaison de ces codes et d'autres codes GRMHD dans O. Porth et al. 2019 (en préparation), qui montre que les différences entre les intégrations d'un modèle d'accrétion standard avec des codes différents sont moins importantes que les fluctuations dans les simulations individuelles

À partir de la bibliothèque de simulation, nous avons généré une grande bibliothèque d'images synthétiques. Des instantanés des évolutions de GRMHD ont été produits en utilisant les schémas de traçage de rayons relativistes généraux (GRRT) ipole (Mościbrodzka & Gammie 2018), RAPTOR (Bronzwaer et al. 2018) ou BHOSS (Z. Younsi et al. 2019b, en préparation). On peut trouver une comparaison de ces codes et d'autres codes GRRT dans Gold et al. (2019), qui montre que les différences entre les codes sont faibles.

Dans les modèles GRMHD, le gros de l'émission de 1,3 mm est produit à l'intérieur du $ \ lesssim 10 \, r _

r

du trou noir, où les modèles peuvent atteindre un état statistiquement stable. Il est donc possible de calculer des modèles radiatifs prédictifs pour cette composante compacte de la source sans représenter avec précision le flux d'accrétion à tous les rayons.

Nous notons que les modèles actuels de pointe pour M87 sont des modèles GRMHD de rayonnement qui incluent la rétroaction radiative et la thermodynamique électron-ion (Ryan et al. 2018 ; Chael et al. 2019). Ces modèles sont trop coûteux en calcul pour une vaste étude de l'espace des paramètres, de sorte que, dans la présente Lettre, nous ne considérons que les modèles GRMHD non radiatifs avec un traitement paramétré de la thermodynamique des électrons.

3.1. Simulation Library
Toutes les simulations GRMHD sont initialisées avec un tore de plasma faiblement magnétisé en orbite autour du trou équatorial du trou noir (par exemple, De Villiers et al. 2003 ; Gammie et al. 2003 ; McKinney & Blandford 2009 ; Porth et al. 2017). Nous ne considérons pas les modèles inclinés, dans lesquels le moment angulaire du flux d'accrétion est mal aligné avec la rotation du trou noir. Les limites de cette approche sont examinées à la section 7.

The initial torus is driven to a turbulent state by instabilities, including the magnetorotational instability (see e.g., Balbus & Hawley 1991). In all cases the outcome contains a moderately magnetized midplane with orbital frequency comparable to the Keplerian orbital frequency, a corona with gas-to-magnetic-pressure ratio $\beta _\rmp
\equiv p_\mathrmgas/p_\mathrmmag\sim 1$, and a strongly magnetized region over both poles of the black hole with $B^2/\rho c^2\gg 1$. We refer to the strongly magnetized region as the funnel, and the boundary between the funnel and the corona as the funnel wall (De Villiers et al. 2005 ; Hawley & Krolik 2006). All models in the library are evolved from t = 0 to $t=10^4\,r_\rmg

c^-1$.

Le résultat de la simulation dépend de l'intensité et de la géométrie initiales du champ magnétique, dans la mesure où celles-ci affectent le flux magnétique traversant le disque, comme indiqué ci-dessous. Une fois la simulation lancée, le disque passe dans un état turbulent et perd la mémoire de la plupart des détails des conditions initiales. Cet état de turbulence décontracté se trouve à l'intérieur d'un rayon caractéristique qui se développe au cours de la simulation. Pour être sûr de ne représenter que les régions assouplies, nous établissons des instantanés pour les comparer avec les données de \ times 10 ^ 3 \ le t / r _ \ rm g

c ^ - 1 \ le 10 ^ 4 $.

GRMHD models have two key physical parameters. The first is the black hole spin $a_* $, $-1\lt a_* \lt 1$. The second parameter is the absolute magnetic flux $\rm\Phi
_\mathrmBH$ crossing one hemisphere of the event horizon (see Tchekhovskoy et al. 2011 ; O. Porth et al. 2019, in preparation for a definition). It is convenient to recast $\rm\Phi
_\mathrmBH$ in dimensionless form $\phi \equiv \rm\Phi
_\mathrmBH\left(\dotMr_\rmg

^2c\right)^-1/2$.110

Le flux magnétique phgr est non nul car le champ magnétique est envoyé dans l'horizon des événements par le flux d'accrétion et maintenu par les courants dans le plasma environnant. À $ \ phi \ gt \ phi _ \ max \ sim 15 $, 111 simulations numériques montrent que le flux magnétique accumulé explose, écarte le flux d'accrétion et s'échappe (Tchekhovskoy et al. 2011 ; McKinney et al. 2011). 2012). Les modèles avec $ \ phi \ sim 1 $ sont habituellement appelés modèles d'évolution standard et normale (SANE ; Narayan et al. 2012 ; Sa̧dowski et al (2013a)) ; les modèles avec $ \ phi \ sim \ phi _ \ max $ sont classiquement appelés modèles de disques à arrêts magnétiques (MAD ; Igumenshchev et al. 2003 ; Narayan et al. 2003).

La bibliothèque de simulation contient des modèles SANE avec _ * = - 0,94 $, −0,5, 0, 0,5, 0,75, 0,88, 0,94, 0,97, et 0,98 et des modèles MAD avec _ * = - 0,94 $, −0,5, 0, 0,5, 0,75 et 0,94. La bibliothèque de simulation occupe 23 To d'espace disque et contient un total de 43 simulations GRMHD, certaines répétées à plusieurs résolutions avec plusieurs codes, avec des résultats cohérents (O. Porth et al. 2019, en préparation).

3.2. Image Library Generation

Pour produire des images modèles à partir des simulations afin de les comparer aux observations EHT, nous utilisons GRRT pour générer un grand nombre d'images de synthèse et de produits de données VLBI dérivés. Pour créer les images de synthèse, nous devons spécifier les éléments suivants : (1) le champ magnétique, le champ de vitesse et la densité en fonction de la position et de la durée ; (2) les coefficients d'émission et d'absorption en fonction de la position et du temps ; et (3) l'angle d'inclinaison entre le vecteur moment cinétique du flux d'accrétion et la ligne de visée i, l'angle de position $ \ mathrm PA $, la masse du trou noir $ et la distance D à l'observateur. Dans ce qui suit, nous discutons chaque entrée. Le lecteur qui n'est intéressé que par une description de haut niveau de la bibliothèque d'images peut passer à la section 3.3.

(1) GRMHD models provide the absolute velocity field of the plasma flow. Nonradiative GRMHD evolutions are invariant, however, under a rescaling of the density by a factor $\mathscrM$. In particular, they are invariant under $\rho \to \mathscrM\rho $, field strength $B\to \mathscrM

^1/2B$, and internal energy $u\to \mathscrMu$ (the Alfvén speed $B/\rho ^1/2$ and sound speed $\propto \sqrtu/\rho $ are invariant). That is, there is no intrinsic mass scale in a nonradiative model as long as the mass of the accretion flow is negligible in comparison to $M$.112 We use this freedom to adjust $\mathscrM$ so that the average image from a GRMHD model has a 1.3 mm flux density ≈0.5 Jy (see Paper IV). Once $\mathscrM$ is set, the density, internal energy, and magnetic field are fully specified.

The mass unit $\mathscrM$ determines $\dotM$. In our ensemble of models $\dotM$ ranges from $2\times 10^-7\dotM_\mathrmEdd$ to $4\times 10^-4\dotM_\mathrmEdd$. Accretion rates vary by model category. The mean accretion rate for MAD models is $\sim 10^-6\dotM_\mathrmEdd$. For SANE models with $a_* \gt 0$ it is $\sim 5\times 10^-5\dotM_\mathrmEdd ;$ and for $a_* \lt 0$ it is $\sim 2\times 10^-4\dotM_\mathrmEdd$.

(2) Les distributions d'énergie spectrale radioélectrique observées (SED) et les caractéristiques de polarisation de la source indiquent clairement que l'émission de 1,3 mm correspond à un rayonnement synchrotron, typique des noyaux galactiques actifs (AGN). Les coefficients d'absorption et d'émission du synchrotron dépendent du eDF. Dans ce qui suit, nous adoptons un modèle thermique relativiste pour le format eDF (distribution Maxwell-Jüttner ; Jüttner 1911 ; Rezzolla & Zanotti 2013). Nous discutons des limites de cette approche à la section 7.

Tous nos modèles de M87 ont une densité et une température suffisamment basses et élevées pour que le plasma soit sans collision (voir Ryan et al. 2018, pour une discussion du couplage Coulomb en M87). Par conséquent, Te n'est probablement pas égal à la température de L'ion Ti, qui est fournie par les simulations. Nous définissons Te en utilisant la densité de GRMHD ρ, la densité d'énergie interne u, et le plasma
$\beta _\rmp

$ using a simple model :
Equation (7)

où nous avons supposé que le plasma est composé d'hydrogène, les ions sont non relativiste, et les électrons sont relativistes. Here $R\equiv T_i/T_e$ and
Equation (8)
This prescription has one parameter, $R_\mathrmhigh$, and sets $T_e\simeq T_i$ in low $\beta _\rmp
$ regions and $T_e\simeq T_i/R_\mathrmhigh$ in the midplane of the disk. It is adapted from Mościbrodzka et al. (2016) and motivated by models for electron heating in a turbulent, collisionless plasma that preferentially heats the ions for $\beta _\rmp

\gtrsim 1$ (e.g., Howes 2010 ; Kawazura et al. 2018).

(3)Nous devons spécifier l'inclinaison de l'observateur i, l'orientation de l'observateur à travers l'angle de position $\mathrmPA$, la masse du trou noir$, et la distance D à la source. Les contraintes Non-EHT sur i, $\mathrmPA$, et $ sont considérées ci-dessous ; nous avons généré des images à =12^\circ ,17^\circ ,22^\circ ,158^\circ ,163^\circ $, et 168° et quelques-unes à i = 148°. L'angle de position (PA) peut être modifié en tournant simplement l'image. Toutes les caractéristiques des modèles que nous avons examinés, y compris $\dotm$, sont insensibles aux petites variations de I. La morphologie de l'image dépend de si je suis supérieur ou inférieur à 90°, comme nous le montrerons ci-dessous.\n

Les images modèles sont générées avec un champ de vision de 60 \ times 160 \, \ mu \ mathrm as $ et \ mu \ mathrm as $ pixels, ce qui est petit par rapport au $ \ sim 20 \, \ mu \ mathrm as $ résolution nominale de EHT2017. Notre analyse est insensible aux changements de champ de vision et d'échelle de pixel.

Pour $, nous utilisons la valeur la plus probable du travail sur la ligne d'absorption stellaire,.2 \ times 10 ^ 9 M _ \ odot $ (Gebhardt et al. 2011). Pour la distance D, nous utilisons 6,9 \, \, \ mathrm Mpc $, ce qui est très proche de celui utilisé dans le papier VI. Le rapport /(c^2BuchD)3.62\,\mu \ mathrm as $ (ci-après M / D) détermine l'échelle angulaire des images. Pour certains modèles, nous avons également généré des images avec = 3.5 \ times 10 ^ 9 \, M _ \ odot $ pour vérifier que les résultats de l'analyse ne sont pas prédéterminés par la masse du trou noir entrée.

3.3. Image Library Summary
La bibliothèque d'images contient environ 60 000 images. Nous générons des images de 100 à 500 fichiers de sortie distincts à partir de chacun des modèles GRMHD à chacun des _ \ mathrm high = 1,10,20,40,80 $ et 160. En comparant les données, nous ajustons le $ \ mathrm PA $ par rotation, ainsi que le flux total et l'échelle angulaire de l'image en redimensionnant simplement les images à partir des paramètres standard de la bibliothèque d'images (voir la figure 29 du document VI). Les tests indiquent que les comparaisons avec les données sont insensibles à la procédure de redimensionnement sauf si le facteur de mise à l'échelle angulaire ou le facteur de mise à l'échelle du flux est grand.113

The comparisons with the data are also insensitive to image resolution.114

Les figures 2 et 3 présentent un ensemble représentatif d'images de la bibliothèque d'images présentant une moyenne temporelle. Ces figures montrent clairement que la modification des paramètres _ * $, phgr et _ \ mathrm high $ peut changer la largeur et l'asymétrie de l'anneau à photons et introduisent des structures supplémentaires extérieures et intérieures à l'anneau à photons.

Figure 2. Time-averaged 1.3 mm images generated by five SANE GRMHD simulations with varying spin ($a_* =-0.94$ to $a_* =+0.97$ from left to right) and $R_\mathrmhigh$ ($R_\mathrmhigh=1$ to $R_\mathrmhigh=160$ from top to bottom ; increasing $R_\mathrmhigh$ corresponds to decreasing electron temperature). The colormap is linear. All models are imaged at i = 163°. The jet that is approaching Earth is on the right (west) in all the images. The black hole spin vector projected onto the plane of the sky is marked with an arrow and aligned in the east–west direction. When the arrow is pointing left the black hole rotates in a clockwise direction, and when the arrow is pointing right the black hole rotates in a counterclockwise direction. The field of view for each model image is $80\,\mu \mathrmas$ (half of that used for the image libraries) with resolution equal to $1\mu \mathrmas$/pixel (20 times finer than the nominal resolution of EHT2017, and the same employed in the library images).

Figure 3. Same as in Figure 2 but for selected MAD models

The location of the emitting plasma is shown in Figure 4, which shows a map of time- and azimuth-averaged emission regions for four representative $a_* \gt 0$ models. For SANE models, if $R_\mathrmhigh$ is low (high), emission is concentrated more in the disk (funnel wall), and the bright section of the ring is dominated by the disk (funnel wall).115 Appendix B shows images generated by considering emission only from particular regions of the flow, and the results are consistent with Figure 4.

Figure 4. Binned location of the point of origin for all photons that make up an image, summed over azimuth, and averaged over all snapshots from the simulation. The colormap is linear. The event horizon is indicated by the solid white semicircle and the black hole spin axis is along the figure vertical axis. This set of four images shows MAD and SANE models with $R_\mathrmhigh=10$ and 160, all with $a_* =0.94$. The region between the dashed curves is the locus of existence of (unstable) photon orbits (Teo 2003). The green cross marks the location of the innermost stable circular orbit (ISCO) in the equatorial plane. In these images the line of sight (marked by an arrow) is located below the midplane and makes a 163° angle with the disk angular momentum, which coincides with the spin axis of the black hole.

Figures 2 and 3 show that for both MAD and SANE models the bright section of the ring, which is generated by Doppler beaming, shifts from the top for negative spin, to a nearly symmetric ring at $a_* =0$, to the bottom for $a_* \gt 0$ (except the SANE $R_\mathrmhigh=1$ case, where the bright section is always at the bottom when i > 90°). That is, the location of the peak flux in the ring is controlled by the black hole spin : it always lies roughly 90 degrees counterclockwise from the projection of the spin vector on the sky. Some of the ring emission originates in the funnel wall at $r\lesssim 8\,r_\rmg

$. The rotation of plasma in the funnel wall is in the same sense as plasma in the funnel, which is controlled by the dragging of magnetic field lines by the black hole. The funnel wall thus rotates opposite to the accretion flow if $a_* \lt 0$. This effect will be studied further in a later publication (Wong et al. 2019). The resulting relationships between disk angular momentum, black hole angular momentum, and observed ring asymmetry are illustrated in Figure 5.

Figure 5. Illustration of the effect of black hole and disk angular momentum on ring asymmetry. The asymmetry is produced primarily by Doppler beaming : the bright region corresponds to the approaching side. In GRMHD models that fit the data comparatively well, the asymmetry arises in emission generated in the funnel wall. The sense of rotation of both the jet and funnel wall are controlled by the black hole spin. If the black hole spin axis is aligned with the large-scale jet, which points to the right, then the asymmetry implies that the black hole spin is pointing away from Earth (rotation of the black hole is clockwise as viewed from Earth). The blue ribbon arrow shows the sense of disk rotation, and the black ribbon arrow shows black hole spin. Inclination i is defined as the angle between the disk angular momentum vector and the line of sight.
The time-averaged MAD images are almost independent of $R_\mathrmhigh$ and depend mainly on $a_* $. In MAD models much of the emission arises in regions with $\beta _\rmp
\sim 1$, where $R_\mathrmhigh$ has little influence over the electron temperature, so the insensitivity to $R_\mathrmhigh$ is natural (see Figure 4). In SANE models emission arises at $\beta _\rmp
\sim 10$, so the time-averaged SANE images, by contrast, depend strongly on $R_\mathrmhigh$. In low $R_\mathrmhigh$ SANE models, extended emission outside the photon ring, arising near the equatorial plane, is evident at $R_\mathrmhigh=1$. In large $R_\mathrmhigh$ SANE models the inner ring emission arises from the funnel wall, and once again the image looks like a thin ring (see Figure 4).

Figure 6 and the accompanying animation show the evolution of the images, visibility amplitudes, and closure phases over a $5000\,r_\rmg

c^-1\approx 5\,\mathrmyr$ interval in a single simulation for M87. It is evident from the animation that turbulence in the simulations produces large fluctuations in the images, which imply changes in visibility amplitudes and closure phases that are large compared to measurement errors. The fluctuations are central to our procedure for comparing models with the data, described briefly below and in detail in Paper VI.

Figure 6. Single frame from the accompanying animation. This shows the visibility amplitudes (top), closure phases plotted by Euclidean distance in 6D space (middle), and associated model images at full resolution (lower left) and convolved with the EHT2017 beam (lower right). Data from 2017 April 6 high-band are also shown in the top two plots. The video shows frames 1 through 100 and has a duration of 10 s.

The timescale between frames in the animation is $50\,r_\rmg

c^-1\simeq 18$ days, which is long compared to EHT2017 observing campaign. The images are highly correlated on timescales less than the innermost stable circular orbit (ISCO) orbital period, which for $a_* =0$ is $\simeq 15\ r_\rmg

c^-1\simeq 5$ days, i.e., comparable to the duration of the EHT2017 campaign. If drawn from one of our models, we would expect the EHT2017 data to look like a single snapshot (Figures 6) rather than their time averages (Figures 2 and 3).
4. Procedure for Comparison of Models with Data
As described above, each model in the Simulation Library has two dimensionless parameters : black hole spin $a_* $ and magnetic flux phgr. Imaging the model from each simulation adds five new parameters : $R_\mathrmhigh$, i, $\mathrmPA$, $M$, and D, which we set to $16.9\,\mathrmMpc$. After fixing these parameters we draw snapshots from the time evolution at a cadence of 10 to $50\,r_\rmg

c^-1$. We then compare these snapshots to the data.

The simplest comparison computes the $\chi _\nu ^2$ (reduced chi square) distance between the data and a snapshot. In the course of computing $\chi _\nu ^2$ we vary the image scale M/D, flux density Fν, position angle $\mathrmPA$, and the gain at each VLBI station in order to give each image every opportunity to fit the data. The best-fit parameters $(M/D,F_\nu ,\mathrmPA)$ for each snapshot are found by two pipelines independently : the Themis pipeline using a Markov chain Monte Carlo method (A. E. Broderick et al. 2019a, in preparation), and the GENA pipeline using an evolutionary algorithm for multidimensional minimization (Fromm et al. 2019a ; C. Fromm et al. 2019b, in preparation ; see also Section 4 of Paper VI for details). The best-fit parameters contain information about the source and we use the distribution of best-fit parameters to test the model by asking whether or not they are consistent with existing measurements of M/D and estimates of the jet $\mathrmPA$ on larger scales.

The $\chi _\nu ^2$ comparison alone does not provide a sharp test of the models. Fluctuations in the underlying GRMHD model, combined with the high signal-to-noise ratio for EHT2017 data, imply that individual snapshots are highly unlikely to provide a formally acceptable fit with $\chi _\nu ^2\simeq 1$. This is borne out in practice with the minimum $\chi _\nu ^2=1.79$ over the entire set of the more than 60,000 individual images in the Image Library. Nevertheless, it is possible to test if the $\chi _\nu ^2$ from the fit to the data is consistent with the underlying model, using '''Average Image Scoring''' with Themis (Themis-AIS), as described in detail in Appendix F of Paper VI). Themis-AIS measures a $\chi _\nu ^2$ distance (on the space of visibility amplitudes and closure phases) between a trial image and the data. In practice we use the average of the images from a given model as the trial image (hence Themis-AIS), but other choices are possible. We compute the $\chi _\nu ^2$ distance between the trial image and synthetic data produced from each snapshot. The model can then be tested by asking whether the data's $\chi _\nu ^2$ is likely to have been drawn from the model's distribution of $\chi _\nu ^2$. In particular, we can assign a probability p that the data is drawn from a specific model's distribution.

In this Letter we focus on comparisons with a single data set, the 2017 April 6 high-band data (Paper III). The eight EHT2017 data sets, spanning four days with two bands on each day, are highly correlated. Assessing what correlation is expected in the models is a complicated task that we defer to later publications. The 2017 April 6 data set has the largest number of scans, 284 detections in 25 scans (see Paper III) and is therefore expected to be the most constraining.116
5. Model Constraints : EHT2017 Alone

The resolved ring-like structure obtained from the EHT2017 data provides an estimate of M/D (discussed in detail in Paper VI) and the jet $\mathrmPA$ from the immediate environment of the central black hole. As a first test of the models we can ask whether or not these are consistent with what is known from other mass measurements and from the orientation of the large-scale jet.

Figure 7 shows the distributions of best-fit values of M/D for a subset of the models for which spectra and jet power estimates are available (see below). The three lines show the M/D distribution for all snapshots (dotted lines), the best-fit 10% of snapshots (dashed lines), and the best-fit 1% of snapshots (solid lines) within each model. Evidently, as better fits are required, the distribution narrows and peaks close to $M/D\sim 3.6\,\mu \mathrmas$ with a width of about $0.5\mu \mathrmas$.

Figure 7. Distribution of M/D obtained by fitting Image Library snapshots to the 2017 April 6 data, in $\mu \mathrmas$, measured independently using the (left panel) Themis and (right panel) GENA pipelines with qualitatively similar results. Smooth lines were drawn with a Gaussian kernel density estimator. The three lines show the best-fit 1% within each model (solid) ; the best-fit 10% within each model (dashed) ; and all model images (dotted). The vertical lines show $M/D=2.04$ (dashed) and $3.62\,\mu \mathrmas$ (solid), corresponding to M = 3.5 and $6.2\times 10^9\,M_\odot $. The distribution uses a subset of models for which spectra and jet power estimates are available (see Section 6). Only images with $a_* \gt 0$, i > 90° and $a_* \lt 0$, i < 90° (see also the left panel of Figure 5) are considered

The distribution of M/D for the best-fit $\lt 10 \% $ of snapshots is qualitatively similar if we include only MAD or SANE models, only models produced by individual codes (BHAC, H-AMR, iharm, or KORAL), or only individual spins. As the thrust of this Letter is to test the models, we simply note that Figure 7 indicates that the models are broadly consistent with earlier mass estimates (see Paper VI for a detailed discussion). This did not have to be the case : the ring radius could have been significantly larger than $3.6\,\mu \mathrmas$.

We can go somewhat further and ask if any of the individual models favor large or small masses. Figure 8 shows the distributions of best-fit values of M/D for each model (different $a_* $, $R_\mathrmhigh$, and magnetic flux). Most individual models favor M/D close to $3.6\,\mu \mathrmas$. The exceptions are $a_* \leqslant 0$ SANE models with $R_\mathrmhigh=1$, which produce the bump in the M/D distribution near $2\mu \mathrmas$. In these models, the emission is produced at comparatively large radius in the disk (see Figure 2) because the inner edge of the disk (the ISCO) is at a large radius in a counter-rotating disk around a black hole with $| a_* | \sim 1$. For these models, the fitting procedure identifies EHT2017's ring with this outer ring, which forces the photon ring, and therefore M/D, to be small. As we will show later, these models can be rejected because they produce weak jets that are inconsistent with existing jet power estimates (see Section 6.3).
Figure 8. Distributions of M/D and black hole mass with $D=16.9\,\mathrmMpc$ reconstructed from the best-fit 10% of images for MAD (left panel) and SANE (right panel) models (i = 17° for $a_* \le 0$ and 163° for $a_* \gt 0$) with different $R_\mathrmhigh$ and $a_* $, from the Themis (dark red, left), and GENA (dark green, right) pipelines. The white dot and vertical black bar correspond, respectively, to the median and region between the 25th and 75th percentiles for both pipelines combined. The blue and pink horizontal bands show the range of M/D and mass at $D=16.9\,\mathrmMpc$ estimated from the gas dynamical model (Walsh et al. 2013) and stellar dynamical model (Gebhardt et al. 2011), respectively. Constraints on the models based on average image scoring (Themis-AIS) are discussed in Section 5. Constraints based on radiative efficiency, X-ray luminosity, and jet power are discussed in Section 6.

Figure 8 also shows that M/D increases with $a_* $ for SANE models. This is due to the appearance of a secondary inner ring inside the main photon ring. The former is associated with emission produced along the wall of the approaching jet. Because the emission is produced in front of the black hole, lensing is weak and it appears at small angular scale. The inner ring is absent in MAD models (see Figure 3), where the bulk of the emission comes from the midplane at all values of $R_\mathrmhigh$(Figure 4).

We now ask whether or not the PA of the jet is consistent with the orientation of the jet measured at other wavelengths. On large ( mas) scales the extended jet component has a PA of approximately 288° (e.g., Walker et al. 2018). On smaller ($\sim 100\,\mu \mathrmas$) scales the apparent opening angle of the jet is large (e.g., Kim et al. 2018) and the PA is therefore more difficult to measure. Also notice that the jet PA may be time dependent (e.g., Hada et al. 2016 ; Walker et al. 2018). In our model images the jet is relatively dim at 1.3 mm, and is not easily seen with a linear colormap. The model jet axis is, nonetheless, well defined : jets emerge perpendicular to the disk.

Figure 9 shows the distribution of best-fit PA over the same sample of snapshots from the Image Library used in Figure 7. We divide the snapshots into two groups. The first group has the black hole spin pointed away from Earth (i > 90° and $a_* \gt 0$, or i < 90° and $a_* \lt 0$). The spin-away model PA distributions are shown in the top two panels. The second group has the black hole spin pointed toward Earth (i > 90 and $a_* \lt 0$ or i > 90° and $a_* \lt 0$). These spin-toward model PA distributions are shown in the bottom two panels. The large-scale jet orientation lies on the shoulder of the spin-away distribution (the distribution can be approximated as a Gaussian with, for Themis (GENA) mean 209 (203)° and $\sigma _\mathrmPA\,=54\,(55)^\circ ;$ the large-scale jet PA lies $1.5\sigma _\mathrmPA$ from the mean) and is therefore consistent with the spin-away models. On the other hand, the large-scale jet orientation lies off the shoulder of the spin-toward distribution and is inconsistent with the spin-toward models. Evidently models in which the black hole spin is pointing away from Earth are strongly favored.

Figure 9. Top : distribution of best-fit PA (in degree) scored by the Themis (left) and GENA (right) pipelines for models with black hole spin vector pointing away from Earth (i > 90° for $a_* \gt 0$ or i < 90° for $a_* \lt 0$). Bottom : images with black hole spin vector pointing toward Earth (i < 90° for $a_* \gt 0$ or i > 90° for $a_* \lt 0$). Smooth lines were drawn with a wrapped Gaussian kernel density estimator. The three lines show (1) all images in the sample (dotted line) ; (2) the best-fit 10% of images within each model (dashed line) ; and (3) the best-fit 1% of images in each model (solid line). For reference, the vertical line shows the position angle $\mathrmPA\sim 288^\circ $ of the large-scale (mas) jet Walker et al. (2018), with the gray area from (288 – 10)° to (288 + 10)° indicating the observed PA variation.

The width of the spin-away and spin-toward distributions arises naturally in the models from brightness fluctuations in the ring. The distributions are relatively insensitive if split into MAD and SANE categories, although for MAD the averaged PA is $\langle \mathrmPA\rangle =219^\circ $, $\sigma _\mathrmPA=46^\circ $, while for SANE $\langle \mathrmPA\rangle =195^\circ $ and $\sigma _\mathrmPA=58^\circ $. The $a_* =0$ and $a_* \gt 0$ models have similar distributions. Again, EHT2017 data strongly favor one sense of black hole spin : either $| a_* | $ is small, or the spin vector is pointed away from Earth. If the fluctuations are such that the fitted PA for each epoch of observations is drawn from a Gaussian with $\sigma _\mathrmPA\simeq 55^\circ $, then a second epoch will be able to identify the true orientation with accuracy $\sigma _\mathrmPA/\sqrt2\simeq 40^\circ $ and the Nth epoch with accuracy $\sigma _\mathrmPA/\sqrtN$. If the fitted PA were drawn from a Gaussian of width $\sigma _\mathrmPA=54^\circ $ about $\mathrmPA=288^\circ $, as would be expected in a model in which the large-scale jet is aligned normal to the disk, then future epochs have a >90% chance of seeing the peak brightness counterclockwise from its position in EHT2017.

Finally, we can test the models by asking if they are consistent with the data according to Themis-AIS, as introduced in Section 4. Themis-AIS produces a probability p that the $\chi _\nu ^2$ distance between the data and the average of the model images is drawn from the same distribution as the $\chi _\nu ^2$ distance between synthetic data created from the model images, and the average of the model images. Table 1 takes these p values and categorizes them by magnetic flux and by spin, aggregating (averaging) results from different codes, $R_\mathrmhigh$, and i. Evidently, most of the models are formally consistent with the data by this test.

aThe Average Image Scoring (Themis-AIS) is introduced in Section 4. bflux : net magnetic flux on the black hole (MAD or SANE). c $a_* $ : dimensionless black hole spin. d $\langle p\rangle $ : mean of the p value for the aggregated models. e $N_\mathrmmodel$ : number of aggregated models. f $\mathrmMIN(p)$ : minimum p value among the aggregated models. g $\mathrmMAX(p)$ : maximum p value among the aggregated models.

One group of models, however, is rejected by Themis-AIS : MAD models with $a_* =-0.94$. On average this group has p = 0.01, and all models within this group have $p\leqslant 0.04$. Snapshots from MAD models with $a_* =-0.94$ exhibit the highest morphological variability in our ensemble in the sense that the emission breaks up into transient bright clumps. These models are rejected by Themis-AIS because none of the snapshots are as similar to the average image as the data. In other words, it is unlikely that EHT2017 would have captured an $a_* =-0.94$ MAD model in a configuration as unperturbed as the data seem to be.

The remainder of the model categories contain at least some models that are consistent with the data according to the average image scoring test. That is, most models are variable and the associated snapshots lie far from the average image. These snapshots are formally inconsistent with the data, but their distance from the average image is consistent with what is expected from the models. Given the uncertainties in the model—and our lack of knowledge of the source prior to EHT2017—it is remarkable that so many of the models are acceptable. This is likely because the source structure is dominated by the photon ring, which is produced by gravitational lensing, and is therefore relatively insensitive to the details of the accretion flow and jet physics. We can further narrow the range of acceptable models, however, using additional constraints.
6. Model Constraints : EHT2017 Combined with Other Constraints

We can apply three additional arguments to further constrain the source model. (1) The model must be close to radiative equilibrium. (2) The model must be consistent with the observed broadband SED ; in particular, it must not overproduce X-rays. (3) The model must produce a sufficiently powerful jet to match the measurements of the jet kinetic energy at large scales. Our discussions in this Section are based on simulation data that is provided in full detail in Appendix A.
6.1. Radiative Equilibrium

The model must be close to radiative equilibrium. The GRMHD models in the Simulation Library do not include radiative cooling, nor do they include a detailed prescription for particle energization. In nature the accretion flow and jet are expected to be cooled and heated by a combination of synchrotron and Compton cooling, turbulent dissipation, and Coulomb heating, which transfers energy from the hot ions to the cooler electrons. In our suite of simulations the parameter $R_\mathrmhigh$ can be thought of as a proxy for the sum of these processes. In a fully self-consistent treatment, some models would rapidly cool and settle to a lower electron temperature (see Mościbrodzka et al. 2011 ; Ryan et al. 2018 ; Chael et al. 2019). We crudely test for this by calculating the radiative efficiency $\epsilon \equiv L_\mathrmbol/(\dotMc^2)$, where $L_\mathrmbol$ is the bolometric luminosity. If it is larger than the radiative efficiency of a thin, radiatively efficient disk,117 which depends only on $a_* $ (Novikov & Thorne 1973), then we reject the model as physically inconsistent.

We calculate $L_\mathrmbol$ with the Monte Carlo code grmonty (Dolence et al. 2009), which incorporates synchrotron emission, absorption, Compton scattering at all orders, and bremsstrahlung. It assumes the same thermal eDF used in generating the Image Library. We calculate $L_\mathrmbol$ for 20% of the snapshots to minimize computational cost. We then average over snapshots to find $\langle L_\mathrmbol\rangle $. The mass accretion rate $\dotM$ is likewise computed for each snapshot and averaged over time. We reject models with epsilon that is larger than the classical thin disk model. (Table 3 in Appendix A lists epsilon for a large set of models.) All but two of the radiatively inconsistent models are MADs with $a_* \geqslant 0$ and $R_\mathrmhigh=1$. Eliminating all MAD models with $a_* \geqslant 0$ and $R_\mathrmhigh=1$ does not change any of our earlier conclusions.
6.2. X-Ray Constraints

As part of the EHT2017 campaign, we simultaneously observed M87 with the Chandra X-ray observatory and the Nuclear Spectroscopic Telescope Array (NuSTAR). The best fit to simultaneous Chandra and NuSTAR observations on 2017 April 12 and 14 implies a $2\mbox—10\,\mathrmkeV$ luminosity of $L_

\rmX

_\mathrmobs

\,=4.4\pm 0.1\times 10^40\,\,\mathrmerg\,\rms
^-1$. We used the SEDs generated from the simulations while calculating $L_\mathrmbol$ to reject models that consistently overproduce X-rays ; specifically, we reject models with $\mathrmlogL_

\rmX

_\mathrmobs

\lt \mathrmlog\langle L_\rmX

\rangle -2\sigma (\mathrmlogL_\rmX

)$. We do not reject underluminous models because the X-rays could in principle be produced by direct synchrotron emission from nonthermal electrons or by other unresolved sources. Notice that $L_\rmX

$ is highly variable in all models so that the X-ray observations currently reject only a few models. Table 3 in Appendix A shows $\langle L_\rmX

\rangle $ as well as upper and lower limits for a set of models that is distributed uniformly across the parameter space.

In our models the X-ray flux is produced by inverse Compton scattering of synchrotron photons. The X-ray flux is an increasing function of $\tau _TT_e^2$ where τT is a characteristic Thomson optical depth ($\tau _T\sim 10^-5$), and the characteristic amplification factor for photon energies is $\propto T_e^2$ because the X-ray band is dominated by singly scattered photons interacting with relativistic electrons (we include all scattering orders in the Monte Carlo calculation). Increasing $R_\mathrmhigh$ at fixed $F_\nu (230\,\ \mathrmGHz)$ tends to increase $\dotM$ and therefore τT and decrease Te. The increase in Te dominates in our ensemble of models, and so models with small $R_\mathrmhigh$ have larger $L_\rmX
$, while models with large $R_\mathrmhigh$ have smaller $L_\rmX

$. The effect is not strictly monotonic, however, because of noise in our sampling process and the highly variable nature of the X-ray emission.
The overluminous models are mostly SANE models with $R_\mathrmhigh\leqslant 20$. The model with the highest $\langle L_\rmX

\rangle =4.2\,\times 10^42\,\,\mathrmerg\,\rms

^-1$ is a SANE, $a_* =0$, $R_\mathrmhigh=10$ model. The corresponding model with $R_\mathrmhigh=1$ has $\langle L_\rmX

\rangle =2.1\,\times 10^41\,\,\mathrmerg\,\rms

^-1$, and the difference between these two indicates the level of variability and the sensitivity of the average to the brightest snapshot. The upshot of application of the $L_\rmX

$ constraints is that $L_\rmX

$ is sensitive to $R_\mathrmhigh$. Very low values of $R_\mathrmhigh$ are disfavored. $L_\rmX

$ thus most directly constrains the electron temperature model.
6.3. Jet Power
Estimates of M87's jet power ($P_\mathrmjet$) have been reviewed in Reynolds et al. (1996), Li et al. (2009), de Gasperin et al. (2012), Broderick et al. (2015), and Prieto et al. (2016). The estimates range from 1042 to $10^45\,\,\mathrmerg\,\rms

^-1$. This wide range is a consequence of both physical uncertainties in the models used to estimate $P_\mathrmjet$ and the wide range in length and timescales probed by the observations. Some estimates may sample a different epoch and thus provide little information on the state of the central engine during EHT2017. Nevertheless, observations of HST-1 yield $P_\mathrmjet\sim 10^44\ \,\mathrmerg\,\rms
^-1$ (e.g., Stawarz et al. 2006). HST-1 is within $\sim 70\,\mathrmpc$ of the central engine and, taking account of relativistic time foreshortening, may be sampling the central engine $P_\mathrmjet$ over the last few decades. Furthermore, the 1.3 mm light curve of M87 as observed by SMA shows $\lesssim 50 \% $ variability over decade timescales (Bower et al. 2015). Based on these considerations it seems reasonable to adopt a very conservative lower limit on jet power $\equiv P_\mathrmjet,\min =10^42\ \,\mathrmerg\,\rms

^-1$.
To apply this constraint we must define and measure $P_\mathrmjet$ in our models. Our procedure is discussed in detail in Appendix A. In brief, we measure the total energy flux in outflowing regions over the polar caps of the black hole in which the energy per unit rest mass exceeds $2.2\,c^2$, which corresponds to βγ = 1, where $\beta \equiv v/c$ and γ is Lorentz factor. The effect of changing this cutoff is also discussed in Appendix A. Because the cutoff is somewhat arbitrary, we also calculate $P_\mathrmout$ by including the energy flux in all outflowing regions over the polar caps of the black hole ; that is, it includes the energy flux in any wide-angle, low-velocity wind. $P_\mathrmout$ represents a maximal definition of jet power. Table 3 in Appendix A shows $P_\mathrmjet$ as well as a total outflow power $P_\mathrmout$.

The constraint $P_\mathrmjet\gt P_\mathrmjet,\min =10^42\,\mathrmerg\,\rms
^-1$ rejects all $a_* =0$ models. This conclusion is not sensitive to the definition of $P_\mathrmjet$ : all $a_* =0$ models also have total outflow power $P_\mathrmout\,\lt 10^42\,\mathrmerg\,\rms
^-1$. The most powerful $a_* =0$ model is a MAD model with $R_\mathrmhigh=160$, which has $P_\mathrmout=3.7\times 10^41\,\mathrmerg\,\rms
^-1$ and $P_\mathrmjet$ consistent with 0. We conclude that our $a_* =0$ models are ruled out.

Can the $a_* =0$ models be saved by changing the eDF ? Probably not. There is no evidence from the GRMHD simulations that these models are capable of producing a relativistic outflow with $\beta \gamma \gt 1$. Suppose, however, that we are willing to identify the nonrelativistic outflow, whose power is measured by $P_\mathrmout$, with the jet. Can $P_\mathrmout$ be raised to meet our conservative threshold on jet power ? Here the answer is yes, in principle, and this can be done by changing the eDF. The eDF and $P_\mathrmout$ are coupled because $P_\mathrmout$ is determined by $\dotM$, and $\dotM$ is adjusted to produce the observed compact mm flux. The relationship between $\dotM$ and mm flux depends upon the eDF. If the eDF is altered to produce mm photons less efficiently (for example, by lowering Te in a thermal model), then $\dotM$ and therefore $P_\mathrmout$ increase. A typical nonthermal eDF, by contrast, is likely to produce mm photons with greater efficiency by shifting electrons out of the thermal core and into a nonthermal tail. It will therefore lower $\dotM$ and thus $P_\mathrmout$. A thermal eDF with lower Te could have higher $P_\mathrmout$, as is evident in the large $R_\mathrmhigh$ SANE models in Table 3. There are observational and theoretical lower limits on Te, however, including a lower limit provided by the observed brightness temeprature. As Te declines, ne and B increase and that has implications for source linear polarization (Mościbrodzka et al. 2017 ; Jiménez-Rosales & Dexter 2018), which will be explored in future work. As Te declines and ne and ni increase there is also an increase in energy transfer from ions to electrons by Coulomb coupling, and this sets a floor on Te.

The requirement that $P_\mathrmjet\gt P_\mathrmjet,\min $ eliminates many models other than the $a_* =0$ models. All SANE models with $| a_* | =0.5$ fail to produce jets with the required minimum power. Indeed, they also fail the less restrictive condition $P_\mathrmout\gt P_\mathrmjet,\min $, so this conclusion is insensitive to the definition of the jet. We conclude that among the SANE models, only high-spin models survive.

At this point it is worth revisiting the SANE, $R_\mathrmhigh=1$, $a_* =-0.94$ model that favored a low black hole mass in Section 5. These models are not rejected by a naive application of the $P_\mathrmjet\gt P_\mathrmjet,\min $ criterion, but they are marginal. Notice, however, that we needed to assume a mass in applying the this criterion. We have consistently assumed $M=6.2\times 10^9\,M_\odot $. If we use the $M\sim 3\times 10^9\,M_\odot $ implied by the best-fit M/D, then $\dotM$ drops by a factor of two, $P_\mathrmjet$ drops below the threshold and the model is rejected.

The lower limit on jet power $P_\mathrmjet,\min =10^42\,\mathrmerg\,\rms

^-1$ is conservative and the true jet power is likely higher. If we increased $P_\mathrmjet,\min $ to $3\times 10^42\,\mathrmerg\,\rms

^-1$, the only surviving models would have $| a_* | =0.94$ and $R_\mathrmhigh\geqslant 10$. This conclusion is also not sensitive to the definition of the jet power : applying the same cut to $P_\mathrmout$ adds only a single model with $| a_* | \lt 0.94$, the $R_\mathrmhigh=160$, $a_* =0.5$ MAD model. The remainder have $a_* =0.94$. Interestingly, the most powerful jets in our ensemble of models are produced by SANE, $a_* =-0.94$, $R_\mathrmhigh=160$ models, with $P_\mathrmjet\simeq 10^43\,\,\mathrmerg\,\rms

^-1$.
Estimates for $P_\mathrmjet$ extend to $10^45\,\mathrmerg\,\rms
^-1$, but in our ensemble of models the maximum $P_\mathrmjet\sim 10^43\,\,\mathrmerg\,\rms
^-1$. Possible explanations include : (1) $P_\mathrmjet$ is variable and the estimates probe the central engine power at earlier epochs (discussed above) ; (2) the $P_\mathrmjet$ estimates are too large ; or (3) the models are in error. How might our models be modified to produce a larger $P_\mathrmjet$ ? For a given magnetic field configuration the jet power scales with $\dotMc^2$. To increase $P_\mathrmjet$, then, one must reduce the mm flux per accreted nucleon so that at fixed mm flux density $\dotM$ increases.118 Lowering Te in a thermal model is unlikely to work because lower Te implies higher synchrotron optical depth, which increases the ring width. We have done a limited series of experiments that suggest that even a modest decrease in Te would produce a broad ring that is inconsistent with EHT2017 (Paper VI). What is required, then, is a nonthermal (or multitemperature) model with a large population of cold electrons that are invisible at mm wavelength (for a thermal subpopulation, $\rm\Theta
_e,\mathrmcold\lt 1$), and a population of higher-energy electrons that produces the observed mm flux (see Falcke & Biermann 1995). We have not considered such models here, but we note that they are in tension with current ideas about dissipation of turbulence because they require efficient suppression of electron heating.

The $P_\mathrmjet$ in our models is dominated by Poynting flux in the force-free region around the axis (the '''funnel'''), as in the Blandford & Znajek (1977) force-free magnetosphere model. The energy flux is concentrated along the walls of the funnel.119 Tchekhovskoy et al. (2011) provided an expression for the energy flux in the funnel, the so-called Blandford–Znajek power $P_\mathrmBZ$, which becomes, in our units,
Equation (9)

where $f(a_* )\approx a_* ^2\left(1+\sqrt1-a_* ^2\right)^-2$ (a good approximation for $a_* \lt 0.95$) and $\dotM_\mathrmEdd=137\,M_\odot \,\mathrmyr^-1$ for $M=6.2\times 10^9\,M_\odot $. This expression was developed for models with a thin disk in the equatorial plane. $P_\mathrmBZ$ is lower for models where the force-free region is excluded by a thicker disk around the equatorial plane. Clearly $P_\mathrmBZ$ is comparable to observational estimates of $P_\mathrmjet$.

In our models (see Table 3) $P_\mathrmjet$ follows the above scaling relation but with a smaller coefficient. The ratio of coefficients is model dependent and varies from 0.15 to 0.83. This is likely because the force-free region is restricted to a cone around the poles of the black hole, and the width of the cone varies by model. Indeed, the coefficient is larger for MAD than for SANE models, which is consistent with this idea because MAD models have a wide funnel and SANE models have a narrow funnel. This also suggests that future comparison of synthetic 43 and 86 GHz images from our models with lower-frequency VLBI data may further constrain the magnetic flux on the black hole.

The connection between the Poynting flux in the funnel and black hole spin has been discussed for some time in the simulation literature, beginning with McKinney & Gammie (2004 ; see also McKinney 2006 ; McKinney & Narayan 2007). The structure of the funnel magnetic field can be time-averaged and shown to match the analytic solution of Blandford & Znajek (1977). Furthermore, the energy flux density can be time-averaged and traced back to the event horizon. Is the energy contained in black hole spin sufficient to drive the observed jet over the jet lifetime ? The spindown timescale is $\tau =(M-M_\mathrmirr)c^2/P_\mathrmjet$, where $M_\mathrmirr\equiv M\left(\left(1+\sqrt1-a_* ^2\right)/2\right)^1/2$ is the irreducible mass of the black hole. For the $a_* =0.94$ MAD model with $R_\mathrmhigh=160$, $\tau =7.3\times 10^12\,\mathrmyr$, which is long compared to a Hubble time ($\sim 10^10$ yr). Indeed, the spindown time for all models is long compared to the Hubble time.

We conclude that for models that have sufficiently powerful jets and are consistent with EHT2017, $P_\mathrmjet$ is driven by extraction of black hole spin energy through the Blandford–Znajek process.
6.4. Constraint Summary

We have applied constraints from AIS, a radiative self-consistency constraint, a constraint on maximum X-ray luminosity, and a constraint on minimum jet power. Which models survive ? Here we consider only models for which we have calculated $L_\rmX
$ and $L_\mathrmbol$. Table 2 summarizes the results. Here we consider only i = 163° (for $a_* \geqslant 0$) and i = 17° (for $a_* \lt 0$). The first three columns give the model parameters. The next four columns show the result of application of each constraint : Themis-AIS (here broken out by individual model rather than groups of models), radiative efficiency ($\epsilon \lt \epsilon _\mathrmthin\mathrmdisk$), $L_\rmX
$, and $P_\mathrmjet$.

aflux : net magnetic flux on the black hole (MAD, SANE). b $a_* $ : dimensionless black hole spin. c $R_\mathrmhigh$ : electron temperature parameter. See Equation (8). dAverage Image Scoring (Themis-AIS), models are rejected if $\langle p\rangle \leqslant 0.01$. See Section 4 and Table 1. eepsilon : radiative efficiency, models are rejected if epsilon is larger than the corresponding thin disk efficiency. See Section 6.1. f $L_\rmX

$ : X-ray luminosity ; models are rejected if $\langle L_\rmX

\rangle 10^-2\sigma \gt 4.4\times 10^40\,\,\mathrmerg\,\rms

^-1$. See Section 6.2. g $P_\mathrmjet$ : jet power, models are rejected if $P_\mathrmjet\leqslant 10^42\,\,\mathrmerg\,\rms

^-1$. See Section 6.3.

The final column gives the logical AND of the previous four columns, and allows a model to pass only if it passes all tests. Evidently most of the SANE models fail, with the exception of some $a_* =-0.94$ models and a few $a_* =0.94$ models with large $R_\mathrmhigh$. A much larger fraction of the MAD models pass, although $a_* =0$ models all fail because of inadequate jet power. MAD models with small $R_\mathrmhigh$ also fail. It is the jet power constraint that rejects the largest number of models.
7. Discussion

We have interpreted the EHT2017 data using a limited library of models with attendant limitations. Many of the limitations stem from the GRMHD model, which treats the plasma as an ideal fluid governed by equations that encode conservation laws for particle number, momentum, and energy. The eDF, in particular, is described by a number density and temperature, rather than a full distribution function, and the electron temperature Te is assumed to be a function of the local ion temperature and plasma $\beta _\rmp

$. Furthermore, all models assume a Kerr black hole spacetime, but there are alternatives. Here we consider some of the model limitations and possible extensions, including to models beyond general relativity.
7.1. Radiative Effects
Post-processed GRMHD simulations that are consistent with EHT data and the flux density of 1.3 mm emission in M87 can yield unphysically large radiative efficiencies (see Section 6). This implies that the radiative cooling timescale is comparable to or less than the advection timescale. As a consequence, including radiative cooling in simulations may be necessary to recover self-consistent models (see Mościbrodzka et al. 2011 ; Dibi et al. 2012). In our models we use a single parameter, $R_\mathrmhigh$, to adjust Te and account for all effects that might influence the electron energy density. How good is this approximation ?

The importance of radiative cooling can be assessed using newly developed, state-of-the-art general relativistic radiation GRMHD ('''radiation GRMHD''') codes. Sa̧dowski et al. (2013b ; see also Sa̧dowski et al. 2014, 2017 ; McKinney et al. 2014) applied the M1 closure (Levermore 1984), which treats the radiation as a relativistic fluid. Ryan et al. (2015) introduced a Monte Carlo radiation GRMHD method, allowing for full frequency-dependent radiation transport. Models for turbulent dissipation into the electrons and ions, as well as heating and cooling physics that sets the temperature ratio Ti/Te, have been added to GRMHD and radiative GRMHD codes and used in simulations of Sgr A* (Ressler et al. 2015, 2017 ; Chael et al. 2018) and M87 (Ryan et al. 2018 ; Chael et al. 2019). While the radiative cooling and Coulomb coupling physics in these simulations is well understood, the particle heating process, especially the relative heating rates of ions and electrons, remains uncertain.

Radiation GRMHD models are computationally expensive per run and do not have the same scaling freedom as the GRMHD models, so they need to be repeatedly re-run with different initial conditions until they produce the correct 1.3 mm flux density. It is therefore impractical to survey the parameter space using radiation GRMHD. It is possible, however, to check individual GRMHD models against existing radiation GRMHD models of M87 (Ryan et al. 2018 ; Chael et al. 2019).

The SANE radiation GRMHD models of Ryan et al. (2018) with $a_* =0.94$ and $M=6\times 10^9\,M_\odot $ can be compared to GRMHD SANE $a_* =0.94$ models at various values of $R_\mathrmhigh$. The radiative models have $\dotM/\dotM_\mathrmEdd=5.2\times 10^-6$ and $P_\mathrmjet\,=5.1\times 10^41\,\mathrmerg\,\rms
^-1$. The GRMHD models in this work have, for $1\leqslant R_\mathrmhigh\leqslant 160$, $0.36\times 10^-6\leqslant \dotM/\dotM_\mathrmEdd\leqslant 20\times 10^-6$, and $0.22\leqslant P_\mathrmjet/(10^41\,\,\mathrmerg\,\rms
^-1)\leqslant 12$ (Table 3). Evidently the mass accretion rates and jet powers in the GRMHD models span a wide range that depends on $R_\mathrmhigh$, but when we choose $R_\mathrmhigh$ = 10 − 20 they are similar to what is found in the radiative GRMHD model when using the turbulent electron heating model (Howes 2010).

Figure 1. Left panel : an EHT2017 image of M87 from Paper IV of this series (see their Figure 15). Middle panel : a simulated image based on a GRMHD model. Right panel : the model image convolved with a $20\,\mu \mathrmas$ FWHM Gaussian beam. Although the most evident features of the model and data are similar, fine features in the model are not resolved by EHT.

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Four features of the image in the left panel of Figure 1 play an important role in our analysis : (1) the ring-like geometry, (2) the peak brightness temperature, (3) the total flux density, and (4) the asymmetry of the ring. We now consider each in turn.

(1) The compact source shows a bright ring with a central dark area without significant extended components. This bears a remarkable similarity to the long-predicted structure for optically thin emission from a hot plasma surrounding a black hole (Falcke et al. 2000). The central hole surrounded by a bright ring arises because of strong gravitational lensing (e.g., Hilbert 1917 ; von Laue 1921 ; Bardeen 1973 ; Luminet 1979). The so-called '''photon ring''' corresponds to lines of sight that pass close to (unstable) photon orbits (see Teo 2003), linger near the photon orbit, and therefore have a long path length through the emitting plasma. These lines of sight will appear comparatively bright if the emitting plasma is optically thin. The central flux depression is the so-called black hole '''shadow''' (Falcke et al. 2000), and corresponds to lines of sight that terminate on the event horizon. The shadow could be seen in contrast to surrounding emission from the accretion flow or lensed counter-jet in M87 (Broderick & Loeb 2009).

The photon ring is nearly circular for all black hole spins and all inclinations of the black hole spin axis to the line of sight (e.g., Johannsen & Psaltis 2010). For an $a_* =0$ black hole of mass $M$ and distance D, the photon ring angular radius on the sky is
Equation (1)

where we have scaled to the most likely mass from Gebhardt et al. (2011) and a distance of $16.9\,\mathrmMpc$ (see also EHT Collaboration et al. 2019e, (hereafter Paper VI ; Blakeslee et al. 2009 ; Bird et al. 2010 ; Cantiello et al. 2018). The photon ring angular radius for other inclinations and values of $a_* $ differs by at most 13% from Equation (1), and most of this variation occurs at $1-| a_* | \ll 1$ (e.g., Takahashi 2004 ; Younsi et al. 2016). Evidently the angular radius of the observed photon ring is approximately $\sim 20\,\mu \mathrmas$ (Figure 1 and Paper IV), which is close to the prediction of the black hole model given in Equation (1).

(2) The observed peak brightness temperature of the ring in Figure 1 is $T_b,pk\sim 6\times 10^9\,\rmK$, which is consistent with past EHT mm-VLBI measurements at 230 GHz (Doeleman et al. 2012 ; Akiyama et al. 2015), and GMVA 3 mm-VLBI measurements of the core region (Kim et al. 2018). Expressed in electron rest-mass (me) units, $\rm\Theta
_b,pk\equiv k_\rmB
T_b,pk/(m_ec^2)\simeq 1$, where $k_\rmB

$ is Boltzmann's constant. The true peak brightness temperature of the source is higher if the ring is unresolved by EHT, as is the case for the model image in the center panel of Figure 1.

The 1.3 mm emission from M87 shown in Figure 1 is expected to be generated by the synchrotron process (see Yuan & Narayan 2014, and references therein) and thus depends on the electron distribution function (eDF). If the emitting plasma has a thermal eDF, then it is characterized by an electron temperature $T_e\geqslant T_b$, or $\rm\Theta

_e\equiv k_\rmB

T_e/(m_ec^2)\gt 1$, because $\rm\Theta

_e\gt \rm\Theta
_b,pk$ if the ring is unresolved or optically thin.

Is the observed brightness temperature consistent with what one would expect from phenomenological models of the source ? Radiatively inefficient accretion flow models of M87 (Reynolds et al. 1996 ; Di Matteo et al. 2003) produce mm emission in a geometrically thick donut of plasma around the black hole. The emitting plasma is collisionless : Coulomb scattering is weak at these low densities and high temperatures. Therefore, the electron and ion temperatures need not be the same (e.g., Spitzer 1962). In radiatively inefficient accretion flow models, the ion temperature is slightly less than the ion virial temperature,
Equation (2)

where $r_\rmg

\equiv GM/c^2$ is the gravitational radius, r is the Boyer–Lindquist or Kerr–Schild radius, and mp is the proton mass. Most models have an electron temperature $T_e\lt T_i$ because of electron cooling and preferential heating of the ions by turbulent dissipation (e.g., Yuan & Narayan 2014 ; Mościbrodzka et al. 2016). If the emission arises at $\sim 5\,r_\rmg

$, then $\rm\Theta

_e\simeq 37(T_e/T_i)$, which is then consistent with the observed $\rm\Theta
_b,pk$ if the source is unresolved or optically thin.

(3) The total flux density in the image at $1.3\,\mathrmmm$ is $\simeq 0.5$ Jy. With a few assumptions we can use this to estimate the electron number density ne and magnetic field strength B in the source. We adopt a simple, spherical, one-zone model for the source with radius $r\simeq 5\,r_\rmg

$, pressure $n_ikT_i+n_ekT_e=\beta _\rmp

B^2/(8\pi )$ with $\beta _\rmp

\equiv p_\mathrmgas/p_\mathrmmag\sim 1$, $T_i\simeq 3T_e$, and temperature $\theta _e\simeq 10\theta _b,pk$, which is consistent with the discussion in (2) above. Setting ne = ni (i.e., assuming a fully ionized hydrogen plasma), the values of B and ne required to produce the observed flux density can be found by solving a nonlinear equation (assuming an average angle between the field and line of sight, 60°). The solution can be approximated as a power law :
Equation (3)

Equation (4)

assuming that $M=6.2\times 10^9\,M_\odot $ and $D=16.9\,\mathrmMpc$, and using the approximate thermal emissivity of Leung et al. (2011). Then the synchrotron optical depth at $1.3\,\mathrmmm$ is 0.2. One can now estimate an accretion rate from (3) using
Equation (5)

assuming spherical symmetry. The Eddington accretion rate is
Equation (6)

where $L_\mathrmEdd\equiv 4\pi GMcm_p/\sigma _T$ is the Eddington luminosity ($\sigma _T$ is the Thomson cross section). Setting the efficiency $\epsilon =0.1$ and $M=6.2\times 10^9\,M_\odot $, $\dotM_\mathrmEdd=137\,M_\odot \,\mathrmyr^-1$, and therefore $\dotM/\dotM_\mathrmEdd\,\sim 2.0\times 10^-5$.

This estimate is similar to but slightly larger than the upper limit inferred from the 230 GHz linear polarization properties of M87 (Kuo et al. 2014).

(4) The ring is brighter in the south than the north. This can be explained by a combination of motion in the source and Doppler beaming. As a simple example we consider a luminous, optically thin ring rotating with speed v and an angular momentum vector inclined at a viewing angle i > 0° to the line of sight. Then the approaching side of the ring is Doppler boosted, and the receding side is Doppler dimmed, producing a surface brightness contrast of order unity if v is relativistic. The approaching side of the large-scale jet in M87 is oriented west–northwest (position angle $\mathrmPA\approx 288^\circ ;$ in Paper VI this is called $\mathrmPA_\mathrmFJ$), or to the right and slightly up in the image. Walker et al. (2018) estimated that the angle between the approaching jet and the line of sight is 17°. If the emission is produced by a rotating ring with an angular momentum vector oriented along the jet axis, then the plasma in the south is approaching Earth and the plasma in the north is receding. This implies a clockwise circulation of the plasma in the source, as projected onto the plane of the sky. This sense of rotation is consistent with the sense of rotation in ionized gas at arcsecond scales (Harms et al. 1994 ; Walsh et al. 2013). Notice that the asymmetry of the ring is consistent with the asymmetry inferred from 43 GHz observations of the brightness ratio between the north and south sides of the jet and counter-jet (Walker et al. 2018).

All of these estimates present a picture of the source that is remarkably consistent with the expectations of the black hole model and with existing GRMHD models (e.g., Dexter et al. 2012 ; Mościbrodzka et al. 2016). They even suggest a sense of rotation of gas close to the black hole. A quantitative comparison with GRMHD models can reveal more.
3. Models

Consistent with the discussion in Section 2, we now adopt the working hypothesis that M87 contains a turbulent, magnetized accretion flow surrounding a Kerr black hole. To test this hypothesis quantitatively against the EHT2017 data we have generated a Simulation Library of 3D time-dependent ideal GRMHD models. To generate this computationally expensive library efficiently and with independent checks on the results, we used several different codes that evolved matching initial conditions using the equations of ideal GRMHD. The codes used include BHAC (Porth et al. 2017), H-AMR (Liska et al. 2018 ; K. Chatterjee et al. 2019, in preparation), iharm (Gammie et al. 2003), and KORAL (Sa̧dowski et al. 2013b, 2014). A comparison of these and other GRMHD codes can be found in O. Porth et al. 2019 (in preparation), which shows that the differences between integrations of a standard accretion model with different codes is smaller than the fluctuations in individual simulations.

From the Simulation Library we have generated a large Image Library of synthetic images. Snapshots of the GRMHD evolutions were produced using the general relativistic ray-tracing (GRRT) schemes ipole (Mościbrodzka & Gammie 2018), RAPTOR (Bronzwaer et al. 2018), or BHOSS (Z. Younsi et al. 2019b, in preparation). A comparison of these and other GRRT codes can be found in Gold et al. (2019), which shows that the differences between codes is small.

In the GRMHD models the bulk of the 1.3 mm emission is produced within $\lesssim 10\,r_\rmg

$ of the black hole, where the models can reach a statistically steady state. It is therefore possible to compute predictive radiative models for this compact component of the source without accurately representing the accretion flow at all radii.

We note that the current state-of-the-art models for M87 are radiation GRMHD models that include radiative feedback and electron-ion thermodynamics (Ryan et al. 2018 ; Chael et al. 2019). These models are too computationally expensive for a wide survey of parameter space, so that in this Letter we consider only nonradiative GRMHD models with a parameterized treatment of the electron thermodynamics.
3.1. Simulation Library

All GRMHD simulations are initialized with a weakly magnetized torus of plasma orbiting in the equatorial plane of the black hole (e.g., De Villiers et al. 2003 ; Gammie et al. 2003 ; McKinney & Blandford 2009 ; Porth et al. 2017). We do not consider tilted models, in which the accretion flow angular momentum is misaligned with the black hole spin. The limitations of this approach are discussed in Section 7.

The initial torus is driven to a turbulent state by instabilities, including the magnetorotational instability (see e.g., Balbus & Hawley 1991). In all cases the outcome contains a moderately magnetized midplane with orbital frequency comparable to the Keplerian orbital frequency, a corona with gas-to-magnetic-pressure ratio $\beta _\rmp

\equiv p_\mathrmgas/p_\mathrmmag\sim 1$, and a strongly magnetized region over both poles of the black hole with $B^2/\rho c^2\gg 1$. We refer to the strongly magnetized region as the funnel, and the boundary between the funnel and the corona as the funnel wall (De Villiers et al. 2005 ; Hawley & Krolik 2006). All models in the library are evolved from t = 0 to $t=10^4\,r_\rmg

c^-1$.

The simulation outcome depends on the initial magnetic field strength and geometry insofar as these affect the magnetic flux through the disk, as discussed below. Once the simulation is initiated the disk transitions to a turbulent state and loses memory of most of the details of the initial conditions. This relaxed turbulent state is found inside a characteristic radius that grows over the course of the simulation. To be confident that we are imaging only those regions that have relaxed, we draw snapshots for comparison with the data from $5\times 10^3\le t/r_\rmg

c^-1\le 10^4$.

GRMHD models have two key physical parameters. The first is the black hole spin $a_* $, $-1\lt a_* \lt 1$. The second parameter is the absolute magnetic flux $\rm\Phi
_\mathrmBH$ crossing one hemisphere of the event horizon (see Tchekhovskoy et al. 2011 ; O. Porth et al. 2019, in preparation for a definition). It is convenient to recast $\rm\Phi
_\mathrmBH$ in dimensionless form $\phi \equiv \rm\Phi
_\mathrmBH\left(\dotMr_\rmg

^2c\right)^-1/2$.110

The magnetic flux phgr is nonzero because magnetic field is advected into the event horizon by the accretion flow and sustained by currents in the surrounding plasma. At $\phi \gt \phi _\max \sim 15$,111 numerical simulations show that the accumulated magnetic flux erupts, pushes aside the accretion flow, and escapes (Tchekhovskoy et al. 2011 ; McKinney et al. 2012). Models with $\phi \sim 1$ are conventionally referred to as Standard and Normal Evolution (SANE ; Narayan et al. 2012 ; Sa̧dowski et al (2013a)) models ; models with $\phi \sim \phi _\max $ are conventionally referred to as Magnetically Arrested Disk (MAD ; Igumenshchev et al. 2003 ; Narayan et al. 2003) models.

The Simulation Library contains SANE models with $a_* =-0.94$, −0.5, 0, 0.5, 0.75, 0.88, 0.94, 0.97, and 0.98, and MAD models with $a_* =-0.94$, −0.5, 0, 0.5, 0.75, and 0.94. The Simulation Library occupies 23 TB of disk space and contains a total of 43 GRMHD simulations, with some repeated at multiple resolutions with multiple codes, with consistent results (O. Porth et al. 2019, in preparation).
3.2. Image Library Generation

To produce model images from the simulations for comparison with EHT observations we use GRRT to generate a large number of synthetic images and derived VLBI data products. To make the synthetic images we need to specify the following : (1) the magnetic field, velocity field, and density as a function of position and time ; (2) the emission and absorption coefficients as a function of position and time ; and (3) the inclination angle between the accretion flow angular momentum vector and the line of sight i, the position angle $\mathrmPA$, the black hole mass $M$, and the distance D to the observer. In the following we discuss each input in turn. The reader who is only interested in a high-level description of the Image Library may skip ahead to Section 3.3.

(1) GRMHD models provide the absolute velocity field of the plasma flow. Nonradiative GRMHD evolutions are invariant, however, under a rescaling of the density by a factor $\mathscrM$. In particular, they are invariant under $\rho \to \mathscrM\rho $, field strength $B\to \mathscrM

^1/2B$, and internal energy $u\to \mathscrMu$ (the Alfvén speed $B/\rho ^1/2$ and sound speed $\propto \sqrtu/\rho $ are invariant). That is, there is no intrinsic mass scale in a nonradiative model as long as the mass of the accretion flow is negligible in comparison to $M$.112 We use this freedom to adjust $\mathscrM$ so that the average image from a GRMHD model has a 1.3 mm flux density ≈0.5 Jy (see Paper IV). Once $\mathscrM$ is set, the density, internal energy, and magnetic field are fully specified.

The mass unit $\mathscrM$ determines $\dotM$. In our ensemble of models $\dotM$ ranges from $2\times 10^-7\dotM_\mathrmEdd$ to $4\times 10^-4\dotM_\mathrmEdd$. Accretion rates vary by model category. The mean accretion rate for MAD models is $\sim 10^-6\dotM_\mathrmEdd$. For SANE models with $a_* \gt 0$ it is $\sim 5\times 10^-5\dotM_\mathrmEdd ;$ and for $a_* \lt 0$ it is $\sim 2\times 10^-4\dotM_\mathrmEdd$.

(2) The observed radio spectral energy distributions (SEDs) and the polarization characteristics of the source make clear that the 1.3 mm emission is synchrotron radiation, as is typical for active galactic nuclei (AGNs). Synchrotron absorption and emission coefficients depend on the eDF. In what follows, we adopt a relativistic, thermal model for the eDF (a Maxwell-Jüttner distribution ; Jüttner 1911 ; Rezzolla & Zanotti 2013). We discuss the limitations of this approach in Section 7.

All of our models of M87 are in a sufficiently low-density, high-temperature regime that the plasma is collisionless (see Ryan et al. 2018, for a discussion of Coulomb coupling in M87). Therefore, Te likely does not equal the ion temperature Ti, which is provided by the simulations. We set Te using the GRMHD density ρ, internal energy density u, and plasma $\beta _\rmp

$ using a simple model :
Equation (7)

where we have assumed that the plasma is composed of hydrogen, the ions are nonrelativistic, and the electrons are relativistic. Here $R\equiv T_i/T_e$ and
Equation (8)
This prescription has one parameter, $R_\mathrmhigh$, and sets $T_e\simeq T_i$ in low $\beta _\rmp
$ regions and $T_e\simeq T_i/R_\mathrmhigh$ in the midplane of the disk. It is adapted from Mościbrodzka et al. (2016) and motivated by models for electron heating in a turbulent, collisionless plasma that preferentially heats the ions for $\beta _\rmp

\gtrsim 1$ (e.g., Howes 2010 ; Kawazura et al. 2018).

(3) We must specify the observer inclination i, the orientation of the observer through the position angle $\mathrmPA$, the black hole mass $M$, and the distance D to the source. Non-EHT constraints on i, $\mathrmPA$, and $M$ are considered below ; we have generated images at $i=12^\circ ,17^\circ ,22^\circ ,158^\circ ,163^\circ $, and 168° and a few at i = 148°. The position angle (PA) can be changed by simply rotating the image. All features of the models that we have examined, including $\dotM$, are insensitive to small changes in i. The image morphology does depend on whether i is greater than or less than 90°, as we will show below.

The model images are generated with a $160\times 160\,\mu \mathrmas$ field of view and $1\mu \mathrmas$ pixels, which are small compared to the $\sim 20\,\mu \mathrmas$ nominal resolution of EHT2017. Our analysis is insensitive to changes in the field of view and the pixel scale.

For $M$ we use the most likely value from the stellar absorption-line work, $6.2\times 10^9M_\odot $ (Gebhardt et al. 2011). For the distance D we use $16.9\,\,\mathrmMpc$, which is very close to that employed in Paper VI. The ratio $GM/(c^2D)=3.62\,\mu \mathrmas$ (hereafter M/D) determines the angular scale of the images. For some models we have also generated images with $M=3.5\times 10^9\,M_\odot $ to check that the analysis results are not predetermined by the input black hole mass.
3.3. Image Library Summary
The Image Library contains of order 60,000 images. We generate images from 100 to 500 distinct output files from each of the GRMHD models at each of $R_\mathrmhigh=1,10,20,40,80$, and 160. In comparing to the data we adjust the $\mathrmPA$ by rotation and the total flux and angular scale of the image by simply rescaling images from the standard parameters in the Image Library (see Figure 29 in Paper VI). Tests indicate that comparisons with the data are insensitive to the rescaling procedure unless the angular scaling factor or flux scaling factor is large.113

The comparisons with the data are also insensitive to image resolution.114

A representative set of time-averaged images from the Image Library are shown in Figures 2 and 3. From these figures it is clear that varying the parameters $a_* $, phgr, and $R_\mathrmhigh$ can change the width and asymmetry of the photon ring and introduce additional structures exterior and interior to the photon ring.
Figure 2.

Figure 2. Time-averaged 1.3 mm images generated by five SANE GRMHD simulations with varying spin ($a_* =-0.94$ to $a_* =+0.97$ from left to right) and $R_\mathrmhigh$ ($R_\mathrmhigh=1$ to $R_\mathrmhigh=160$ from top to bottom ; increasing $R_\mathrmhigh$ corresponds to decreasing electron temperature). The colormap is linear. All models are imaged at i = 163°. The jet that is approaching Earth is on the right (west) in all the images. The black hole spin vector projected onto the plane of the sky is marked with an arrow and aligned in the east–west direction. When the arrow is pointing left the black hole rotates in a clockwise direction, and when the arrow is pointing right the black hole rotates in a counterclockwise direction. The field of view for each model image is $80\,\mu \mathrmas$ (half of that used for the image libraries) with resolution equal to $1\mu \mathrmas$/pixel (20 times finer than the nominal resolution of EHT2017, and the same employed in the library images).

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Figure 3.

Figure 3. Same as in Figure 2 but for selected MAD models.

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The location of the emitting plasma is shown in Figure 4, which shows a map of time- and azimuth-averaged emission regions for four representative $a_* \gt 0$ models. For SANE models, if $R_\mathrmhigh$ is low (high), emission is concentrated more in the disk (funnel wall), and the bright section of the ring is dominated by the disk (funnel wall).115 Appendix B shows images generated by considering emission only from particular regions of the flow, and the results are consistent with Figure 4.
Figure 4.

Figure 4. Binned location of the point of origin for all photons that make up an image, summed over azimuth, and averaged over all snapshots from the simulation. The colormap is linear. The event horizon is indicated by the solid white semicircle and the black hole spin axis is along the figure vertical axis. This set of four images shows MAD and SANE models with $R_\mathrmhigh=10$ and 160, all with $a_* =0.94$. The region between the dashed curves is the locus of existence of (unstable) photon orbits (Teo 2003). The green cross marks the location of the innermost stable circular orbit (ISCO) in the equatorial plane. In these images the line of sight (marked by an arrow) is located below the midplane and makes a 163° angle with the disk angular momentum, which coincides with the spin axis of the black hole.

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Figures 2 and 3 show that for both MAD and SANE models the bright section of the ring, which is generated by Doppler beaming, shifts from the top for negative spin, to a nearly symmetric ring at $a_* =0$, to the bottom for $a_* \gt 0$ (except the SANE $R_\mathrmhigh=1$ case, where the bright section is always at the bottom when i > 90°). That is, the location of the peak flux in the ring is controlled by the black hole spin : it always lies roughly 90 degrees counterclockwise from the projection of the spin vector on the sky. Some of the ring emission originates in the funnel wall at $r\lesssim 8\,r_\rmg

$. The rotation of plasma in the funnel wall is in the same sense as plasma in the funnel, which is controlled by the dragging of magnetic field lines by the black hole. The funnel wall thus rotates opposite to the accretion flow if $a_* \lt 0$. This effect will be studied further in a later publication (Wong et al. 2019). The resulting relationships between disk angular momentum, black hole angular momentum, and observed ring asymmetry are illustrated in Figure 5.
Figure 5.

Figure 5. Illustration of the effect of black hole and disk angular momentum on ring asymmetry. The asymmetry is produced primarily by Doppler beaming : the bright region corresponds to the approaching side. In GRMHD models that fit the data comparatively well, the asymmetry arises in emission generated in the funnel wall. The sense of rotation of both the jet and funnel wall are controlled by the black hole spin. If the black hole spin axis is aligned with the large-scale jet, which points to the right, then the asymmetry implies that the black hole spin is pointing away from Earth (rotation of the black hole is clockwise as viewed from Earth). The blue ribbon arrow shows the sense of disk rotation, and the black ribbon arrow shows black hole spin. Inclination i is defined as the angle between the disk angular momentum vector and the line of sight.

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The time-averaged MAD images are almost independent of $R_\mathrmhigh$ and depend mainly on $a_* $. In MAD models much of the emission arises in regions with $\beta _\rmp
\sim 1$, where $R_\mathrmhigh$ has little influence over the electron temperature, so the insensitivity to $R_\mathrmhigh$ is natural (see Figure 4). In SANE models emission arises at $\beta _\rmp
\sim 10$, so the time-averaged SANE images, by contrast, depend strongly on $R_\mathrmhigh$. In low $R_\mathrmhigh$ SANE models, extended emission outside the photon ring, arising near the equatorial plane, is evident at $R_\mathrmhigh=1$. In large $R_\mathrmhigh$ SANE models the inner ring emission arises from the funnel wall, and once again the image looks like a thin ring (see Figure 4).

Figure 6 and the accompanying animation show the evolution of the images, visibility amplitudes, and closure phases over a $5000\,r_\rmg

c^-1\approx 5\,\mathrmyr$ interval in a single simulation for M87. It is evident from the animation that turbulence in the simulations produces large fluctuations in the images, which imply changes in visibility amplitudes and closure phases that are large compared to measurement errors. The fluctuations are central to our procedure for comparing models with the data, described briefly below and in detail in Paper VI.

Figure 6. Single frame from the accompanying animation. This shows the visibility amplitudes (top), closure phases plotted by Euclidean distance in 6D space (middle), and associated model images at full resolution (lower left) and convolved with the EHT2017 beam (lower right). Data from 2017 April 6 high-band are also shown in the top two plots. The video shows frames 1 through 100 and has a duration of 10 s.

(An animation of this figure is available.)

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The timescale between frames in the animation is $50\,r_\rmg

c^-1\simeq 18$ days, which is long compared to EHT2017 observing campaign. The images are highly correlated on timescales less than the innermost stable circular orbit (ISCO) orbital period, which for $a_* =0$ is $\simeq 15\ r_\rmg

c^-1\simeq 5$ days, i.e., comparable to the duration of the EHT2017 campaign. If drawn from one of our models, we would expect the EHT2017 data to look like a single snapshot (Figures 6) rather than their time averages (Figures 2 and 3).
4. Procedure for Comparison of Models with Data
As described above, each model in the Simulation Library has two dimensionless parameters : black hole spin $a_* $ and magnetic flux phgr. Imaging the model from each simulation adds five new parameters : $R_\mathrmhigh$, i, $\mathrmPA$, $M$, and D, which we set to $16.9\,\mathrmMpc$. After fixing these parameters we draw snapshots from the time evolution at a cadence of 10 to $50\,r_\rmg

c^-1$. We then compare these snapshots to the data.

The simplest comparison computes the $\chi _\nu ^2$ (reduced chi square) distance between the data and a snapshot. In the course of computing $\chi _\nu ^2$ we vary the image scale M/D, flux density Fν, position angle $\mathrmPA$, and the gain at each VLBI station in order to give each image every opportunity to fit the data. The best-fit parameters $(M/D,F_\nu ,\mathrmPA)$ for each snapshot are found by two pipelines independently : the Themis pipeline using a Markov chain Monte Carlo method (A. E. Broderick et al. 2019a, in preparation), and the GENA pipeline using an evolutionary algorithm for multidimensional minimization (Fromm et al. 2019a ; C. Fromm et al. 2019b, in preparation ; see also Section 4 of Paper VI for details). The best-fit parameters contain information about the source and we use the distribution of best-fit parameters to test the model by asking whether or not they are consistent with existing measurements of M/D and estimates of the jet $\mathrmPA$ on larger scales.

The $\chi _\nu ^2$ comparison alone does not provide a sharp test of the models. Fluctuations in the underlying GRMHD model, combined with the high signal-to-noise ratio for EHT2017 data, imply that individual snapshots are highly unlikely to provide a formally acceptable fit with $\chi _\nu ^2\simeq 1$. This is borne out in practice with the minimum $\chi _\nu ^2=1.79$ over the entire set of the more than 60,000 individual images in the Image Library. Nevertheless, it is possible to test if the $\chi _\nu ^2$ from the fit to the data is consistent with the underlying model, using '''Average Image Scoring''' with Themis (Themis-AIS), as described in detail in Appendix F of Paper VI). Themis-AIS measures a $\chi _\nu ^2$ distance (on the space of visibility amplitudes and closure phases) between a trial image and the data. In practice we use the average of the images from a given model as the trial image (hence Themis-AIS), but other choices are possible. We compute the $\chi _\nu ^2$ distance between the trial image and synthetic data produced from each snapshot. The model can then be tested by asking whether the data's $\chi _\nu ^2$ is likely to have been drawn from the model's distribution of $\chi _\nu ^2$. In particular, we can assign a probability p that the data is drawn from a specific model's distribution.

In this Letter we focus on comparisons with a single data set, the 2017 April 6 high-band data (Paper III). The eight EHT2017 data sets, spanning four days with two bands on each day, are highly correlated. Assessing what correlation is expected in the models is a complicated task that we defer to later publications. The 2017 April 6 data set has the largest number of scans, 284 detections in 25 scans (see Paper III) and is therefore expected to be the most constraining.116
5. Model Constraints : EHT2017 Alone

The resolved ring-like structure obtained from the EHT2017 data provides an estimate of M/D (discussed in detail in Paper VI) and the jet $\mathrmPA$ from the immediate environment of the central black hole. As a first test of the models we can ask whether or not these are consistent with what is known from other mass measurements and from the orientation of the large-scale jet.

Figure 7 shows the distributions of best-fit values of M/D for a subset of the models for which spectra and jet power estimates are available (see below). The three lines show the M/D distribution for all snapshots (dotted lines), the best-fit 10% of snapshots (dashed lines), and the best-fit 1% of snapshots (solid lines) within each model. Evidently, as better fits are required, the distribution narrows and peaks close to $M/D\sim 3.6\,\mu \mathrmas$ with a width of about $0.5\mu \mathrmas$.
Figure 7.

Figure 7. Distribution of M/D obtained by fitting Image Library snapshots to the 2017 April 6 data, in $\mu \mathrmas$, measured independently using the (left panel) Themis and (right panel) GENA pipelines with qualitatively similar results. Smooth lines were drawn with a Gaussian kernel density estimator. The three lines show the best-fit 1% within each model (solid) ; the best-fit 10% within each model (dashed) ; and all model images (dotted). The vertical lines show $M/D=2.04$ (dashed) and $3.62\,\mu \mathrmas$ (solid), corresponding to M = 3.5 and $6.2\times 10^9\,M_\odot $. The distribution uses a subset of models for which spectra and jet power estimates are available (see Section 6). Only images with $a_* \gt 0$, i > 90° and $a_* \lt 0$, i < 90° (see also the left panel of Figure 5) are considered.

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The distribution of M/D for the best-fit $\lt 10 \% $ of snapshots is qualitatively similar if we include only MAD or SANE models, only models produced by individual codes (BHAC, H-AMR, iharm, or KORAL), or only individual spins. As the thrust of this Letter is to test the models, we simply note that Figure 7 indicates that the models are broadly consistent with earlier mass estimates (see Paper VI for a detailed discussion). This did not have to be the case : the ring radius could have been significantly larger than $3.6\,\mu \mathrmas$.

We can go somewhat further and ask if any of the individual models favor large or small masses. Figure 8 shows the distributions of best-fit values of M/D for each model (different $a_* $, $R_\mathrmhigh$, and magnetic flux). Most individual models favor M/D close to $3.6\,\mu \mathrmas$. The exceptions are $a_* \leqslant 0$ SANE models with $R_\mathrmhigh=1$, which produce the bump in the M/D distribution near $2\mu \mathrmas$. In these models, the emission is produced at comparatively large radius in the disk (see Figure 2) because the inner edge of the disk (the ISCO) is at a large radius in a counter-rotating disk around a black hole with $| a_* | \sim 1$. For these models, the fitting procedure identifies EHT2017's ring with this outer ring, which forces the photon ring, and therefore M/D, to be small. As we will show later, these models can be rejected because they produce weak jets that are inconsistent with existing jet power estimates (see Section 6.3).
Figure 8.
Figure 8. Distributions of M/D and black hole mass with $D=16.9\,\mathrmMpc$ reconstructed from the best-fit 10% of images for MAD (left panel) and SANE (right panel) models (i = 17° for $a_* \le 0$ and 163° for $a_* \gt 0$) with different $R_\mathrmhigh$ and $a_* $, from the Themis (dark red, left), and GENA (dark green, right) pipelines. The white dot and vertical black bar correspond, respectively, to the median and region between the 25th and 75th percentiles for both pipelines combined. The blue and pink horizontal bands show the range of M/D and mass at $D=16.9\,\mathrmMpc$ estimated from the gas dynamical model (Walsh et al. 2013) and stellar dynamical model (Gebhardt et al. 2011), respectively. Constraints on the models based on average image scoring (Themis-AIS) are discussed in Section 5. Constraints based on radiative efficiency, X-ray luminosity, and jet power are discussed in Section 6.

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Figure 8 also shows that M/D increases with $a_* $ for SANE models. This is due to the appearance of a secondary inner ring inside the main photon ring. The former is associated with emission produced along the wall of the approaching jet. Because the emission is produced in front of the black hole, lensing is weak and it appears at small angular scale. The inner ring is absent in MAD models (see Figure 3), where the bulk of the emission comes from the midplane at all values of $R_\mathrmhigh$(Figure 4).

We now ask whether or not the PA of the jet is consistent with the orientation of the jet measured at other wavelengths. On large ( mas) scales the extended jet component has a PA of approximately 288° (e.g., Walker et al. 2018). On smaller ($\sim 100\,\mu \mathrmas$) scales the apparent opening angle of the jet is large (e.g., Kim et al. 2018) and the PA is therefore more difficult to measure. Also notice that the jet PA may be time dependent (e.g., Hada et al. 2016 ; Walker et al. 2018). In our model images the jet is relatively dim at 1.3 mm, and is not easily seen with a linear colormap. The model jet axis is, nonetheless, well defined : jets emerge perpendicular to the disk.

Figure 9 shows the distribution of best-fit PA over the same sample of snapshots from the Image Library used in Figure 7. We divide the snapshots into two groups. The first group has the black hole spin pointed away from Earth (i > 90° and $a_* \gt 0$, or i < 90° and $a_* \lt 0$). The spin-away model PA distributions are shown in the top two panels. The second group has the black hole spin pointed toward Earth (i > 90 and $a_* \lt 0$ or i > 90° and $a_* \lt 0$). These spin-toward model PA distributions are shown in the bottom two panels. The large-scale jet orientation lies on the shoulder of the spin-away distribution (the distribution can be approximated as a Gaussian with, for Themis (GENA) mean 209 (203)° and $\sigma _\mathrmPA\,=54\,(55)^\circ ;$ the large-scale jet PA lies $1.5\sigma _\mathrmPA$ from the mean) and is therefore consistent with the spin-away models. On the other hand, the large-scale jet orientation lies off the shoulder of the spin-toward distribution and is inconsistent with the spin-toward models. Evidently models in which the black hole spin is pointing away from Earth are strongly favored.
Figure 9.

Figure 9. Top : distribution of best-fit PA (in degree) scored by the Themis (left) and GENA (right) pipelines for models with black hole spin vector pointing away from Earth (i > 90° for $a_* \gt 0$ or i < 90° for $a_* \lt 0$). Bottom : images with black hole spin vector pointing toward Earth (i < 90° for $a_* \gt 0$ or i > 90° for $a_* \lt 0$). Smooth lines were drawn with a wrapped Gaussian kernel density estimator. The three lines show (1) all images in the sample (dotted line) ; (2) the best-fit 10% of images within each model (dashed line) ; and (3) the best-fit 1% of images in each model (solid line). For reference, the vertical line shows the position angle $\mathrmPA\sim 288^\circ $ of the large-scale (mas) jet Walker et al. (2018), with the gray area from (288 – 10)° to (288 + 10)° indicating the observed PA variation.

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The width of the spin-away and spin-toward distributions arises naturally in the models from brightness fluctuations in the ring. The distributions are relatively insensitive if split into MAD and SANE categories, although for MAD the averaged PA is $\langle \mathrmPA\rangle =219^\circ $, $\sigma _\mathrmPA=46^\circ $, while for SANE $\langle \mathrmPA\rangle =195^\circ $ and $\sigma _\mathrmPA=58^\circ $. The $a_* =0$ and $a_* \gt 0$ models have similar distributions. Again, EHT2017 data strongly favor one sense of black hole spin : either $| a_* | $ is small, or the spin vector is pointed away from Earth. If the fluctuations are such that the fitted PA for each epoch of observations is drawn from a Gaussian with $\sigma _\mathrmPA\simeq 55^\circ $, then a second epoch will be able to identify the true orientation with accuracy $\sigma _\mathrmPA/\sqrt2\simeq 40^\circ $ and the Nth epoch with accuracy $\sigma _\mathrmPA/\sqrtN$. If the fitted PA were drawn from a Gaussian of width $\sigma _\mathrmPA=54^\circ $ about $\mathrmPA=288^\circ $, as would be expected in a model in which the large-scale jet is aligned normal to the disk, then future epochs have a >90% chance of seeing the peak brightness counterclockwise from its position in EHT2017.

Finally, we can test the models by asking if they are consistent with the data according to Themis-AIS, as introduced in Section 4. Themis-AIS produces a probability p that the $\chi _\nu ^2$ distance between the data and the average of the model images is drawn from the same distribution as the $\chi _\nu ^2$ distance between synthetic data created from the model images, and the average of the model images. Table 1 takes these p values and categorizes them by magnetic flux and by spin, aggregating (averaging) results from different codes, $R_\mathrmhigh$, and i. Evidently, most of the models are formally consistent with the data by this test.

Table 1. Average Image Scoringa Summary
Fluxb $a_* $ c $\langle p\rangle $ d $N_\mathrmmodel$ e $\mathrmMIN(p)$ f $\mathrmMAX(p)$ g
SANE −0.94 0.33 24 0.01 0.88
SANE −0.5 0.19 24 0.01 0.73
SANE 0 0.23 24 0.01 0.92
SANE 0.5 0.51 30 0.02 0.97
SANE 0.75 0.74 6 0.48 0.98
SANE 0.88 0.65 6 0.26 0.94
SANE 0.94 0.49 24 0.01 0.92
SANE 0.97 0.12 6 0.06 0.40
MAD −0.94 0.01 18 0.01 0.04
MAD −0.5 0.75 18 0.34 0.98
MAD 0 0.22 18 0.01 0.62
MAD 0.5 0.17 18 0.02 0.54
MAD 0.75 0.28 18 0.01 0.72
MAD 0.94 0.21 18 0.02 0.50

Notes.
aThe Average Image Scoring (Themis-AIS) is introduced in Section 4. bflux : net magnetic flux on the black hole (MAD or SANE). c $a_* $ : dimensionless black hole spin. d $\langle p\rangle $ : mean of the p value for the aggregated models. e $N_\mathrmmodel$ : number of aggregated models. f $\mathrmMIN(p)$ : minimum p value among the aggregated models. g $\mathrmMAX(p)$ : maximum p value among the aggregated models.

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One group of models, however, is rejected by Themis-AIS : MAD models with $a_* =-0.94$. On average this group has p = 0.01, and all models within this group have $p\leqslant 0.04$. Snapshots from MAD models with $a_* =-0.94$ exhibit the highest morphological variability in our ensemble in the sense that the emission breaks up into transient bright clumps. These models are rejected by Themis-AIS because none of the snapshots are as similar to the average image as the data. In other words, it is unlikely that EHT2017 would have captured an $a_* =-0.94$ MAD model in a configuration as unperturbed as the data seem to be.

The remainder of the model categories contain at least some models that are consistent with the data according to the average image scoring test. That is, most models are variable and the associated snapshots lie far from the average image. These snapshots are formally inconsistent with the data, but their distance from the average image is consistent with what is expected from the models. Given the uncertainties in the model—and our lack of knowledge of the source prior to EHT2017—it is remarkable that so many of the models are acceptable. This is likely because the source structure is dominated by the photon ring, which is produced by gravitational lensing, and is therefore relatively insensitive to the details of the accretion flow and jet physics. We can further narrow the range of acceptable models, however, using additional constraints.
6. Model Constraints : EHT2017 Combined with Other Constraints

We can apply three additional arguments to further constrain the source model. (1) The model must be close to radiative equilibrium. (2) The model must be consistent with the observed broadband SED ; in particular, it must not overproduce X-rays. (3) The model must produce a sufficiently powerful jet to match the measurements of the jet kinetic energy at large scales. Our discussions in this Section are based on simulation data that is provided in full detail in Appendix A.
6.1. Radiative Equilibrium

The model must be close to radiative equilibrium. The GRMHD models in the Simulation Library do not include radiative cooling, nor do they include a detailed prescription for particle energization. In nature the accretion flow and jet are expected to be cooled and heated by a combination of synchrotron and Compton cooling, turbulent dissipation, and Coulomb heating, which transfers energy from the hot ions to the cooler electrons. In our suite of simulations the parameter $R_\mathrmhigh$ can be thought of as a proxy for the sum of these processes. In a fully self-consistent treatment, some models would rapidly cool and settle to a lower electron temperature (see Mościbrodzka et al. 2011 ; Ryan et al. 2018 ; Chael et al. 2019). We crudely test for this by calculating the radiative efficiency $\epsilon \equiv L_\mathrmbol/(\dotMc^2)$, where $L_\mathrmbol$ is the bolometric luminosity. If it is larger than the radiative efficiency of a thin, radiatively efficient disk,117 which depends only on $a_* $ (Novikov & Thorne 1973), then we reject the model as physically inconsistent.

We calculate $L_\mathrmbol$ with the Monte Carlo code grmonty (Dolence et al. 2009), which incorporates synchrotron emission, absorption, Compton scattering at all orders, and bremsstrahlung. It assumes the same thermal eDF used in generating the Image Library. We calculate $L_\mathrmbol$ for 20% of the snapshots to minimize computational cost. We then average over snapshots to find $\langle L_\mathrmbol\rangle $. The mass accretion rate $\dotM$ is likewise computed for each snapshot and averaged over time. We reject models with epsilon that is larger than the classical thin disk model. (Table 3 in Appendix A lists epsilon for a large set of models.) All but two of the radiatively inconsistent models are MADs with $a_* \geqslant 0$ and $R_\mathrmhigh=1$. Eliminating all MAD models with $a_* \geqslant 0$ and $R_\mathrmhigh=1$ does not change any of our earlier conclusions.
6.2. X-Ray Constraints

As part of the EHT2017 campaign, we simultaneously observed M87 with the Chandra X-ray observatory and the Nuclear Spectroscopic Telescope Array (NuSTAR). The best fit to simultaneous Chandra and NuSTAR observations on 2017 April 12 and 14 implies a $2\mbox—10\,\mathrmkeV$ luminosity of $L_

\rmX

_\mathrmobs

\,=4.4\pm 0.1\times 10^40\,\,\mathrmerg\,\rms
^-1$. We used the SEDs generated from the simulations while calculating $L_\mathrmbol$ to reject models that consistently overproduce X-rays ; specifically, we reject models with $\mathrmlogL_

\rmX

_\mathrmobs

\lt \mathrmlog\langle L_\rmX

\rangle -2\sigma (\mathrmlogL_\rmX

)$. We do not reject underluminous models because the X-rays could in principle be produced by direct synchrotron emission from nonthermal electrons or by other unresolved sources. Notice that $L_\rmX

$ is highly variable in all models so that the X-ray observations currently reject only a few models. Table 3 in Appendix A shows $\langle L_\rmX

\rangle $ as well as upper and lower limits for a set of models that is distributed uniformly across the parameter space.

In our models the X-ray flux is produced by inverse Compton scattering of synchrotron photons. The X-ray flux is an increasing function of $\tau _TT_e^2$ where τT is a characteristic Thomson optical depth ($\tau _T\sim 10^-5$), and the characteristic amplification factor for photon energies is $\propto T_e^2$ because the X-ray band is dominated by singly scattered photons interacting with relativistic electrons (we include all scattering orders in the Monte Carlo calculation). Increasing $R_\mathrmhigh$ at fixed $F_\nu (230\,\ \mathrmGHz)$ tends to increase $\dotM$ and therefore τT and decrease Te. The increase in Te dominates in our ensemble of models, and so models with small $R_\mathrmhigh$ have larger $L_\rmX
$, while models with large $R_\mathrmhigh$ have smaller $L_\rmX

$. The effect is not strictly monotonic, however, because of noise in our sampling process and the highly variable nature of the X-ray emission.
The overluminous models are mostly SANE models with $R_\mathrmhigh\leqslant 20$. The model with the highest $\langle L_\rmX

\rangle =4.2\,\times 10^42\,\,\mathrmerg\,\rms

^-1$ is a SANE, $a_* =0$, $R_\mathrmhigh=10$ model. The corresponding model with $R_\mathrmhigh=1$ has $\langle L_\rmX

\rangle =2.1\,\times 10^41\,\,\mathrmerg\,\rms

^-1$, and the difference between these two indicates the level of variability and the sensitivity of the average to the brightest snapshot. The upshot of application of the $L_\rmX

$ constraints is that $L_\rmX

$ is sensitive to $R_\mathrmhigh$. Very low values of $R_\mathrmhigh$ are disfavored. $L_\rmX

$ thus most directly constrains the electron temperature model.
6.3. Jet Power
Estimates of M87's jet power ($P_\mathrmjet$) have been reviewed in Reynolds et al. (1996), Li et al. (2009), de Gasperin et al. (2012), Broderick et al. (2015), and Prieto et al. (2016). The estimates range from 1042 to $10^45\,\,\mathrmerg\,\rms

^-1$. This wide range is a consequence of both physical uncertainties in the models used to estimate $P_\mathrmjet$ and the wide range in length and timescales probed by the observations. Some estimates may sample a different epoch and thus provide little information on the state of the central engine during EHT2017. Nevertheless, observations of HST-1 yield $P_\mathrmjet\sim 10^44\ \,\mathrmerg\,\rms
^-1$ (e.g., Stawarz et al. 2006). HST-1 is within $\sim 70\,\mathrmpc$ of the central engine and, taking account of relativistic time foreshortening, may be sampling the central engine $P_\mathrmjet$ over the last few decades. Furthermore, the 1.3 mm light curve of M87 as observed by SMA shows $\lesssim 50 \% $ variability over decade timescales (Bower et al. 2015). Based on these considerations it seems reasonable to adopt a very conservative lower limit on jet power $\equiv P_\mathrmjet,\min =10^42\ \,\mathrmerg\,\rms

^-1$.
To apply this constraint we must define and measure $P_\mathrmjet$ in our models. Our procedure is discussed in detail in Appendix A. In brief, we measure the total energy flux in outflowing regions over the polar caps of the black hole in which the energy per unit rest mass exceeds $2.2\,c^2$, which corresponds to βγ = 1, where $\beta \equiv v/c$ and γ is Lorentz factor. The effect of changing this cutoff is also discussed in Appendix A. Because the cutoff is somewhat arbitrary, we also calculate $P_\mathrmout$ by including the energy flux in all outflowing regions over the polar caps of the black hole ; that is, it includes the energy flux in any wide-angle, low-velocity wind. $P_\mathrmout$ represents a maximal definition of jet power. Table 3 in Appendix A shows $P_\mathrmjet$ as well as a total outflow power $P_\mathrmout$.

The constraint $P_\mathrmjet\gt P_\mathrmjet,\min =10^42\,\mathrmerg\,\rms
^-1$ rejects all $a_* =0$ models. This conclusion is not sensitive to the definition of $P_\mathrmjet$ : all $a_* =0$ models also have total outflow power $P_\mathrmout\,\lt 10^42\,\mathrmerg\,\rms
^-1$. The most powerful $a_* =0$ model is a MAD model with $R_\mathrmhigh=160$, which has $P_\mathrmout=3.7\times 10^41\,\mathrmerg\,\rms
^-1$ and $P_\mathrmjet$ consistent with 0. We conclude that our $a_* =0$ models are ruled out.

Can the $a_* =0$ models be saved by changing the eDF ? Probably not. There is no evidence from the GRMHD simulations that these models are capable of producing a relativistic outflow with $\beta \gamma \gt 1$. Suppose, however, that we are willing to identify the nonrelativistic outflow, whose power is measured by $P_\mathrmout$, with the jet. Can $P_\mathrmout$ be raised to meet our conservative threshold on jet power ? Here the answer is yes, in principle, and this can be done by changing the eDF. The eDF and $P_\mathrmout$ are coupled because $P_\mathrmout$ is determined by $\dotM$, and $\dotM$ is adjusted to produce the observed compact mm flux. The relationship between $\dotM$ and mm flux depends upon the eDF. If the eDF is altered to produce mm photons less efficiently (for example, by lowering Te in a thermal model), then $\dotM$ and therefore $P_\mathrmout$ increase. A typical nonthermal eDF, by contrast, is likely to produce mm photons with greater efficiency by shifting electrons out of the thermal core and into a nonthermal tail. It will therefore lower $\dotM$ and thus $P_\mathrmout$. A thermal eDF with lower Te could have higher $P_\mathrmout$, as is evident in the large $R_\mathrmhigh$ SANE models in Table 3. There are observational and theoretical lower limits on Te, however, including a lower limit provided by the observed brightness temeprature. As Te declines, ne and B increase and that has implications for source linear polarization (Mościbrodzka et al. 2017 ; Jiménez-Rosales & Dexter 2018), which will be explored in future work. As Te declines and ne and ni increase there is also an increase in energy transfer from ions to electrons by Coulomb coupling, and this sets a floor on Te.

The requirement that $P_\mathrmjet\gt P_\mathrmjet,\min $ eliminates many models other than the $a_* =0$ models. All SANE models with $| a_* | =0.5$ fail to produce jets with the required minimum power. Indeed, they also fail the less restrictive condition $P_\mathrmout\gt P_\mathrmjet,\min $, so this conclusion is insensitive to the definition of the jet. We conclude that among the SANE models, only high-spin models survive.

At this point it is worth revisiting the SANE, $R_\mathrmhigh=1$, $a_* =-0.94$ model that favored a low black hole mass in Section 5. These models are not rejected by a naive application of the $P_\mathrmjet\gt P_\mathrmjet,\min $ criterion, but they are marginal. Notice, however, that we needed to assume a mass in applying the this criterion. We have consistently assumed $M=6.2\times 10^9\,M_\odot $. If we use the $M\sim 3\times 10^9\,M_\odot $ implied by the best-fit M/D, then $\dotM$ drops by a factor of two, $P_\mathrmjet$ drops below the threshold and the model is rejected.

The lower limit on jet power $P_\mathrmjet,\min =10^42\,\mathrmerg\,\rms

^-1$ is conservative and the true jet power is likely higher. If we increased $P_\mathrmjet,\min $ to $3\times 10^42\,\mathrmerg\,\rms

^-1$, the only surviving models would have $| a_* | =0.94$ and $R_\mathrmhigh\geqslant 10$. This conclusion is also not sensitive to the definition of the jet power : applying the same cut to $P_\mathrmout$ adds only a single model with $| a_* | \lt 0.94$, the $R_\mathrmhigh=160$, $a_* =0.5$ MAD model. The remainder have $a_* =0.94$. Interestingly, the most powerful jets in our ensemble of models are produced by SANE, $a_* =-0.94$, $R_\mathrmhigh=160$ models, with $P_\mathrmjet\simeq 10^43\,\,\mathrmerg\,\rms

^-1$.
Estimates for $P_\mathrmjet$ extend to $10^45\,\mathrmerg\,\rms
^-1$, but in our ensemble of models the maximum $P_\mathrmjet\sim 10^43\,\,\mathrmerg\,\rms
^-1$. Possible explanations include : (1) $P_\mathrmjet$ is variable and the estimates probe the central engine power at earlier epochs (discussed above) ; (2) the $P_\mathrmjet$ estimates are too large ; or (3) the models are in error. How might our models be modified to produce a larger $P_\mathrmjet$ ? For a given magnetic field configuration the jet power scales with $\dotMc^2$. To increase $P_\mathrmjet$, then, one must reduce the mm flux per accreted nucleon so that at fixed mm flux density $\dotM$ increases.118 Lowering Te in a thermal model is unlikely to work because lower Te implies higher synchrotron optical depth, which increases the ring width. We have done a limited series of experiments that suggest that even a modest decrease in Te would produce a broad ring that is inconsistent with EHT2017 (Paper VI). What is required, then, is a nonthermal (or multitemperature) model with a large population of cold electrons that are invisible at mm wavelength (for a thermal subpopulation, $\rm\Theta
_e,\mathrmcold\lt 1$), and a population of higher-energy electrons that produces the observed mm flux (see Falcke & Biermann 1995). We have not considered such models here, but we note that they are in tension with current ideas about dissipation of turbulence because they require efficient suppression of electron heating.

The $P_\mathrmjet$ in our models is dominated by Poynting flux in the force-free region around the axis (the '''funnel'''), as in the Blandford & Znajek (1977) force-free magnetosphere model. The energy flux is concentrated along the walls of the funnel.119 Tchekhovskoy et al. (2011) provided an expression for the energy flux in the funnel, the so-called Blandford–Znajek power $P_\mathrmBZ$, which becomes, in our units,
Equation (9)

where $f(a_* )\approx a_* ^2\left(1+\sqrt1-a_* ^2\right)^-2$ (a good approximation for $a_* \lt 0.95$) and $\dotM_\mathrmEdd=137\,M_\odot \,\mathrmyr^-1$ for $M=6.2\times 10^9\,M_\odot $. This expression was developed for models with a thin disk in the equatorial plane. $P_\mathrmBZ$ is lower for models where the force-free region is excluded by a thicker disk around the equatorial plane. Clearly $P_\mathrmBZ$ is comparable to observational estimates of $P_\mathrmjet$.

In our models (see Table 3) $P_\mathrmjet$ follows the above scaling relation but with a smaller coefficient. The ratio of coefficients is model dependent and varies from 0.15 to 0.83. This is likely because the force-free region is restricted to a cone around the poles of the black hole, and the width of the cone varies by model. Indeed, the coefficient is larger for MAD than for SANE models, which is consistent with this idea because MAD models have a wide funnel and SANE models have a narrow funnel. This also suggests that future comparison of synthetic 43 and 86 GHz images from our models with lower-frequency VLBI data may further constrain the magnetic flux on the black hole.

The connection between the Poynting flux in the funnel and black hole spin has been discussed for some time in the simulation literature, beginning with McKinney & Gammie (2004 ; see also McKinney 2006 ; McKinney & Narayan 2007). The structure of the funnel magnetic field can be time-averaged and shown to match the analytic solution of Blandford & Znajek (1977). Furthermore, the energy flux density can be time-averaged and traced back to the event horizon. Is the energy contained in black hole spin sufficient to drive the observed jet over the jet lifetime ? The spindown timescale is $\tau =(M-M_\mathrmirr)c^2/P_\mathrmjet$, where $M_\mathrmirr\equiv M\left(\left(1+\sqrt1-a_* ^2\right)/2\right)^1/2$ is the irreducible mass of the black hole. For the $a_* =0.94$ MAD model with $R_\mathrmhigh=160$, $\tau =7.3\times 10^12\,\mathrmyr$, which is long compared to a Hubble time ($\sim 10^10$ yr). Indeed, the spindown time for all models is long compared to the Hubble time.

We conclude that for models that have sufficiently powerful jets and are consistent with EHT2017, $P_\mathrmjet$ is driven by extraction of black hole spin energy through the Blandford–Znajek process.
6.4. Constraint Summary

We have applied constraints from AIS, a radiative self-consistency constraint, a constraint on maximum X-ray luminosity, and a constraint on minimum jet power. Which models survive ? Here we consider only models for which we have calculated $L_\rmX
$ and $L_\mathrmbol$. Table 2 summarizes the results. Here we consider only i = 163° (for $a_* \geqslant 0$) and i = 17° (for $a_* \lt 0$). The first three columns give the model parameters. The next four columns show the result of application of each constraint : Themis-AIS (here broken out by individual model rather than groups of models), radiative efficiency ($\epsilon \lt \epsilon _\mathrmthin\mathrmdisk$), $L_\rmX
$, and $P_\mathrmjet$.

Table 2. Rejection Table
Fluxa $a_* $ b $R_\mathrmhigh$ c AISd epsilone $L_\rmX
$ f $P_\mathrmjet$ g
SANE −0.94 1 Fail Pass Pass Pass Fail
SANE −0.94 10 Pass Pass Pass Pass Pass
SANE −0.94 20 Pass Pass Pass Pass Pass
SANE −0.94 40 Pass Pass Pass Pass Pass
SANE −0.94 80 Pass Pass Pass Pass Pass
SANE −0.94 160 Fail Pass Pass Pass Fail
SANE −0.5 1 Pass Pass Fail Fail Fail
SANE −0.5 10 Pass Pass Fail Fail Fail
SANE −0.5 20 Pass Pass Pass Fail Fail
SANE −0.5 40 Pass Pass Pass Fail Fail
SANE −0.5 80 Fail Pass Pass Fail Fail
SANE −0.5 160 Pass Pass Pass Fail Fail
SANE 0 1 Pass Pass Pass Fail Fail
SANE 0 10 Pass Pass Pass Fail Fail
SANE 0 20 Pass Pass Fail Fail Fail
SANE 0 40 Pass Pass Pass Fail Fail
SANE 0 80 Pass Pass Pass Fail Fail
SANE 0 160 Pass Pass Pass Fail Fail
SANE +0.5 1 Pass Pass Pass Fail Fail
SANE +0.5 10 Pass Pass Pass Fail Fail
SANE +0.5 20 Pass Pass Pass Fail Fail
SANE +0.5 40 Pass Pass Pass Fail Fail
SANE +0.5 80 Pass Pass Pass Fail Fail
SANE +0.5 160 Pass Pass Pass Fail Fail
SANE +0.94 1 Pass Fail Pass Fail Fail
SANE +0.94 10 Pass Fail Pass Fail Fail
SANE +0.94 20 Pass Pass Pass Fail Fail
SANE +0.94 40 Pass Pass Pass Fail Fail
SANE +0.94 80 Pass Pass Pass Pass Pass
SANE +0.94 160 Pass Pass Pass Pass Pass
MAD −0.94 1 Fail Fail Pass Pass Fail
MAD −0.94 10 Fail Pass Pass Pass Fail
MAD −0.94 20 Fail Pass Pass Pass Fail
MAD −0.94 40 Fail Pass Pass Pass Fail
MAD −0.94 80 Fail Pass Pass Pass Fail
MAD −0.94 160 Fail Pass Pass Pass Fail
MAD −0.5 1 Pass Fail Pass Fail Fail
MAD −0.5 10 Pass Pass Pass Fail Fail
MAD −0.5 20 Pass Pass Pass Pass Pass
MAD −0.5 40 Pass Pass Pass Pass Pass
MAD −0.5 80 Pass Pass Pass Pass Pass
MAD −0.5 160 Pass Pass Pass Pass Pass
MAD 0 1 Pass Fail Pass Fail Fail
MAD 0 10 Pass Pass Pass Fail Fail
MAD 0 20 Pass Pass Pass Fail Fail
MAD 0 40 Pass Pass Pass Fail Fail
MAD 0 80 Pass Pass Pass Fail Fail
MAD 0 160 Pass Pass Pass Fail Fail
MAD +0.5 1 Pass Fail Pass Fail Fail
MAD +0.5 10 Pass Pass Pass Pass Pass
MAD +0.5 20 Pass Pass Pass Pass Pass
MAD +0.5 40 Pass Pass Pass Pass Pass
MAD +0.5 80 Pass Pass Pass Pass Pass
MAD +0.5 160 Pass Pass Pass Pass Pass
MAD +0.94 1 Pass Fail Fail Pass Fail
MAD +0.94 10 Pass Fail Pass Pass Fail
MAD +0.94 20 Pass Pass Pass Pass Pass
MAD +0.94 40 Pass Pass Pass Pass Pass
MAD +0.94 80 Pass Pass Pass Pass Pass
MAD +0.94 160 Pass Pass Pass Pass Pass

Notes.
aflux : net magnetic flux on the black hole (MAD, SANE). b $a_* $ : dimensionless black hole spin. c $R_\mathrmhigh$ : electron temperature parameter. See Equation (8). dAverage Image Scoring (Themis-AIS), models are rejected if $\langle p\rangle \leqslant 0.01$. See Section 4 and Table 1. eepsilon : radiative efficiency, models are rejected if epsilon is larger than the corresponding thin disk efficiency. See Section 6.1. f $L_\rmX

$ : X-ray luminosity ; models are rejected if $\langle L_\rmX

\rangle 10^-2\sigma \gt 4.4\times 10^40\,\,\mathrmerg\,\rms

^-1$. See Section 6.2. g $P_\mathrmjet$ : jet power, models are rejected if $P_\mathrmjet\leqslant 10^42\,\,\mathrmerg\,\rms

^-1$. See Section 6.3.

Download table as : ASCIITypeset image

The final column gives the logical AND of the previous four columns, and allows a model to pass only if it passes all tests. Evidently most of the SANE models fail, with the exception of some $a_* =-0.94$ models and a few $a_* =0.94$ models with large $R_\mathrmhigh$. A much larger fraction of the MAD models pass, although $a_* =0$ models all fail because of inadequate jet power. MAD models with small $R_\mathrmhigh$ also fail. It is the jet power constraint that rejects the largest number of models.
7. Discussion

We have interpreted the EHT2017 data using a limited library of models with attendant limitations. Many of the limitations stem from the GRMHD model, which treats the plasma as an ideal fluid governed by equations that encode conservation laws for particle number, momentum, and energy. The eDF, in particular, is described by a number density and temperature, rather than a full distribution function, and the electron temperature Te is assumed to be a function of the local ion temperature and plasma $\beta _\rmp

$. Furthermore, all models assume a Kerr black hole spacetime, but there are alternatives. Here we consider some of the model limitations and possible extensions, including to models beyond general relativity.
7.1. Radiative Effects
Post-processed GRMHD simulations that are consistent with EHT data and the flux density of 1.3 mm emission in M87 can yield unphysically large radiative efficiencies (see Section 6). This implies that the radiative cooling timescale is comparable to or less than the advection timescale. As a consequence, including radiative cooling in simulations may be necessary to recover self-consistent models (see Mościbrodzka et al. 2011 ; Dibi et al. 2012). In our models we use a single parameter, $R_\mathrmhigh$, to adjust Te and account for all effects that might influence the electron energy density. How good is this approximation ?

The importance of radiative cooling can be assessed using newly developed, state-of-the-art general relativistic radiation GRMHD ('''radiation GRMHD''') codes. Sa̧dowski et al. (2013b ; see also Sa̧dowski et al. 2014, 2017 ; McKinney et al. 2014) applied the M1 closure (Levermore 1984), which treats the radiation as a relativistic fluid. Ryan et al. (2015) introduced a Monte Carlo radiation GRMHD method, allowing for full frequency-dependent radiation transport. Models for turbulent dissipation into the electrons and ions, as well as heating and cooling physics that sets the temperature ratio Ti/Te, have been added to GRMHD and radiative GRMHD codes and used in simulations of Sgr A* (Ressler et al. 2015, 2017 ; Chael et al. 2018) and M87 (Ryan et al. 2018 ; Chael et al. 2019). While the radiative cooling and Coulomb coupling physics in these simulations is well understood, the particle heating process, especially the relative heating rates of ions and electrons, remains uncertain.

Radiation GRMHD models are computationally expensive per run and do not have the same scaling freedom as the GRMHD models, so they need to be repeatedly re-run with different initial conditions until they produce the correct 1.3 mm flux density. It is therefore impractical to survey the parameter space using radiation GRMHD. It is possible, however, to check individual GRMHD models against existing radiation GRMHD models of M87 (Ryan et al. 2018 ; Chael et al. 2019).

The SANE radiation GRMHD models of Ryan et al. (2018) with $a_* =0.94$ and $M=6\times 10^9\,M_\odot $ can be compared to GRMHD SANE $a_* =0.94$ models at various values of $R_\mathrmhigh$. The radiative models have $\dotM/\dotM_\mathrmEdd=5.2\times 10^-6$ and $P_\mathrmjet\,=5.1\times 10^41\,\mathrmerg\,\rms
^-1$. The GRMHD models in this work have, for $1\leqslant R_\mathrmhigh\leqslant 160$, $0.36\times 10^-6\leqslant \dotM/\dotM_\mathrmEdd\leqslant 20\times 10^-6$, and $0.22\leqslant P_\mathrmjet/(10^41\,\,\mathrmerg\,\rms
^-1)\leqslant 12$ (Table 3). Evidently the mass accretion rates and jet powers in the GRMHD models span a wide range that depends on $R_\mathrmhigh$, but when we choose $R_\mathrmhigh$ = 10 − 20 they are similar to what is found in the radiative GRMHD model when using the turbulent electron heating model (Howes 2010).

Table 3. Model Table
Flux phgr Spin $R_\mathrmhigh$ $L_\mathrmbol/\left(\dotM\,c^2\right)$ $L_\rmX
$ (cgs) $P_\mathrmjet$ (cgs) $P_\mathrmjet/\left(\dotM\,c^2\right)$ $P_\mathrmout$ (cgs) $P_\mathrmout/\left(\dotM\,c^2\right)$ $P_\mathrmjet,\mathrmem/P_\mathrmjet$ $\dotM/\dotM_\mathrmEdd$
SANE 1.02 −0.94 1 1.27 × 10−2 $3.18_\gt 0.20^\lt 49.55\times 10^41$ 1.16 × 1042 5.34 × 10−3 1.19 × 1042 5.48 × 10−3 0.84 2.77 × 10−5
SANE 1.02 −0.94 10 1.6 × 10−3 $9.62_\gt 1.44^\lt 64.42\times 10^40$ 4.94 × 1042 5.34 × 10−3 5.07 × 1042 5.48 × 10−3 0.84 1.19 × 10−4
SANE 1.02 −0.94 20 6.09 × 10−4 $3.26_\gt 0.90^\lt 11.86\times 10^40$ 5.8 × 1042 5.34 × 10−3 5.96 × 1042 5.48 × 10−3 0.84 1.39 × 10−4
SANE 1.02 −0.94 40 2.45 × 10−4 $8.89_\gt 1.56^\lt 50.53\times 10^39$ 7.02 × 1042 5.34 × 10−3 7.21 × 1042 5.48 × 10−3 0.84 1.69 × 10−4
SANE 1.02 −0.94 80 1.33 × 10−4 $2.65_\gt 0.39^\lt 18.26\times 10^39$ 8.89 × 1042 5.34 × 10−3 9.13 × 1042 5.48 × 10−3 0.84 2.13 × 10−4
SANE 1.02 −0.94 160 7.12 × 10−5 $6.36_\gt 0.73^\lt 55.27\times 10^38$ 1.2 × 1043 5.34 × 10−3 1.23 × 1043 5.48 × 10−3 0.84 2.87 × 10−4
SANE 1.11 −0.5 1 1.62 × 10−2 $1.97_\gt 0.98^\lt 3.94\times 10^41$ 2.62 × 1040 1.86 × 10−4 3.84 × 1040 2.72 × 10−4 0.88 1.81 × 10−5
SANE 1.11 −0.5 10 2.17 × 10−3 $1.94_\gt 0.69^\lt 5.40\times 10^41$ 1.95 × 1041 1.86 × 10−4 2.85 × 1041 2.72 × 10−4 0.88 1.34 × 10−4
SANE 1.11 −0.5 20 6.69 × 10−4 $3.72_\gt 1.80^\lt 7.72\times 10^40$ 2.26 × 1041 1.86 × 10−4 3.31 × 1041 2.72 × 10−4 0.88 1.56 × 10−4
SANE 1.11 −0.5 40 2.47 × 10−4 $9.44_\gt 6.67^\lt 13.37\times 10^39$ 2.62 × 1041 1.86 × 10−4 3.83 × 1041 2.72 × 10−4 0.88 1.81 × 10−4
SANE 1.11 −0.5 80 1.26 × 10−4 $1.23_\gt 0.33^\lt 4.58\times 10^39$ 3.2 × 1041 1.86 × 10−4 4.68 × 1041 2.72 × 10−4 0.88 2.21 × 10−4
SANE 1.11 −0.5 160 7.86 × 10−5 $3.72_\gt 0.83^\lt 16.68\times 10^38$ 4.21 × 1041 1.86 × 10−4 6.16 × 1041 2.72 × 10−4 0.88 2.9 × 10−4
SANE 0.99 0 1 3.17 × 10−2 $2.08_\gt 0.02^\lt 194.22\times 10^41$ 2.24 × 1036 4.4 × 10−8 5.22 × 1039 1.03 × 10−4 1.01 6.5 × 10−6
SANE 0.99 0 10 1.88 × 10−2 $4.2_\gt 0.04^\lt 425.40\times 10^42$ 4.38 × 1037 4.4 × 10−8 1.02 × 1041 1.03 × 10−4 1.01 1.27 × 10−4
SANE 0.99 0 20 5.83 × 10−3 $1.57_\gt 0.06^\lt 39.69\times 10^42$ 8.02 × 1037 4.4 × 10−8 1.87 × 1041 1.03 × 10−4 1.01 2.33 × 10−4
SANE 0.99 0 40 7.8 × 10−4 $8.92_\gt 1.92^\lt 41.45\times 10^40$ 9.16 × 1037 4.4 × 10−8 2.14 × 1041 1.03 × 10−4 1.01 2.66 × 10−4
SANE 0.99 0 80 1.69 × 10−4 $2.5_\gt 0.33^\lt 19.17\times 10^39$ 1.03 × 1038 4.4 × 10−8 2.41 × 1041 1.03 × 10−4 1.01 3 × 10−4
SANE 0.99 0 160 1.08 × 10−4 $3.44_\gt 0.89^\lt 13.32\times 10^38$ 1.23 × 1038 4.4 × 10−8 2.87 × 1041 1.03 × 10−4 1.01 3.57 × 10−4
SANE 1.10 0.5 1 4.97 × 10−2 $5.5_\gt 0.88^\lt 34.41\times 10^40$ 2.57 × 1039 1.63 × 10−4 9.19 × 1039 5.86 × 10−4 0.88 2.01 × 10−6
SANE 1.10 0.5 10 5.98 × 10−3 $4.73_\gt 0.25^\lt 88.59\times 10^40$ 1.91 × 1040 1.64 × 10−4 6.84 × 1040 5.86 × 10−4 0.88 1.5 × 10−5
SANE 1.10 0.5 20 3.33 × 10−3 $3.83_\gt 0.30^\lt 49.18\times 10^40$ 4.09 × 1040 1.64 × 10−4 1.47 × 1041 5.86 × 10−4 0.88 3.2 × 10−5
SANE 1.10 0.5 40 1.74 × 10−3 $2.52_\gt 0.28^\lt 22.73\times 10^40$ 8.02 × 1040 1.64 × 10−4 2.87 × 1041 5.86 × 10−4 0.88 6.28 × 10−5
SANE 1.10 0.5 80 6.95 × 10−4 $7.84_\gt 0.67^\lt 91.92\times 10^39$ 1.27 × 1041 1.64 × 10−4 4.55 × 1041 5.86 × 10−4 0.88 9.95 × 10−5
SANE 1.10 0.5 160 2.78 × 10−4 $1.37_\gt 0.08^\lt 22.85\times 10^39$ 1.69 × 1041 1.63 × 10−4 6.06 × 1041 5.86 × 10−4 0.88 1.33 × 10−4
SANE 1.64 0.94 1 1.4 $2.38_\gt 0.02^\lt 359.03\times 10^41$ 2.2 × 1040 7.76 × 10−3 3.38 × 1040 1.19 × 10−2 0.82 3.63 × 10−7
SANE 1.64 0.94 10 2.7 × 10−1 $2.79_\gt 0.02^\lt 508.99\times 10^41$ 1.4 × 1041 7.76 × 10−3 2.15 × 1041 1.19 × 10−2 0.82 2.31 × 10−6
SANE 1.64 0.94 20 1.74 × 10−1 $5.75_\gt 0.02^\lt 1685.98\times 10^41$ 3.22 × 1041 7.76 × 10−3 4.94 × 1041 1.19 × 10−2 0.82 5.31 × 10−6
SANE 1.64 0.94 40 7.2 × 10−2 $4.71_\gt 0.01^\lt 2490.36\times 10^41$ 5.97 × 1041 7.76 × 10−3 9.17 × 1041 1.19 × 10−2 0.82 9.84 × 10−6
SANE 1.64 0.94 80 2.38 × 10−2 $1.42_\gt 0.00^\lt 860.83\times 10^41$ 8.87 × 1041 7.76 × 10−3 1.36 × 1042 1.19 × 10−2 0.82 1.46 × 10−5
SANE 1.64 0.94 160 8.45 × 10−3 $3.22_\gt 0.01^\lt 1687.88\times 10^40$ 1.23 × 1042 7.76 × 10−3 1.89 × 1042 1.19 × 10−2 0.82 2.03 × 10−5
MAD 8.04 −0.94 1 7.61 × 10−1 $2.12_\gt 0.25^\lt 17.74\times 10^41$ 1.36 × 1042 2.09 × 10−1 1.6 × 1042 2.46 × 10−1 0.75 8.32 × 10−7
MAD 8.04 −0.94 10 7.54 × 10−2 $5.76_\gt 0.49^\lt 68.06\times 10^40$ 1.97 × 1042 2.09 × 10−1 2.32 × 1042 2.46 × 10−1 0.75 1.21 × 10−6
MAD 8.04 −0.94 20 3.76 × 10−2 $2.27_\gt 0.18^\lt 29.09\times 10^40$ 2.38 × 1042 2.09 × 10−1 2.8 × 1042 2.46 × 10−1 0.75 1.46 × 10−6
MAD 8.04 −0.94 40 2.07 × 10−2 $6.18_\gt 0.49^\lt 77.36\times 10^39$ 3 × 1042 2.09 × 10−1 3.54 × 1042 2.46 × 10−1 0.75 1.84 × 10−6
MAD 8.04 −0.94 80 1.17 × 10−2 $1.32_\gt 0.07^\lt 26.36\times 10^39$ 3.99 × 1042 2.09 × 10−1 4.71 × 1042 2.46 × 10−1 0.75 2.45 × 10−6
MAD 8.04 −0.94 160 6.52 × 10−3 $2.57_\gt 0.14^\lt 46.76\times 10^38$ 5.7 × 1042 2.09 × 10−1 6.73 × 1042 2.46 × 10−1 0.75 3.5 × 10−6
MAD 12.25 −0.5 1 2.96 × 10−1 $1.39_\gt 0.17^\lt 11.56\times 10^41$ 3.43 × 1041 4.91 × 10−2 6.04 × 1041 8.64 × 10−2 0.82 8.95 × 10−7
MAD 12.25 −0.5 10 4.53 × 10−2 $2.43_\gt 0.30^\lt 19.86\times 10^40$ 5.31 × 1041 4.92 × 10−2 9.33 × 1041 8.64 × 10−2 0.82 1.38 × 10−6
MAD 12.25 −0.5 20 2.67 × 10−2 $8.18_\gt 0.86^\lt 77.51\times 10^39$ 6.45 × 1041 4.92 × 10−2 1.13 × 1042 8.64 × 10−2 0.82 1.68 × 10−6
MAD 12.25 −0.5 40 1.69 × 10−2 $2.17_\gt 0.21^\lt 22.33\times 10^39$ 8.07 × 1041 4.92 × 10−2 1.42 × 1042 8.64 × 10−2 0.82 2.1 × 10−6
MAD 12.25 −0.5 80 1.07 × 10−2 $4.87_\gt 0.47^\lt 50.76\times 10^38$ 1.05 × 1042 4.92 × 10−2 1.85 × 1042 8.64 × 10−2 0.82 2.74 × 10−6
MAD 12.25 −0.5 160 6.43 × 10−3 $1.09_\gt 0.17^\lt 7.06\times 10^38$ 1.46 × 1042 4.92 × 10−2 2.57 × 1042 8.64 × 10−2 0.82 3.81 × 10−6
MAD 15.44 0 1 2.67 × 10−1 $1.22_\gt 0.10^\lt 14.60\times 10^41$ 0.0 0.0 8.39 × 1040 1.51 × 10−2 0.00 7.12 × 10−7
MAD 15.44 0 10 4.53 × 10−2 $1.86_\gt 0.11^\lt 31.55\times 10^40$ 0.0 0.0 1.39 × 1041 1.51 × 10−2 0.00 1.18 × 10−6
MAD 15.44 0 20 2.81 × 10−2 $5.98_\gt 0.35^\lt 101.81\times 10^39$ 0.0 0.0 1.71 × 1041 1.51 × 10−2 0.00 1.46 × 10−6
MAD 15.44 0 40 1.85 × 10−2 $1.63_\gt 0.10^\lt 27.75\times 10^39$ 0.0 0.0 2.15 × 1041 1.51 × 10−2 0.00 1.82 × 10−6
MAD 15.44 0 80 1.21 × 10−2 $3.51_\gt 0.20^\lt 61.34\times 10^38$ 0.0 0.0 2.77 × 1041 1.51 × 10−2 0.00 2.35 × 10−6
MAD 15.44 0 160 7.63 × 10−3 $8.06_\gt 0.81^\lt 80.62\times 10^37$ 0.0 0.0 3.73 × 1041 1.51 × 10−2 0.00 3.17 × 10−6
MAD 15.95 0.5 1 5.45 × 10−1 $1.57_\gt 0.21^\lt 11.98\times 10^41$ 4.64 × 1041 1.16 × 10−1 6.74 × 1041 1.69 × 10−1 0.85 5.11 × 10−7
MAD 15.95 0.5 10 9.45 × 10−2 $2.71_\gt 0.20^\lt 36.30\times 10^40$ 8.07 × 1041 1.16 × 10−1 1.17 × 1042 1.69 × 10−1 0.85 8.89 × 10−7
MAD 15.95 0.5 20 5.54 × 10−2 $9.67_\gt 0.74^\lt 126.69\times 10^39$ 1.02 × 1042 1.16 × 10−1 1.49 × 1042 1.69 × 10−1 0.85 1.13 × 10−6
MAD 15.95 0.5 40 3.5 × 10−2 $3.3_\gt 0.28^\lt 39.01\times 10^39$ 1.32 × 1042 1.16 × 10−1 1.92 × 1042 1.69 × 10−1 0.85 1.45 × 10−6
MAD 15.95 0.5 80 2.22 × 10−2 $8_\gt 0.70^\lt 91.84\times 10^38$ 1.74 × 1042 1.16 × 10−1 2.52 × 1042 1.69 × 10−1 0.85 1.92 × 10−6
MAD 15.95 0.5 160 1.35 × 10−2 $1.79_\gt 0.38^\lt 8.44\times 10^38$ 2.38 × 1042 1.16 × 10−1 3.46 × 1042 1.69 × 10−1 0.85 2.62 × 10−6
MAD 12.78 0.94 1 3.65 $5.19_\gt 0.62^\lt 43.60\times 10^41$ 1.97 × 1042 8.23 × 10−1 2.29 × 1042 9.55 × 10−1 0.80 3.07 × 10−7
MAD 12.78 0.94 10 3.68 × 10−1 $1.3_\gt 0.13^\lt 13.22\times 10^41$ 3.04 × 1042 8.23 × 10−1 3.52 × 1042 9.55 × 10−1 0.80 4.73 × 10−7
MAD 12.78 0.94 20 1.79 × 10−1 $5_\gt 0.44^\lt 56.22\times 10^40$ 3.73 × 1042 8.23 × 10−1 4.33 × 1042 9.55 × 10−1 0.80 5.81 × 10−7
MAD 12.78 0.94 40 9.43 × 10−2 $1.54_\gt 0.11^\lt 22.13\times 10^40$ 4.74 × 1042 8.23 × 10−1 5.5 × 1042 9.55 × 10−1 0.80 7.38 × 10−7
MAD 12.78 0.94 80 5.19 × 10−2 $3.74_\gt 0.17^\lt 80.85\times 10^39$ 6.26 × 1042 8.23 × 10−1 7.27 × 1042 9.55 × 10−1 0.80 9.75 × 10−7
MAD 12.78 0.94 160 2.82 × 10−2 $6.97_\gt 0.26^\lt 186.48\times 10^38$ 8.75 × 1042 8.23 × 10−1 1.02 × 1043 9.55 × 10−1 0.80 1.36 × 10−6

Download table as : ASCIITypeset images : 1 2

We have also directly compared the Te distribution in the emitting region, and the radiation GRMHD model is quite close to the $R_\mathrmhigh=10$ model. The resulting images are qualitatively similar, with an asymmetric photon ring that is brighter in the south and a weak inner ring associated with the funnel wall emission as in Figure 2. The radiation GRMHD SANE model, like all our nonradiative GRMHD SANE models (except the $R_\mathrmhigh=160$ model), would be ruled out by the condition $P_\mathrmjet\gt 10^42\,\mathrmerg\,\rms

^-1$.
The MAD radiation GRMHD models of Chael et al. (2019) with $a_* =0.94$ and $M=6.2\times 10^9M_\odot $ can be compared to GRMHD MAD $a_* =0.94$ models at various values of $R_\mathrmhigh$. Chael et al. (2019) uses two dissipation models : the Howes (2010, hereafter H10) model of heating from a Landau-damped turbulent cascade, and the Rowan et al. (2017, hereafter R17) model of heating based on simulations of transrelativistic magnetic reconnection. The (H10, R17) models have $\dotM/\dotM_\mathrmEdd=(3.6,2.3)\times 10^-6$ and $P_\mathrmjet=(6.6,13)\,\times 10^42\,\mathrmerg\,\rms
^-1$. The GRMHD models have, for $1\leqslant R_\mathrmhigh\,\leqslant 160$, $0.13\times 10^-6\leqslant \dotM/\dotM_\mathrmEdd\leqslant 1.4\times 10^-6$ and $2.3\leqslant P_\mathrmjet/(10^42\,\,\mathrmerg\,\rms
^-1)\leqslant 8.8$ (Table 3). In the radiation GRMHD MAD models $\dotM$ lies in the middle of the range spanned by the nonradiative GRMHD models, and jet power lies at the upper end of the range spanned by the nonradiative GRMHD models. The Te distributions in the radiative and nonradiative MAD models differ : the mode of the radiation GRMHD model Te distribution is about a factor of 3 below the mode of the Te distribution in the $R_\mathrmhigh=20$ GRMHD model, and the GRMHD model has many more zones at $\rm\Theta
_e\sim 100$ that contribute to the final image than the radiation GRMHD models. This difference is a consequence of the $R_\mathrmhigh$ model for Te : in MAD models almost all the emission emerges at $\beta _\rmp
\lesssim 1$, so $R_\mathrmhigh$, which changes Te in the $\beta _\rmp

\gt 1$ region, offers little control over Te in the emission region. Nevertheless, the jet power and accretion rates are similar in the radiative and nonradiative MAD models, and the time-averaged radiative and nonradiative images are qualitatively indistinguishable. This suggests that the image is determined mainly by the spacetime geometry and is insensitive to the details of the plasma evolution.

This review of radiative effects is encouraging but incomplete : it only considers a limited selection of models and a narrow set of observational constraints. Future studies of time dependence and polarization are likely to sharpen the contrast between radiative and nonradiative models.
7.2. Nonthermal Electrons

Throughout this Letter we have considered only a thermal eDF. While a thermal eDF can account for the observed emission at mm wavelengths in M87 (e.g., Mościbrodzka et al. 2016 ; Prieto et al. 2016 ; Ryan et al. 2018 ; Chael et al. 2019), eDFs that include a nonthermal tail can also explain the observed SED (Broderick & Loeb 2009 ; Yu et al. 2011 ; Dexter et al. 2012 ; Li et al. 2016 ; Davelaar et al. 2018 ; J. Davelaar et al. 2019, in preparation).

The role of nonthermal electrons (and positrons) in producing the observed compact emission is not a settled question, and cannot be settled in this first investigation of EHT2017 models, but there are constraints. The number density, mean velocity, and energy density of the eDF are fixed or limited by the GRMHD models. In addition, the eDF cannot on average sustain features that would be erased by kinetic instabilities on timescales short compared to $r_\rmg

c^-1$. Some nonthermal eDFs increase $F_\nu /\dotM$ in comparison to a thermal eDF, implying lower values of $\dotM$ than quoted above (Ball et al. 2018 ; Davelaar et al. 2018 ; J. Davelaar et al. 2019, in preparation). These lower values of $\dotM$ can slightly change the source morphology, e.g., by decreasing the visibility of the approaching jet (e.g., Dexter et al. 2012).

One can evaluate the influence of nonthermal eDFs in several ways. For example, it is possible to study simplified, phenomenological models. Emission features due to the cooling of nonthermal electrons may then reveal how and where the nonthermal electrons are produced (Pu et al. 2017). Emission features created by the injection of nonthermal electrons within GRMHD models of the jet and their subsequent cooling will be studied separately (T. Kawashima et al. 2019, in preparation). The effect of nonthermal eDFs can also be studied by post-processing of ideal GRMHD models if one assumes that the electrons have a fixed, parameterized form such as a power-law distribution (Dexter et al. 2012) or a κ-distribution (Davelaar et al. 2018 ; J. Davelaar et al. 2019, in preparation). These parameterized models produce SEDs that agree with radio to near-infrared data, but they are approximations to the underlying physics and do not resolve the microscopic processes that accelerate particles. One can also include dissipative processes explicitly in the GRMHD models, including scalar resistivity (Palenzuela et al. 2009 ; Dionysopoulou et al. 2013 ; Del Zanna et al. 2016 ; Qian et al. 2017 ; Ripperda et al. 2019), heat fluxes and viscosities (pressure anisotropies ; Chandra et al. 2015 ; Ressler et al. 2015 ; Foucart et al. 2017), and particle acceleration (e.g., Chael et al. 2017). Ultimately special and general relativistic particle-in-cell codes (Watson & Nishikawa 2010 ; Chen et al. 2018 ; Levinson & Cerutti 2018 ; Parfrey et al. 2019) will enable direct investigations of kinetic processes.
7.3. Other Models and Analysis Limitations

We have used a number of other approximations in generating our models. Among the most serious ones are as follows.

(1) Fast Light Approximation. A GRMHD simulation produces a set of dump files containing the model state at a single global (Kerr–Schild) coordinate time. Because the dynamical time is only slightly longer than the light-crossing time, in principle one needs to trace rays through a range of coordinate times, i.e., by interpolation between multiple closely spaced dump files. In practice this is difficult because a high cadence of output files is required, limiting the speed of the GRMHD simulations and requiring prohibitively large data storage. In addition, the cost of ray tracing through multiple output files is high. Because of this, we adopt the commonly used fast light approximation in which GRMHD variables are read from a single dump file and held steady during the ray tracing. Including light-travel time delays produces minor changes to the small-scale image structure and to light curves (e.g., Dexter et al. 2010 ; Bronzwaer et al. 2018 ; Z. Younsi et al. 2019b, in preparation), although it is essential for the study of variability on the light-crossing timescale.

(2) Untilted Disks. We have assumed that the disk angular momentum vector and black hole spin vector are (anti-) aligned. There is no reason for the angular momentum vector of the accretion flow on large scales to align with the black hole spin vector, and there is abundant evidence for misaligned disks in AGNs (e.g., Miyoshi et al. 1995). How might disk tilt affect our results ?

Tilting the disk by as little as 15° is enough to set up a standing, two-armed spiral shock close to the ISCO (Fragile & Blaes 2008). This shock directly affects the morphology of mm wavelength images, especially at low inclination, in models of Sgr A* (Dexter & Fragile 2013, especially Figure 5), producing an obvious two-armed spiral pattern on the sky. If this structure were also present in images of tilted models of M87, then it is possible that even a modest tilt could be ruled out.

If a modest tilt is present in M87 it is unlikely to affect our conclusion regarding the sign of black hole spin. That conclusion depends on emission from funnel wall plasma in counter-rotating ($a_* \lt 0$) disks. The funnel wall plasma is loaded onto funnel plasma field lines by local instabilities at the wall and then rotates with the funnel and therefore the black hole (Wong et al. 2019). The funnel wall is already unsteady, fluctuating by tens of degrees in azimuth and in time, so a modest tilt seems unlikely to dramatically alter the funnel wall structure.

Is there observational evidence for tilt in M87 ? In numerical studies of tilted disks the jet emerges perpendicular to the disk (Liska et al. 2018), and tilted disks are expected to precess. One might then expect that a tilted source would produce a jet that exhibits periodic variations, or periodic changes in jet direction with distance from the source, as seen in other sources. There is little evidence of this in M87 (see Park et al. 2019 for a discussion of possible misaligned structure in the jet). Indeed, Walker et al. (2018) saw at most small displacements of the jet with time and distance from the source at mas scales. In sum, there is therefore little observational motivation for considering tilted disk models.

Tilted disk models of M87 are an interesting area for future study. It is possible that the inner disk may align with the black hole via a thick-disk variant of the Bardeen & Petterson (1975) effect. Existing tilted thick-disk GRMHD simulations (e.g., Fragile et al. 2007 ; McKinney et al. 2013 ; Shiokawa 2013 ; Liska et al. 2018) show some evidence for alignment and precession (McKinney et al. 2013 ; Shiokawa 2013 ; Liska et al. 2018), but understanding of the precession and alignment timescales is incomplete. It will be challenging to extend the Image Library to include a survey of tilted disk models, however, because with tilted disks there are two new parameters : the two angles that describe the orientation of the outer disk with respect to the black hole spin vector and the line of sight.

(3) Pair Production. In some models of M87 the mm emission is dominated by electron-positron pairs within the funnel, even close to the horizon scale (see Beskin et al. 1992 ; Levinson & Rieger 2011 ; Mościbrodzka et al. 2011 ; Broderick & Tchekhovskoy 2015 ; Hirotani & Pu 2016). The pairs are produced from the background radiation field or from a pair-cascade process following particle acceleration by unscreened electric fields, which we cannot evaluate using ideal GRMHD models. We leave it to future work to assess whether or not these models can plausibly suppress emission from the disk and funnel wall, and simultaneously produce a sufficiently powerful jet.

(4) Numerical Treatment of Low-density Regions. Virtually all MHD simulations, including ours, use a '''floor''' procedure that resets the density if it falls below a minimum value. If this is not done, then truncation error accumulates dramatically in the low-density regions and the solution is corrupted. If the volume where floors are activated contains only a small fraction of the simulation mass, momentum, and energy, then most aspects of the solution are unaffected by this procedure (e.g., McKinney & Gammie 2004).
In regions where the floors are activated the temperature of the plasma is no longer reliable. This is why we cut off emission from regions with $B^2/\rho \gt 1$, where floors are commonly activated. In models where floors are only activated in the funnel (e.g., most SANE models), the resulting images are insensitive to the choice of cutoff $B^2/\rho $. In MAD models the regions of low and high density are mixed because lightly loaded magnetic field lines that are trapped in the hole bubbles outward through the disk. In this case emission at $\nu \,\gt 230$ GHz can be sensitive to the choice of cutoff $B^2/\rho $ Chael et al. (2019). The sense of the effect is that greater cutoff $B^2/\rho $ implies more emission at high frequency. Our use of a cutoff $B^2/\rho =1$ is therefore likely to underestimate mm emission and therefore overestimate $\dotM$ and $P_\mathrmjet$. Accurate treatment of the dynamics and thermodynamics of low-density regions and especially sharp boundaries between low- and high-density regions is a fundamental numerical problem in black hole accretion flow modeling that merits further attention.
7.4. Alternatives to Kerr Black Holes

Although our working hypothesis has been that M87 contains a Kerr black hole, it is interesting to consider whether or not the data is also consistent with alternative models for the central object. These alternatives can be grouped into three main categories : (i) black holes within general relativity that include additional fields ; (ii) black hole solutions from alternative theories of gravity or incorporating quantum effects ; (iii) black hole '''mimickers,''' i.e., compact objects, both within general relativity or in alternative theories, whose properties could be fine-tuned to resemble those of black holes.

The first category includes, for example, black holes in Einstein–Maxwell–dilaton-axion gravity (e.g., García et al. 1995 ; Mizuno et al. 2018), black holes with electromagnetic or Newman–Unti-Tamburino (NUT) charges (e.g., Grenzebach et al. 2014), regular black holes in nonlinear electrodynamics (e.g., Abdujabbarov et al. 2016), black hole metrics affected by a cosmological constant (e.g., Dymnikova 1992) or a dark matter halo (e.g., Hou et al. 2018), and black holes with scalar wigs (e.g., Barranco et al. 2017) or hair (e.g., Herdeiro & Radu 2014). While the shadows of this class of compact objects are expected to be similar to Kerr and therefore cannot be ruled out immediately by current observations (Mizuno et al. 2018), the most extreme examples of black holes surrounded by massive scalar field configurations should produce additional lobes in the shadow or disconnected dark regions (Cunha et al. 2015). As these features are not found in the EHT2017 image, these alternatives are not viable models for M87.

The second category comprises black hole solutions with classical modifications to general relativity, as well as effects coming from approaches to quantum gravity (see, e.g., Moffat 2015 ; Dastan et al. 2016 ; Younsi et al. 2016 ; Amir et al. 2018 ; Eiroa & Sendra 2018 ; Giddings & Psaltis 2018). These alternatives have shadows that are qualitatively very similar to those of Kerr black holes and are not distinguishable with present EHT capabilities. However, higher-frequency observations, together with the degree of polarization of the emitted radiation or the variability of the accretion flow, can be used to assess their viability.

Finally, the third category comprises compact objects such as spherically symmetric naked singularities (e.g., Joshi et al. 2014), superspinars (Kerr with $| a_* | \gt 1$, which are axisymmetric spacetime with naked singularities), and regular horizonless objects, either with or without a surface. Examples of regular surfaceless objects are : boson stars (Kaup 1968), traversable wormholes, and clumps of self-interacting dark matter (Saxton et al. 2016), while examples of black hole mimickers with a surface are gravastars (Mazur & Mottola 2004) and collapsed polymers (Brustein & Medved 2017), to cite only a few. Because the exotic genesis of these black hole mimickers is essentially unknown, their physical properties are essentially unconstrained, thus making the distinction from black holes rather challenging (see, however, Chirenti & Rezzolla 2007, 2016). Nevertheless, some conclusions can drawn already. For instance, the shadow of a superspinar is very different from that of a black hole (Bambi & Freese 2009), and the EHT2017 observations rule out any superspinar model for M87. Similarly, for certain parameter ranges, the shadows of spherically symmetric naked singularities have been found to consist of a filled disk with no dark region120 in the center (Shaikh et al. 2019) ; clearly, this class of models is ruled out. In the same vein, because the shadows of wormholes can exhibit large deviations from those of black holes (see, e.g., Bambi 2013 ; Nedkova et al. 2013 ; Shaikh 2018), a large portion of the corresponding space of parameters can be constrained with the present observations.

A comparison of EHT2017 data with the boson star model, as a representative horizonless and surfaceless black hole mimicker, and a gravastar model as a representative horizonless black hole mimicker, will be presented in Olivares et al. (2019a). Both models produce images with ring-like features similar to those observed by EHT2017, which are consistent with the results of Broderick & Narayan (2006), who also consider black hole alternatives with a surface. The boson star generically requires masses that are substantially different from that expected for M87 (H. Olivares et al. 2019b, in preparation), while the gravastar has accretion variability that is considerably different from that onto a black hole.

In summary, because each of the many exotic alternatives to Kerr black holes can span an enormous space of parameters that is only poorly constrained, the comparisons carried out here must be considered preliminary. Nevertheless, they show that the EHT2017 observations are not consistent with several of the alternatives to Kerr black holes, and that some of those models that produce similar images show rather different dynamics in the accretion flow and in its variability. Future observations and more detailed theoretical modeling, combined with multiwavelength campaigns and polarimetric measurements, will further constrain alternatives to Kerr black holes.
8. Conclusion

In this Letter we have made a first attempt at understanding the physical implications of a single, high-quality EHT data set for M87. We have compared the data to a library of mock images produced from GRMHD simulations by GRRT calculations. The library covers a parameter space that is substantially larger than earlier model surveys. The results of this comparison are consistent with the hypothesis that the compact 1.3 mm emission in M87 arises within a few $r_\rmg

$ of a Kerr black hole, and that the ring-like structure of the image is generated by strong gravitational lensing and Doppler beaming. The models predict that the asymmetry of the image depends on the sense of black hole spin. If this interpretation is accurate, then the spin vector of the black hole in M87 points away from Earth (the black hole spins clockwise on the sky). The models also predict that there is a strong energy flux directed away from the poles of the black hole, and that this energy flux is electromagnetically dominated. If the models are correct, then the central engine for the M87 jet is powered by the electromagnetic extraction of free energy associated with black hole spin via the Blandford–Znajek process.

In our models, M87's compact mm emission is generated by the synchrotron mechanism. Our ability to make physical inferences based on the models is therefore intimately tied to the quality of our understanding of the eDF. We have used a thermal model with a single free parameter that adjusts the ratio of ion to electron temperature in regions with plasma $\beta _\rmp

\gt 1$ (i.e., regions where magnetic pressure is less than gas pressure). This simple model does not span the range of possible plasma behavior. The theory of high temperature, collisionless plasmas must be better understood if this core physical uncertainty of sub-Eddington black hole accretion is to be eliminated. At present our understanding is inadequate, and alternative eDF models occupy a large, difficult-to-explore parameter space with the potential to surprise. Despite these uncertainties, many of the models produce images with similar morphology that is consistent with EHT2017 data. This suggests that the image shape is controlled mainly by gravitational lensing and the spacetime geometry, rather than details of the plasma physics.

Although the EHT2017 images are consistent with the vast majority of our models, parts of the parameter space can be rejected on physical grounds or by comparison with contemporaneous data at other wavelengths. We reject some models because, even though all models are variable, some models are too variable to be consistent with the data. We can also reject models based on a radiative efficiency cut (the models are not self-consistent and would cool quickly if radiative effects were included), an X-ray luminosity cut using contemporaneous Chandra and NuSTAR data, and on a jet-power cut. The requirement that the jet power exceed a conservative lower limit of $10^42\,\mathrmerg\,\rms

^-1$ turns out to eliminate many models, including all models with $a_* =0$.

We have examined the astrophysical implications of only a subset of EHT2017 data ; much remains to be done, and there are significant opportunities for further constraining the models. EHT2017 data includes tracks from four separate days of observing ; each day is $2.8\,r_\rmg

c^-1$ (see Paper IV). This timescale is short compared to the decorrelation timescale of simulated images, which is $\sim 50\,r_\rmg

c^-1$, and smaller than the light-crossing time of the source plasma. Analysis techniques that use short-timescale variations in the data will need to be developed and are likely to recover new, more stringent constraints on the model from the EHT2017 data set. EHT2017 took polarized data as well. Our simulations already predict full polarization maps, albeit for our simple eDF model. Comparison of model polarization maps of the source with EHT2017 data are likely to sharply limit the space of allowed models (Mościbrodzka et al. 2017). Finally, in this Letter the only multiwavelength companion data that we consider are X-ray observations. Simultaneous data are available at many other wavelengths, from the radio to the gamma-rays, and is likely to further limit the range of acceptable models and guide the implementation of predictive electron physics models.

In this Letter we have focused on the time-dependent ideal GRMHD model. Physically motivated, semi-analytic models including nonthermal emission have not been applied yet and will be discussed in future papers (A. E. Broderick et al. 2019b, in preparation ; T. Kawashima et al. 2019, in preparation ; H.-Y. Pu et al. 2019, in preparation).

We have also not yet considered how the physical properties of the jet are constrained by lower-frequency VLBI observations, which constrain jet kinematics (Mertens et al. 2016 ; Britzen et al. 2017 ; Hada et al. 2017 ; Kim et al. 2018 ; Walker et al. 2018), the jet width profile (Asada & Nakamura 2012 ; Hada et al. 2013 ; Nakamura et al. 2018), the total jet power at kilo-parsec scale (Owen et al. 2000 ; Stawarz et al. 2006), the jet power (e.g., Kino et al. 2014, 2015), the core shift (Hada et al. 2011), and the symmetric limb-brightening structure (Takahashi et al. 2018 ; Kim et al. 2018). The jet width profile is potentially very interesting because it depends on the magnetic flux phgr : the jet internal magnetic pressure $\propto \phi ^2$. We therefore expect (and see in our numerical simulations ; see Figure 4) that MAD jets are wider at the base than SANE jets. Future theoretical work will help connect the ring-like structure seen in EHT2017 to the large-scale jet (M. Nakamura et al. 2019, in preparation).

A second epoch of observations ($\gtrsim 50\,r_\rmg

c^-1\sim 2$ weeks after EHT2017, when the models suggest that source structure will decorrelate) will increase the power of the average image analysis to reject models. The EHT2017 data were able to reject one entire category of models with confidence : high magnetic flux (MAD), retrograde, high-spin models. Other categories of models, such as the low magnetic flux, high-spin models, are assigned comparatively low probabilities by the average image scoring scheme. Data taken later, more than a decorrelation time after EHT2017 (model decorrelation times are of order two weeks), will provide an independent realization of the source. The probabilities attached to individual models by average image scoring will then multiply. For example, a model with probability 0.05 that is assigned probability 0.05 in comparison to a second epoch of observation would then have probability $0.05^2=2.5\times 10^-3$, and would be strongly disfavored by the average image scoring criterion (see Section 4).

Future EHT 345 GHz campaigns (Paper II) will provide excellent constraints, particularly on the width of the ring. The optical depth on every line of sight through the source is expected to decrease (the drop is model and location dependent). In our models this makes the ring narrower, better defined, easier to measure accurately from VLBI data, and less dependent on details of the source plasma model.

Certain features of the model are geometric and should be present in future EHT observations. The photon ring is a persistent feature of the model related to the mass and distance to the black hole. It should be present in the next EHT campaign unless there is a dramatic change in $\dotM$, which would be evident in the SED. The asymmetry in the photon ring is also a persistent feature of the model because, we have argued, it is controlled by the black hole spin. The asymmetry should therefore remain in the southern half of the ring for the next EHT campaign, unless there is a dramatic tilt of the inner accretion flow. If the small-scale and large-scale jet are aligned, then EHT2017 saw the brightest region at unusually small PA, and future campaigns are likely (but not certain) to see the peak brightness shift further to the west. Future 230 GHz EHT campaigns (Paper II) will thus sharply test the GRMHD source models.

Together with complementary studies that are presently targeting either the supermassive black hole candidate at the Galactic Center (Eckart & Genzel 1997 ; Ghez et al. 1998 ; Gravity Collaboration et al. 2018a, 2018b) or stellar-mass binary black holes whose gravitational-wave emission is recorded by the LIGO and Virgo detectors (Abbott et al. 2016), the results provided here are consistent with the existence of astrophysical black holes. More importantly, they clearly indicate that their phenomenology, despite being observed on mass scales that differ by eight orders of magnitude, follows very closely the one predicted by general relativity. This demonstrates the complementarity of experiments studying black holes on all scales, promising much imp roved tests of gravity in its most extreme regimes.

The authors of this Letter thank the following organizations and programs : the Academy of Finland (projects 274477, 284495, 312496) ; the Advanced European Network of E-infrastructures for Astronomy with the SKA (AENEAS) project, supported by the European Commission Framework Programme Horizon 2020 Research and Innovation action under grant agreement 731016 ; the Alexander von Humboldt Stiftung ; the Black Hole Initiative at Harvard University, through a grant (60477) from the John Templeton Foundation ; the China Scholarship Council ; Comisión Nacional de Investigación Científica y Tecnológica (CONICYT, Chile, via PIA ACT172033, Fondecyt 1171506, BASAL AFB-170002, ALMA-conicyt 31140007) ; Consejo Nacional de Ciencia y Tecnológica (CONACYT, Mexico, projects 104497, 275201, 279006, 281692) ; the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute ; Dirección General de Asuntos del Personal Académico—Universidad Nacional Autónoma de México (DGAPA—UNAM, project IN112417) ; the European Research Council Synergy Grant '''BlackHoleCam : Imaging the Event Horizon of Black Holes''' (grant 610058) ; the Generalitat Valenciana postdoctoral grant APOSTD/2018/177 ; the Gordon and Betty Moore Foundation (grants GBMF-3561, GBMF-5278) ; the Istituto Nazionale di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEONGRAV ; the International Max Planck Research School for Astronomy and Astrophysics at the Universities of Bonn and Cologne ; the Jansky Fellowship program of the National Radio Astronomy Observatory (NRAO) ; the Japanese Government (Monbukagakusho : MEXT) Scholarship ; the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for JSPS Research Fellowship (JP17J08829) ; JSPS Overseas Research Fellowships ; the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJ-SSW-SYS008) ; the Leverhulme Trust Early Career Research Fellowship ; the Max-Planck-Gesellschaft (MPG) ; the Max Planck Partner Group of the MPG and the CAS ; the MEXT/JSPS KAKENHI (grants 18KK0090, JP18K13594, JP18K03656, JP18H03721, 18K03709, 18H01245, 25120007) ; the MIT International Science and Technology Initiatives (MISTI) Funds ; the Ministry of Science and Technology (MOST) of Taiwan (105-2112-M-001-025-MY3, 106-2112-M-001-011, 106-2119-M-001-027, 107-2119-M-001-017, 107-2119-M-001-020, and 107-2119-M-110-005) ; the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC17K0649) ; the National Institute of Natural Sciences (NINS) of Japan ; the National Key Research and Development Program of China (grant 2016YFA0400704, 2016YFA0400702) ; the National Science Foundation (NSF, grants AST-0096454, AST-0352953, AST-0521233, AST-0705062, AST-0905844, AST-0922984, AST-1126433, AST-1140030, DGE-1144085, AST-1207704, AST-1207730, AST-1207752, MRI-1228509, OPP-1248097, AST-1310896, AST-1312651, AST-1337663, AST-1440254, AST-1555365, AST-1715061, AST-1614868, AST-1615796, AST-1716327, OISE-1743747, AST-1816420) ; the Natural Science Foundation of China (grants 11573051, 11633006, 11650110427, 10625314, 11721303, 11725312, 11873028, 11873073, U1531245, 11473010) ; the Natural Sciences and Engineering Research Council of Canada (NSERC, including a Discovery Grant and the NSERC Alexander Graham Bell Canada Graduate Scholarships-Doctoral Program) ; the National Youth Thousand Talents Program of China ; the National Research Foundation of Korea (the Global PhD Fellowship Grant : grants NRF-2015H1A2A1033752, 2015-R1D1A1A01056807, the Korea Research Fellowship Program : NRF-2015H1D3A1066561) ; the Netherlands Organization for Scientific Research (NWO) VICI award (grant 639.043.513) and Spinoza Prize SPI 78-409 ; the New Scientific Frontiers with Precision Radio Interferometry Fellowship awarded by the South African Radio Astronomy Observatory (SARAO), which is a facility of the National Research Foundation (NRF), an agency of the Department of Science and Technology (DST) of South Africa ; the Onsala Space Observatory (OSO) national infrastructure, for the provisioning of its facilities/observational support (OSO receives funding through the Swedish Research Council under grant 2017-00648) the Perimeter Institute for Theoretical Physics (research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade) ; the Russian Science Foundation (grant 17-12-01029) ; the Spanish Ministerio de Economía y Competitividad (grants AYA2015-63939-C2-1-P, AYA2016-80889-P) ; the State Agency for Research of the Spanish MCIU through the '''Center of Excellence Severo Ochoa''' award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709) ; the Toray Science Foundation ; the US Department of Energy (USDOE) through the Los Alamos National Laboratory (operated by Triad National Security, LLC, for the National Nuclear Security Administration of the USDOE (Contract 89233218CNA000001)) ; the Italian Ministero dell'Istruzione Università e Ricerca through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001) ; ALMA North America Development Fund ; Chandra TM6-17006X and DD7-18089X ; a Sprows Family VURF Fellowship ; a NSERC Discovery Grant ; the FRQNT Nouveaux Chercheurs program ; CIFAR ; the NINS program of Promoting Research by Networking among Institutions(Grant Number 01421701) ; MEXT as a priority issue (Elucidation of the fundamental laws and evolution of the universe) to be tackled by using post-K Computer and JICFuS ; part of this work used XC50 at the Center for Computational Astrophysics, National Astronomical Observatory of Japan.This work used the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF grant ACI-1548562, and CyVerse, supported by NSF grants DBI-0735191, DBI-1265383, and DBI-1743442. XSEDE Stampede2 resource at TACC was allocated through TG-AST170024 and TG-AST080026N. XSEDE JetStream resource at PTI and TACC was allocated through AST170028. The simulations were performed in part on the SuperMUC cluster at the LRZ in Garching, on the LOEWE cluster in CSC in Frankfurt, and on the HazelHen cluster at the HLRS in Stuttgart. This research was enabled in part by support provided by Compute Ontario (http://computeontario.ca), Calcul Quebec (http://www.calculquebec.ca) and Compute Canada (http://www.computecanada.ca). Results in this Letter are based in part on observations made by the Chandra X-ray Observatory (Observation IDs 20034, 20035, 19457, 19458, 00352, 02707, 03717) and the Nuclear Spectroscopic Telescope Array (NuSTAR ; Observation IDs 90202052002, 90202052004, 60201016002, 60466002002). The authors thank Belinda Wilkes, Fiona Harrison, Pat Slane, Joshua Wing, Karl Forster, and the Chandra and NuSTAR scheduling, data processing, and archive teams for making these challenging simultaneous observations possible. We thank the staff at the participating observatories, correlation centers, and institutions for their enthusiastic support. This Letter makes use of the following ALMA data : ADS/JAO.ALMA#2016.1.01154.V. ALMA is a partnership of the European Southern Observatory (ESO ; Europe, representing its member states), NSF, and National Institutes of Natural Sciences of Japan, together with National Research Council (Canada), Ministry of Science and Technology (MOST ; Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA ; Taiwan), and Korea Astronomy and Space Science Institute (KASI ; Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, Associated Universities, Inc. (AUI)/NRAO, and the National Astronomical Observatory of Japan (NAOJ). The NRAO is a facility of the NSF operated under cooperative agreement by AUI. APEX is a collaboration between the Max-Planck-Institut für Radioastronomie (Germany), ESO, and the Onsala Space Observatory (Sweden). The SMA is a joint project between the SAO and ASIAA and is funded by the Smithsonian Institution and the Academia Sinica. The JCMT is operated by the East Asian Observatory on behalf of the NAOJ, ASIAA, and KASI, as well as the Ministry of Finance of China, Chinese Academy of Sciences, and the National Key R&D Program (No. 2017YFA0402700) of China. Additional funding support for the JCMT is provided by the Science and Technologies Facility Council (UK) and participating universities in the UK and Canada. The LMT project is a joint effort of the Instituto Nacional de Astrofísica, Óptica y Electrónica (Mexico) and the University of Massachusetts at Amherst (USA). The IRAM 30-m telescope on Pico Veleta, Spain is operated by IRAM and supported by CNRS (Centre National de la Recherche Scientifique, France), MPG (Max-Planck-Gesellschaft, Germany) and IGN (Instituto Geográfico Nacional, Spain). The SMT is operated by the Arizona Radio Observatory, a part of the Steward Observatory of the University of Arizona, with financial support of operations from the State of Arizona and financial support for instrumentation development from the NSF. Partial SPT support is provided by the NSF Physics Frontier Center award (PHY-0114422) to the Kavli Institute of Cosmological Physics at the University of Chicago (USA), the Kavli Foundation, and the GBMF (GBMF-947). The SPT hydrogen maser was provided on loan from the GLT, courtesy of ASIAA. The SPT is supported by the National Science Foundation through grant PLR- 1248097. Partial support is also provided by the NSF Physics Frontier Center grant PHY-1125897 to the Kavli Institute of Cosmological Physics at the University of Chicago, the Kavli Foundation and the Gordon and Betty Moore Foundation grant GBMF-947.The EHTC has received generous donations of FPGA chips from Xilinx Inc., under the Xilinx University Program. The EHTC has benefited from technology shared under open-source license by the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER). The EHT project is grateful to T4Science and Microsemi for their assistance with Hydrogen Masers. This research has made use of NASA's Astrophysics Data System. We gratefully acknowledge the support provided by the extended staff of the ALMA, both from the inception of the ALMA Phasing Project through the observational campaigns of 2017 and 2018. We would like to thank A. Deller and W. Brisken for EHT-specific support with the use of DiFX. We acknowledge the significance that Maunakea, where the SMA and JCMT EHT stations are located, has for the indigenous Hawaiʻian people.
Appendix A : Table of Simulation Results
Below we provide a table of simulation results for models with a standard inclination of 17° between the approaching jet and the line of sight. In the notation of this Letter this corresponds to i = 17° for $a_* \lt 0$ or i = 163° for $a_* \geqslant 0$. The table shows models for which we were able to calculate $L_\mathrmbol$ and $L_\rmX
$. When $M$ is needed to calculate, e.g., $P_\mathrmjet$, we assume $M=6.2\times 10^9\,M_\odot $.

The first, third, and fourth columns in the table identify the model parameters : SANE or MAD based on dimensionless flux, $a_* $, and $R_\mathrmhigh$. Once these parameters are specified, an average value of $\dotM$ for the model, which is shown in last column, can be found from the requirement that the average flux density of 1.3 mm emission is 0.5 Jy (see Paper IV). This $\dotM$ is shown in units of the Eddington accretion rate $\dotM_\mathrmEdd=137M_\odot \,\mathrmyr^-1$. The measured average dimensionless magnetic flux phgr is shown in the second column. Notice that phgr is determined solely from the GRMHD simulation and is independent of the mass scaling $\mathscrM$ and the mass $M$ used to fix the flux density. It is also independent of the electron thermodynamics ($R_\mathrmhigh$).

The fifth column shows the radiative efficiency, which is the bolometric luminosity $L_\mathrmbol$ over $\dotMc^2$. Here $L_\mathrmbol$ was found from a relativistic Monte Carlo radiative transport model that includes synchrotron emission, Compton scattering (all orders), and bremsstrahlung. The Monte Carlo calculation makes no approximations in treating the Compton scattering (see Dolence et al. 2009). Bremsstrahlung is negligible in all models.

The sixth column shows predicted X-ray luminosity $L_\rmX
$ in the $2\mbox—10\,\mathrmkeV$ band. This was calculated using the same relativistic Monte Carlo radiative transport model as for $L_\mathrmbol$. There are three numbers in this column : the average $\langle L_\rmX
\rangle $ (left) of the 20 sample spectra used in the calculation, and a maximum and minimum value. The maximum and minimum are obtained by taking the standard deviation $\sigma (\mathrmlog_10L_\rmX

)$ and setting the maximum (minimum) to $10^+2\sigma \langle L_\rmX

\rangle $ ($10^-2\sigma \langle L_\rmX

\rangle $).

The seventh column shows the jet power
Equation (10)

The integral is evaluated at $r=40\,r_\rmg

$ for SANE models and $r=100\,r_\rmg
$ for MAD models. These radii were chosen because they are close to the outer boundary of the computational domain. Here $\rm\Delta t$ is the duration of the time-average, $-T^r_t$ is a component of the stress-energy tensor representing outward radial energy flux, g is the determinant of the (covariant) metric, ρ is the rest-mass density, and ur is the radial component of the four-velocity. Here we use Kerr–Schild $t,r,\theta ,\phi $ for clarity ; in practice, the integral is evaluated in simulation coordinates. The quantity in parentheses is the outward energy flux with the rest-mass energy flux subtracted off. The θ integral is done after time averaging and azimuthal integration over the region where
Equation (11)
Here βγ would be the radial four-velocity as $r\to \infty $ if the flow were steady and all internal magnetic and internal energy were converted to kinetic energy. In Table 3 we use $(\beta \gamma )_\mathrmcut^2=1$ to define the jet. This is equivalent to restricting the jet to regions where the total energy per unit rest-mass (including the rest-mass energy) exceeds $\sqrt5c^2\simeq 2.2c^2$.
The ninth column shows the total outflow power $P_\mathrmout$, defined using the same integral as in Equation (10), but with the θ integral carried out over the entire region around the poles where there is steady outflow (and $\theta \lt 1$, although the result is insensitive to this condition). $P_\mathrmout$ thus includes both the narrow, fast, relativistic jet and any wide-angle, slow, or nonrelativistic outflow. It is the maximal $P_\mathrmjet$ under any definition of jet power.

Finally, the tenth column shows the ratio of the electromagnetic to total energy flux in the jet. In most cases this number is close to 1 ; i.e., the jet is Poynting dominated. This measurement is sensitive to the numerical treatment of low-density regions in the jet where the jet can be artificially loaded with plasma by numerical '''floors''' in the GRMHD evolution. More accurate treatment of the funnel would raise values in this column.

Our choice of $(\beta \gamma )_\mathrmcut^2$, and therefore $P_\mathrmjet$, is somewhat arbitrary. To probe the sensitivity of $P_\mathrmjet$ to $(\beta \gamma )_\mathrmcut^2$, Figure 10 shows the ratio $P_\mathrmjet$/$P_\mathrmout$ (which is determined by the GRMHD model and is thus independent of the electron thermodynamics, i.e., $R_\mathrmhigh$) as a function o

Figure 10. Ratio $P_\mathrmjet$/$P_\mathrmout$ as a function of the outflow velocity cutoff parameter $\beta \gamma _\mathrmcut$. Evidently, as the cut is decreased, so that the maximum asymptotic speed of the jet flow is decreased, an increasing fraction of $P_\mathrmout$ is classified as $P_\mathrmjet$. Our nominal cutoff is $\beta \gamma =1$, which corresponds to $\beta \equiv v^r/c=1/\sqrt2$. Using this definition, $P_\mathrmjet$ for $a_* =0$ models is small because the energy flux in the relativistic outflow is small.

The eighth and tenth columns show the jet and outflow efficiency. This is determined by the GRMHD evolution, i.e., it is independent of electron thermodynamics ($R_\mathrmhigh$). It is $\gt 0.1$ only for MAD models with $a_* \geqslant 0.5$.

The eleventh column shows the fraction of $P_\mathrmjet$ in Poynting flux. This fraction is large for all models, and meaningless for the $a_* =0$ models, which have $P_\mathrmjet$ that is so small that it is difficult to measure accurately.

The problem of defining $P_\mathrmjet$ and $P_\mathrmout$ has been discussed extensively in the literature (e.g., Narayan et al. 2012 ; Yuan et al. 2015 ; Mościbrodzka et al. 2016), where alternative definitions of unbound regions and of the jet have been used, some based on a fluid Bernoulli parameter $B_e\,\equiv -u_t(\rho +u+p)/\rho -1$, while others use μ (the ratio of energy flux to rest mass flux), which is directly related to our βγ.
Appendix B : Image Decomposition into Midplane, Nearside, and Farside Components

In Section 3.3 we presented representative images from the Image Library spanning a broad range of values in both $a_* $ and $R_\mathrmhigh$. It was noted that for SANEs with low values of $R_\mathrmhigh$ the emission is concentrated more in the midplane, whereas for larger values of $R_\mathrmhigh$ this emission is concentrated in the funnel wall. In particular, Figure 4 presented temporal- and azimuthal-averaged images of the point of origin of photons comprising images from $a_* =0.94$ MAD and SANE simulations with $R_\mathrmhigh=10$ and 160.

Figure 11 presents the decomposition of the four images in Figure 4 into components that we refer to as : midplane (material within 32fdg7 of the midplane), nearside (material within 1 radian, or 57fdg3, of the polar axis nearest to the observer), and farside (material within 1 radian of the polar axis furthest from the observer). From inspection of the first three models (rows) in Figure 11, the ratio of nearside to farside flux in the simulations is small (compared to the midplane) and of order unity and the midplane emission is dominant, as in Figure 4.

Figure 11. Decomposition of time-averaged 1.3 mm images from Figure 4 into midplane, nearside, and farside components (MAD and SANE models with $a_* =0.94$). Each model (row) of the figure corresponds to a simulation in Figure 4. The percentage of the total image flux from each component is indicated in the bottom right of each panel. The color scale is logarithmic and spans three decades in total flux with respect to the total image from each model, chosen in order to emphasize both nearside and farside components, which are nearly invisible when shown in a linear scale. The field of view is $80\,\mu \mathrmas$.

However, for the SANE, $R_\mathrmhigh=160$ model the farside emission contributes a flux that exceeds that produced from the midplane, and is significantly brighter than the nearside emission. This is in agreement with what is seen in the bottom-right panel of Figures 4, and can be understood to arise from the SANE model possessing an optically thin disk and bright funnel wall in the $R_\mathrmhigh=160$ case, compared to SANE, $R_\mathrmhigh=10$, as also seen in Figures 2 and 3. Due to the reduced opacity along the line of sight in this case, mm photons can pass through both the intervening nearside material and the midplane without significant attenuation, before reaching the photospheric boundary in the farside component (where τ 1), where they originate. The image decomposition and its application to M87's image structure will be explored further in Z. Younsi et al. 2019a (in preparation).

M87-6 L'ombre et la masse du trou noir central
Footnotes

110

phgr is determined by the outcome of the simulation and cannot be trivially predicted from the initial conditions, but by repeated experiment it is possible to manipulate the size of the initial torus and strength and geometry of the initial field to produce a target phgr.

111

In Heaviside units, where a factor of $\sqrt4\pi $ is absorbed into the definition of B, $\phi _\max \simeq 15$. In the Gaussian units used in some earlier papers, $\phi _\max \simeq 50$.

112

For a black hole accreting at the Eddington rate, the ratio of the accreting mass onto a black hole mass is $\sim 10^-22(M/M_\odot ) ;$ in our models mass accretion rate is far below the Eddington rate.

113

In particular the distribution of best-fit M/D, which is defined in Section 4, have mean and standard deviation of $M/D=3.552\pm 0.605\,\mu \mathrmas$ when the images are made with an input $M/D=3.62\,\mu \mathrmas$, and $3.564\pm 0.537\,\mu \mathrmas$ when the images are made with an input $M/D=2.01\,\mu \mathrmas$. We have also checked images made with an input 1.3 mm flux ranging from 0.1 to 1.5 Jy and find relative changes in M/D and $\mathrmPA$ of less than 1%.

114

In particular, doubling the image resolution changes the mean best-fit M/D by 7 nano-arcsec, and the best-fit $\mathrmPA$ by 0fdg3.

115

In GRMHD models the jet core is effectively empty and the density is set by numerical '''floors.''' In our radiative transfer calculations emission from regions with $B^2/\rho \gt 1$ is explicitly set to zero.

116

Paper I and Paper IV focus instead on the April 11 data set.

117

The thin disk radiative efficiency is 0.038 for $a_* =-1$, 0.057 for $a_* =0$, and 0.42 for $a_* =1$. See Equations (2.12) and (2.21) of Bardeen et al. (1972) ; the efficiency is $1-E/\mu _p$, where $\mu _p$ is the rest mass of the particle. The rejected model list is identical if instead one simply rejects all models with $\epsilon \gt 0.2$.

118

The compact mm flux density could be a factor of 2 larger than our assumed 0.5 Jy. That would raise $P_\mathrmjet$ by slightly less than a factor of 2.

119

The total energy flux inside a cone of opening angle $\theta _0$ is proportional to $\sin ^4\theta _0$ in the Blandford & Znajek (1977) monopole model if the field strength is fixed, and $\sin ^2\theta _0$ if the magnetic flux is fixed.

120

The width of the ring, the central flux depression, and a quantitative discussion of the black hole shadow can be found in Paper VI.

M87-4 Imaging the Central Supermassive Black Hole

bruno — 2019-04-15T02:46:34Z

M87-5 Origine Physique de l'anneau asymétrique

M87-3 Data Processing and Calibration

bruno — 2019-04-15T02:46:31Z

III. Data Processing and Calibration

Abstract

We present the calibration and reduction of Event Horizon Telescope (EHT) 1.3 mm radio wavelength observations of the supermassive black hole candidate at the center of the radio galaxy M87 and the quasar 3C 279, taken during the 2017 April 5–11 observing campaign. These global very long baseline interferometric observations include for the first time the highly sensitive Atacama Large Millimeter/submillimeter Array (ALMA) ; reaching an angular resolution of 25 μas, with characteristic sensitivity limits of 1 mJy on baselines to ALMA and 10 mJy on other baselines. The observations present challenges for existing data processing tools, arising from the rapid atmospheric phase fluctuations, wide recording bandwidth, and highly heterogeneous array. In response, we developed three independent pipelines for phase calibration and fringe detection, each tailored to the specific needs of the EHT. The final data products include calibrated total intensity amplitude and phase information. They are validated through a series of quality assurance tests that show consistency across pipelines and set limits on baseline systematic errors of 2% in amplitude and 1° in phase. The M87 data reveal the presence of two nulls in correlated flux density at 3.4 and 8.3 Gλ and temporal evolution in closure quantities, indicating intrinsic variability of compact structure on a timescale of days, or several light-crossing times for a few billion solar-mass black hole. These measurements provide the first opportunity to image horizon-scale structure in M87.

1. Introduction

The principle of very long baseline interferometry (VLBI) is to connect distant radio telescopes to create a single virtual telescope. On the ground, VLBI enables baseline lengths comparable to the size of the Earth. This significantly boosts angular resolution, at the expense of having a non-uniform filling of the aperture. In order to reconstruct the brightness distribution of an observed source, VLBI requires cross-correlation between the individual signals recorded independently at each station, brought to a common time reference using local atomic clocks paired with the Global Positioning System (GPS) for coarse synchronization. The resulting complex correlation coefficients need to be calibrated for residual clock and phase errors, and then scaled to physical flux density units using time-dependent and station-specific sensitivity estimates. Once this process is completed, further analysis in the image domain can refine the calibration using model-dependent self-calibration techniques (e.g., Pearson & Readhead 1984 ; Wilkinson 1989). For more details on the principles of VLBI, see, e.g., Thompson et al. (2017).

At centimeter wavelengths, the technique of VLBI is well established. Correlation and calibration have been optimized over decades, resulting in standard procedures for the processing of data obtained at national and international facility instruments, such as the Very Long Baseline Array103 (VLBA), the Australian Long Baseline Array104 (LBA), the East Asian VLBI Network105 (EAVN), and the European VLBI Network106 (EVN). At higher frequencies, the increased effects from atmospheric opacity and turbulence pose major challenges. The characteristic atmospheric coherence timescale is only a few seconds for millimeter wavelengths, and sensitivity must be sufficient to track phase variation over correspondingly short timescales. Large collecting areas and wide bandwidths prove essential when observing even the brightest continuum sources over a range of elevations and reasonable weather conditions. Furthermore, the transfer of phase solutions from a bright calibrator to a weak source, typically done at centimeter wavelengths, is not feasible at high frequencies, because differential atmospheric propagation effects are more significant, and because there are few bright, compact calibrators.

The Event Horizon Telescope (EHT) is a global VLBI array of millimeter- and submillimeter-wavelength observatories with the primary goal of studying the strong gravity, near-horizon environments of the supermassive black holes in the Galactic Center, Sagittarius A* (Sgr A*), and at the center of the nearby radio galaxy M87 (Doeleman et al. 2009 ; EHT Collaboration et al. 2019b, hereafter Paper II). In 2017 April, the EHT conducted science observations at a wavelength of λ sime 1.3 mm, corresponding to a frequency of ν sime 230 GHz. The network was joined for the first time by the Atacama Large Millimeter/submillimeter Array (ALMA) configured as a phased array, a capability developed by the ALMA Phasing Project (APP ; Doeleman 2010 ; Fish et al. 2013 ; Matthews et al. 2018). The addition of ALMA, as a highly sensitive central anchor station, drastically changes the overall characteristics and sensitivity limits of the global array (Paper II).

Although operating as a single instrument spanning the globe, the EHT remains a mixture of new and well-exercised stations, single-dish telescopes, and phased arrays with varying designs and operations. Each observing cycle over the last several years has been accompanied by the introduction of new telescopes to the array, and/or significant changes and upgrades to existing stations, data acquisition hardware, and recorded bandwidth (Paper II). EHT observations result in data spanning a wide range of signal-to-noise ratio (S/N) due to the heterogeneous nature of the array, and the high observing frequency produces data that are particularly sensitive to systematics in the signal chain. These factors, along with the typical challenges associated with VLBI, have motivated the development of specialized processing and calibration techniques.

In this Letter we describe the full data processing pathway and pipeline convergence leading to the first science release (SR1) of the EHT 2017 data. Given the uniqueness of the data set and scientific goal of the EHT observations, our processing focuses on the use of unbiased automated procedures, reproducibility, and extensive review and cross-validation. In particular, data reduction is carried out with three independent phase calibration (fringe-fitting) and reduction pipelines. The Haystack Observatory Processing System (HOPS ; Whitney et al. 2004) has been the standard for calibrating EHT data from prior observations (e.g., Doeleman et al. 2008, 2012 ; Fish et al. 2011, 2016 ; Akiyama et al. 2015 ; Johnson et al. 2015 ; Lu et al. 2018). HOPS reduction of the 2017 data is supported by a suite of auxiliary calibration scripts to form the EHT-HOPS pipeline (Blackburn et al. 2019). The Common Astronomy Software Applications package (CASA ; McMullin et al. 2007) is primarily aimed at processing connected-element interferometer data. The recent addition of a fringe fitter and reduction pipeline has enabled the use of CASA for high-frequency VLBI data processing (Janssen et al. 2019a, I. van Bemmel et al. 2019, in preparation). The NRAO Astronomical Image Processing System (AIPS ; Greisen 2003) is the most commonly used reduction package for centimeter VLBI data. For this work, an automated ParselTongue (Kettenis et al. 2006) pipeline was constructed and tailored to the needs of EHT data reduction in AIPS.

The SR1 data consist of Stokes I complex interferometric visibilities of M87 and the quasar 3C 279, corresponding to spatial frequencies of the sky brightness distribution sampled by the interferometer. M87 data indicate the presence of a resolved compact emission structure on a spatial scale of a few tens of μas, persistent throughout the week-long observing campaign. Closure phases and closure amplitudes unambiguously reflect non-trivial brightness distributions on M87 for the first time. They display broad consistency over different days, and in certain cases show clear evolution. A detailed analysis of this near-horizon-scale structure is the subject of companion Letters (EHT Collaboration et al. 2019a, 2019c, 2019d, 2019e, hereafter Papers I, IV, V, and VI, respectively).

This Letter is organized as follows. Section 2 presents an overview of the 2017 April observations. In Section 3 we outline the data flow from observations to science-ready data sets. We describe the correlation process in Section 4, the phase calibration process via three independent fringe-fitting pipelines in Section 5, and the common flux density calibration scheme and amplitude error budget in Section 6. We give an overview of SR1 data products and a rudimentary description of their most evident, remarkable properties in Section 7. We present data set validation procedures and tests, estimates of systematic errors, and inter-pipeline comparisons in Section 8. Conclusions are given in Section 9.
2. Observations

The EHT 2017 science observing run was scheduled for 5 nights during the 10-night 2017 April 5–14 (UTC) window with eight participating observatories at six distinct geographical locations, shown in Figure 1 : the ALMA and the Atacama Pathfinder Experiment (APEX) in the Atacama Desert in Chile, the Large Millimeter Telescope Alfonso Serrano (LMT) on the Volcán Sierra Negra in Mexico, the South Pole Telescope (SPT) at the geographic south pole, the IRAM 30 m telescope (PV) on Pico Veleta in Spain, the Submillimeter Telescope (SMT) on Mt. Graham in Arizona, and the Submillimeter Array (SMA) and the James Clerk Maxwell Telescope (JCMT) on Maunakea in Hawaiʻi. A detailed description of the EHT array is presented in Paper II. The 2017 science observing run consisted of observations of six science targets : the primary EHT targets Sgr A* and M87, and the secondary targets 3C 279, OJ 287, Centaurus A, and NGC 1052.

Figure 1. The eight EHT 2017 stations over six geographic locations as viewed from the equatorial plane. Solid baselines represent mutual visibility on M87 (+12° decl.), while dashed baselines to SPT are also present for 3C 279 (−6° decl.).

An array-wide go/no-go decision was made a few hours before the start of each night's schedule, based on weather conditions and technical readiness at each of the participating observatories. A dry run of the go/no-go decision making was performed on April 4 to assess triggering and readiness procedures. All sites were technically ready and with good weather on the first night of the observing window. Observations were triggered on 2017 April 5, 6, 7, 10, and 11. Table 1 shows the median zenith sky opacities for each of the triggered days. April 8 was not triggered due to thunderstorms at the LMT, SMT shutdown due to strong winds, and the need to run technical tests at ALMA. April 9 was not triggered due to a chance of the SMT remaining closed due to strong winds and LMT snow forecast. Weather was good to excellent for all other stations throughout the observing window.

Table 1. Median Zenith Sky Opacities (1.3 mm) at EHT Sites during the 2017 April Observations
Note. Median zenith sky opacities are measured at each site and reported through station log files and the VLBImonitor as described in Paper II.

In addition to favorable weather conditions, operations at all sites were successful and resulted in fringe detections across the entire array. A number of mild to moderate site and data issues were uncovered during the analysis, and their detailed characterization and mitigation are given in the Appendix. Notable issues affecting processing, calibration, and data interpretation are : (1) a clock frequency instability at PV resulting in 50% amplitude loss to that station ; (2) recorder configuration issues at APEX resulting in a significant number of data gaps and low data validity at correlation ; (3) pointing errors at LMT, large compared to the beam, resulting in unpredictable amplitude loss and inter- and intra-scan gain variability ; and (4) a common local oscillator (LO) used at SMA and JCMT resulting in opposite sideband contamination at the level of 15% for short integration times, making the SMA–JCMT intra-site baseline less useful for calibration. All known issues with a significant effect on the data are addressed at various stages of processing and calibration, although some (such as residual gains at the LMT, and SMA–JCMT sideband contamination) necessitate additional care taken during data interpretation.

M87 (αJ2000 = 12h30m49fs42, δJ2000 = 12°23'28farcs04) was observed as a target source on three nights (2017 April 5, 6, and 11). In addition, seven scans on M87 were included as a calibration source (for 3C 279) on 2017 April 10. Each of the four tracks consists of multiple scans lasting between 3 and 7 minutes. In most tracks, VLBI scans on M87 began when it rose at the LMT and ended when it set below 20° elevation at ALMA. Scans on M87 were interleaved with scans on the quasar 3C 279 (αJ2000 = 12h56m11fs17, δJ2000 = −05°47'21farcs52), another EHT target with a similar R.A. The observed schedules for M87 and 3C 279 during the 2017 campaign are shown in Figure 2. The schedules were optimized for wide (u, v) coverage on all target sources when possible. All stations apart from the JCMT observed with full polarization. The JCMT observed a single circular polarization component per night (right circular polarization (RCP) for April 5 and 6, left circular polarization (LCP) for April 10 and 11).

Figure 2. EHT 2017 observing schedules for M87 and 3C 279 covering the four days of observations. Empty rectangles represent scans that were scheduled, but were not observed successfully due to weather, insufficient sensitivity, or technical issues. The filled rectangles represent scans corresponding to detections available in the final data set. Scan duration varies between 3 and 7 minutes, as reflected by the width of each rectangle.

The 2017 observing run recorded two 2 GHz bands, low and high, centered at sky frequencies of 227.1 and 229.1 GHz, respectively, onto Mark 6 VLBI recorders (Whitney et al. 2013) at an aggregate recording rate of 32 Gbps with 2-bit sampling. All telescopes apart from ALMA observed in circular polarization with the installation of quarter-wave plates. Single-dish sites used block downconverters to convert the intermediate frequency (IF) signal from the front-ends to a common 0–2 GHz baseband, which was digitally sampled via Reconfigurable Open Architecture Computing Hardware 2 (ROACH2) digital backends (R2DBEs ; Vertatschitsch et al. 2015). The SMA observed as a phased array of six or seven antennas, for which the phased-sum signal was processed in the SMA Wideband Astronomical ROACH2 Machine (SWARM) correlator (see Primiani et al. 2016 ; Young et al. 2016, for more details). ALMA observed as a phased array of usually 37 dual linear polarization antennas, for which the phased-sum signal was processed in the Phasing Interface Cards installed at the ALMA baseline correlator (see Matthews et al. 2018 for more details). Instrumentation development leading up to the 2017 observations is presented in Paper II.
3. Data Flow

The EHT data flow from recording to analysis is outlined in Figure 3. Through the receiver and backend electronics at each telescope, the sky signal is mixed to baseband, digitized, and recorded directly to hard disk, resulting in petabytes of raw VLBI voltage signal data. The correlator uses an a priori Earth geometry and clock/delay model to align the signals from each telescope to a common time reference, and estimates the pair-wise complex correlation coefficient (rij) between antennas. For signals xi and xj between stations i and j
Equation (1)

where ηQ represents a digital correction factor to compensate for the effects of low-bit quantization. For optimal 2-bit quantization, ηQ ≈ 0.88.

Figure 3. Data processing pathway of an EHT observation from recording to source parameter estimation (images, or other physical parameters). At the calibration stage, instrumental and environmental gain systematics are estimated and removed from the data so that a smaller and simpler data product can be used for source model fitting at a downstream analysis stage

The correlation coefficient may vary with both time and frequency. For FX correlators, signals from each antenna are first taken to the frequency domain using temporal Fourier transforms on short segments (F), and then pair-wise correlated (X). The expectation values in Equation (1) are calculated by averaging over time–frequency volumes where the inner products remain stable. At millimeter wavelengths, a correlator can average around 1 s × 1 MHz, or 2 × 106 samples, before clock errors such as residual delay, delay-rate (e.g., Doppler shift), and stochastic changes in atmospheric path length cause unwanted decoherence in the signal (Section 4). The post-correlation data reduction pipeline models and fits these residual clock systematics, allowing data to be further averaged by a factor of 103 or more, to the limits imposed by intrinsic source structure and variability (Section 5). For many EHT baselines, the astronomical signal is not detectable above the noise until phase corrections resulting from these calibration solutions are applied and the data are coherently (vector) averaged.

In addition to reducing the overall volume and complexity of the data, the calibration process attempts to relate the pair-wise correlation coefficients rij, which are in units of thermal noise of the detector, to correlated flux density in units of Jansky (Jy),
Equation (2)

The visibility function, Vij, represents the mutual coherence of the electric field between ends of the baseline vector joining the sites, projected onto the plane of propagation. For an ideal interferometer, Vij samples a Fourier component of the brightness distribution on the sky (via the van Cittert–Zernike theorem ; van Cittert 1934 ; Zernike 1938 ; Thompson et al. 2017). The dimensionless spatial frequency u = (u, v) of the Fourier component is determined by the projected baseline expressed in units of the observing wavelength. Here, we have made the implicit assumption that the relationship between correlation coefficient and visibility can be factored into complex station-based forward gains γi and γj. This process of flux density calibration requires an a priori assessment of the sensitivity of each antenna in the array, captured by the system-equivalent flux density ($\mathrmSEFD_i=| 1/\gamma _i| ^2$) of the thermal noise power, as described in Section 6.

After the basic calibration and reduction process, the data are passed through additional post-processing tasks to further average the data to a manageable size for source imaging and model fitting, and to apply any network self-calibration constraints based on independent a priori assumptions about the source, such as large-scale (milliarcsecond and larger) structure, total flux density, and degree of total polarization (Section 6.2). The final network-calibrated data products are further averaged to a 10 s segmentation in time and across each 2 GHz band to provide smaller files for downstream analysis (Section 7.1).
4. Correlation

The recorded data from each station were split by frequency band and sent to MIT Haystack Observatory and the Max-Planck-Institut für Radioastronomie (MPIfR) for correlation, as described in Paper II. The Haystack correlator handled the low-frequency band (centered at 227.1 GHz), with MPIfR correlating the high band (centered at 229.1 GHz). Each correlator is a networked computer cluster running a standard installation of the DiFX software package (Deller et al. 2011). The correlators use a model (calc11) of the expected wavefront arrival delay as a function of time on each baseline. The delay model very precisely takes into account the geometry of the observing array at the time of observation, the direction of the source, and a model of atmospheric delay contributions (e.g., Romney 1995). Baseband data on a few high-S/N scans with good coverage were exchanged between the two sites to verify the output of each correlator against the other.

Data were correlated with an accumulation period (AP) of 0.4 s and a frequency resolution of 0.5 MHz (Figure 4). Due to the need to rationalize frequency channelization with the ALMA setup (each 1.875 GHz spectral window at ALMA is broken up into 32 spectral IFs of 62.5 MHz, separated by 58.59375 MHz and thus slightly overlapping ; Matthews et al. 2018), the frequency points are grouped into IFs that are 58 MHz wide (using DiFX zoom mode), each with 116 individual channels and a small amount of bandwidth discarded between spectral IFs

Figure 4. Time and frequency resolution of EHT 2017 data as it is recorded and processed. Correlation parameters for the EHT are chosen to be compatible with ALMA's recorded sub-bands that are 62.5 MHz wide, overlap slightly, and have starting frequencies aligned to 1/(32 μs). The raw output after calibration and reduction maintains the original correlator accumulation of 0.4 s, but averages over each 58 MHz spectral IF, centered on each ALMA sub-band. The data are further averaged at the network amplitude self-calibration stage (not shown) for a more manageable data volume.

At the SMA, the original data are recorded in the frequency domain rather than the time domain, owing to the architecture of the SMA correlator. Moreover, the recorded frequency range of 2288 MHz is slightly larger and offset by 150 MHz from the frequency range at the other non-ALMA sites. An offline pre-processing pipeline, called the Adaptive Phased-array and Heterogeneous Interpolating Downsampler for SWARM (APHIDS ; Primiani et al. 2016), is used to perform the necessary filtering, frequency conversion, and transformation to the time domain, so that the format of the SMA data delivered to the VLBI correlator is the same as for single-dish stations. Part of the necessary offline pre-processing includes deriving clock offsets on a scan-by-scan basis for the delivered data. These offsets are determined by cross-correlating the pre-processed SMA data with separate data recorded with an R2DBE-Mark 6 pair, taking a second IF signal from the SMA reference antenna as input.

The IF from the JCMT was recorded using backend equipment installed at the SMA (Paper II). This was achieved by transporting the first IF from the JCMT to the SMA, where the second downconversion, digitization, and recording were done. Because the second downconversion at the SMA introduces a net offset of 150 MHz with respect to the nominal EHT RF band, this means that the recorded JCMT data sent to the correlator are subject to the same frequency offset. The mismatch eliminates one of the thirty-two 58 MHz spectral IFs in the final correlation for JCMT baselines.

ALMA observes linear polarization, while the rest of the EHT observes circular polarization. The software routine PolConvert (Martí-Vidal et al. 2016 ; Matthews et al. 2018) was created to convert visibilities, output from the correlator in a mixed-polarization basis, to the pure circular basis of the EHT. PolConvert takes auxiliary calibration input from the quality assurance stage 2 (QA2) ALMA interferometric reduction of data (Goddi et al. 2019). Execution of the PolConvert tool completes the correlation (circularized visibilities on baselines to ALMA) and provides final ANTAB107 format data for flux density calibration of the ALMA phased array. The original native (Swinburne format) correlator output from DiFX is converted using available DiFX tools to a Mark4 (Whitney et al. 2004) compatible file format for processing through HOPS, and to FITS-IDI (Greisen 2011) files for further processing with AIPS and CASA.
5. Fringe Detection

In the limit for which all correlator delay model parameters were known perfectly ahead of time and there were no atmospheric variations, the model delays would exactly compensate for the delay on each baseline of the data, and the correlated data could be coherently integrated in time and frequency to build up sensitivity. In practice, many of the model parameters are not known exactly at correlation. For example, the observed source may have structure and may be centered at an offset from the expected coordinates, the position of each telescope may differ from the best estimate, instrumental electronic delays may not be known, or variable water content in the atmosphere may cause the atmospheric delay to deviate from the simple model. It is therefore necessary to search in delay and delay-rate space for small corrections to the model values that maximize the fringe amplitude : in VLBI data processing this process is known as fringe-fitting (e.g., Cotton 1995). In this section, we describe three independent fringe-fitting pipelines for phase calibration, based on three different software packages for VLBI data processing : HOPS (Section 5.1), CASA (Section 5.2), and AIPS (Section 5.3).
5.1. HOPS Pipeline

HOPS108 is a collection of software packages and data framework designed to analyze and reduce output from a Mark III, IV, or DiFX correlator. It has been used extensively for the processing of early EHT data (Doeleman et al. 2008, 2012 ; Fish et al. 2011, 2016 ; Akiyama et al. 2015 ; Johnson et al. 2015 ; Lu et al. 2018). For EHT 2017 observations, HOPS was augmented with a collection of auxiliary calibration scripts, and packaged into an EHT-HOPS pipeline (Blackburn et al. 2019) for automated processing of this and similar data sets. Compared to the reduction of data from previous runs, the EHT-HOPS pipeline is unique in that it finds a single self-consistent global fringe solution (station-based delays, delay-rates, and instrumental and atmospheric phase) for calibration. The pipeline also provides standard UVFITS formatted visibility data products for downstream analysis.

The EHT-HOPS pipeline processes output from the DiFX correlator that has been converted to Mark4 format via the DiFX tool difx2mark4. This conversion process includes normalization by auto-correlation power per 58 MHz spectral IF in each AP of 0.4 s (Figure 4), as well as a 1/0.88252 amplitude correction factor for 2-bit quantization efficiency. Stages of the pipeline (Figure 5) run the HOPS fringe fitter fourfit several times (once per stage) while making iterative corrections to the phase calibration applied to the data before solving for delays and delay-rates. The initial setup (default config, flags—Figure 5) includes manual flagging (removal of bad data) in time and frequency, as well as an ALMA-specific correction for digital phase offsets between spectral IFs.

Figure 5. Stages of the EHT-HOPS pipeline and post-processing steps, as described in the text. The first five stages, shown in the left box, are iterations of HOPS fringe fitter fourfit. Here, a comprehensive phase calibration model is gradually built for the data. At the end of the five fourfit stages, the correlation coefficients are evaluated at a single global (station-based) set of relative delays and delay-rates. The data are then converted to UVFITS format, and a remaining suite of post-processing tools provide amplitude calibration and time-and-polarization-dependent phase calibration

ALMA is used as a reference station for estimating stable instrumental phase (phase bandpass) and relative delay between right and left circular polarization (R-L delay offsets) for remote stations. The estimates are done using S/N-weighted averages of the strong ALMA baseline measurements. Here we make use of the fact that ALMA RCP and LCP data are already delay- and phase-calibrated during the QA2/PolConvert process (Goddi et al. 2019). For rapid nonlinear phase (atmospheric phase) that varies over seconds and that must be calibrated on-source, the strongest station (generally ALMA when it is present ; see also Section 2 of Paper II) is automatically determined for each scan based on signal-to-noise, and is used as a phase reference. Baselines to the reference station are then used to phase stabilize the remaining sites.

Due to the large number of free parameters involved in correcting for atmospheric phase, a leave-out-one cross-estimation approach is adopted for this step to avoid self-tuning. For each baseline, a smooth phase model is estimated by stacking RCP and LCP data over 31 (of 32) spectral IFs. The estimated phase from the 31-IF average is used to correct the remaining IF, and the process cycles through IFs to cover the full band. In this way, phase corrections are never estimated from the same data to which they are applied, which avoids introducing false coherence from self-tuning to random thermal noise and introducing a positive bias to amplitudes. The effective solution interval for the phase model depends on S/N, and is chosen per baseline to balance anticipated atmospheric phase drift with thermal noise in the estimate. Additional a priori corrections for small residual clock frequency offsets after correlation (Appendix) are made here as well.

During a final reduction with fourfit (close fringe solution), rather than fitting for unconstrained delays and delay-rates per baseline and polarization product, a single set of station-based delays and delay-rates is fixed corresponding to a global fringe solution. These are derived from a least-squares solution (as proposed by Alef & Porcas 1986) to relative delays and delay-rates from confident baseline detections with S/N > 7, and stations that remain unconstrained by this process are removed from the data set. No interpolation of these fringe solutions is performed across sources and scans ; instead, precise closure of delay and delay-rate from strong baseline detections is required to report any measurement on a weak baseline. Correlation coefficients on baselines with no detectable signal are still calculated (Figure 11, where S/N < few), but only when the relative clock model is constrained through other baseline detections.

The resulting complex visibility data are converted to UVFITS format, and amplitude calibration is done in the EHT Analysis Toolkit's (eat)109 post-processing framework, shared by all pipelines and described in Section 6. For the HOPS pipeline, the calibration of complex polarization gain ratios is performed in a post-processing stage rather than during fourfit. Deterministic field rotation from parallactic angle and receiver mount type is corrected as a complex polarization-dependent a priori gain factor, and a smoothly varying polynomial model is fit over many sources and used to correct residual RCP−LCP phase drift for each station. Details for all steps can be found in Blackburn et al. (2019).

The EHT-HOPS pipeline was additionally used for the reduction of observations of Sgr A* and calibrators at 86 GHz, with the Global Millimeter VLBI Array110 (GMVA) joined by ALMA. Despite the magnitude difference in bandwidth, a similar reduction to EHT data was performed on the GMVA data set. ALMA baselines were used to estimate stable instrumental phase and delay corrections. Baselines to either ALMA or the Green Bank Telescope (GBT) were used, due to their high S/N, to correct for stochastic atmospheric phase fluctuations on timescales of a few seconds. The performance of the pipeline on the GMVA data is described in Blackburn et al. (2019) while scientific results from the data set are validated against historical observations in Issaoun et al. (2019).
5.2. CASA Pipeline

The CASA (McMullin et al. 2007) package was developed by NRAO to process data acquired with the JVLA and ALMA connected-element interferometers and in recent years has become the standard software for the calibration and analysis of radio-interferometric data. A newly developed fringe-fitting task fringefit (I. van Bemmel et al. 2019, in preparation) has added the necessary delay and delay-rate calibration capabilities for VLBI. The modular, general-purpose rPICARD VLBI data reduction pipeline (Janssen et al. 2019a) is used for the calibration of EHT data. This section describes the incremental rPICARD calibration steps for EHT data, summarized in Figure 6.

Figure 6. EHT data processing stages of rPICARD. Instrumental amplitude calibration effects are described in the top-left box. Phases for the calibrator sources are corrected first to solve for instrumental effects (second box) and science targets are phase-calibrated after the instrumental effects have been solved (third box). Finally, post-processing steps are done outside of CASA for amplitude calibration (fourth box).

The importfitsidi CASA task is used to import the FITS-IDI correlator output into CASA. Additionally, a digital correction factor for the 2-bit recorder sampling is applied when the data are loaded. Bad data are flagged based on text files compiled from station logs and known sources of radio frequency interference in stations' signal chains with the flagdata task before performing the incremental calibration procedures. The accor task is used to scale the auto-correlations to unity and adjust the cross-correlations accordingly, correcting for incorrect sampler settings from the data recording stage. This is done for each 58 MHz spectral IF individually, thereby correcting for a coarse bandpass at each station. This amplitude bandpass is refined by dividing the data by the auto-correlations at the 0.5 MHz channel resolution.

The phase calibration is done with the fringefit task, which solves for station-based residual post-correlation phases, delays, and rates with respect to a chosen reference station (Schwab & Cotton 1983). Unlike the HOPS pipeline, where field rotation angles are corrected a posteriori, rPICARD applies field rotation angle gain solutions on-the-fly, i.e., before each phase calibration correction. The most sensitive station is picked as reference in each scan. Eventually, all fringe solutions are re-referenced with the CASA rerefant task to a common station for each observing track to ensure phase continuity across scans.

Phases are first calibrated for the high S/N calibrator sources, which are used to correct for instrumental effects. Optimal time solution intervals to calibrate atmospheric intra-scan phase fluctuations ($ \mathcal T _\mathrmsol$) are determined automatically based on the S/N of the data. The search is done for short solution intervals, close to the coherence time, which still yield detections on all possible baselines (Janssen et al. 2019a). Typical solution intervals range from 2 to 30 s. Using these solution intervals, phases and rates are calibrated to extend the coherence time of the calibrator scans. This results in high S/N scan-based fringe solutions per 58 MHz spectral IF, which are used to obtain calibration solutions for instrumental effects. ALMA-induced phase offsets between spectral IFs are corrected with the short ALMA–APEX baseline. All baselines in the array are used by the global fringe fitter in the next step to solve for residual instrumental phase and delay offsets for all stations. After removing these instrumental data corruptions, a final fringefit step solves for multi-band delays on the (previously determined) solution intervals. A 60 s median window filter is used to smooth the slowly varying multi-band delays, which effectively removes potential outliers. After fringe fitting, the phases are coherent in time and frequency, and the bandpass task is used to solve for the frequency-dependent phase gains within each 58 MHz spectral IF for each station, using the combined data of all calibrator sources.

After all instrumental effects are calibrated out, the optimal fringe-fit solution intervals $ \mathcal T _\mathrmsol$ are determined for the weaker science targets, and phases, delays, and rates are solved for in a single fringefit step. The intra-scan fringe fritting on short solution intervals flags low S/N segments where no fringes are found to a specific station, e.g., when a station arrived late on source. Finally, the exportuvfits task is used to export the calibrated data from internal Measurement Set format to UVFITS files, which are then flux-density and network-calibrated in the common post-processing framework.

Janssen et al. (2019a) demonstrate the rPICARD calibration capabilities in a close comparison with a traditional AIPS-based calibration using 43 GHz VLBA data of M87. The resultant image of the jet and counter-jet, which reveals a complex collimation profile, is in good agreement with earlier results from the literature (e.g., Walker et al. 2018). The rPICARD pipeline was further used for the generation of synthetic EHT data (Paper IV), where known input delay and phase offsets were recovered as a ground-truth validation.
5.3. AIPS Pipeline

AIPS (Greisen 2003) is the most widely used software package for VLBI data reduction and processing at frequencies at or below 86 GHz. It is commonly used in the VLBI community and was built to process low-S/N data from fairly homogeneous centimeter-wave observatories at low recording bandwidths. The EHT, however, falls in a different category : its high recording bandwidth and heterogeneous array produce data with a wide range of S/N, often dominated by systematic effects instead of thermal noise. These properties required the development of a custom pipeline based on AIPS, deviating from standard fringe-fitting procedures for lower frequency data processing as outlined in e.g., the AIPS Cookbook.111

The custom AIPS pipeline is an automated Python-based script using functions implemented in the eat package. It makes use of ParselTongue (Kettenis et al. 2006), which provides a platform to manipulate AIPS tasks and data outside of the AIPS interface. The pipeline is summarized in Figure 7 and shows individual tasks used for calibration. A suite of diagnostic plots, using tasks VPLOT and POSSM, are also generated at each calibration step within the pipeline.

Figure 7. Stages of the AIPS fringe-fitting pipeline and post-processing steps. The pipeline begins with direct data editing (interactively or via input correction and flag tables) and amplitude normalization (first box). The phase calibration process then follows via four steps with the AIPS fringe fitter KRING to solve for phase and delay offsets and rates (second box). Finally, post-processing steps are done outside of AIPS for amplitude calibration (third box).

The loading of EHT data into AIPS, during which digital corrections for 2-bit quantization efficiency are applied, requires a concatenation of several packaged FITS-IDI files and a careful handling of the JCMT, which observes with a slightly shifted IF setup of the band (Section 4). The pipeline reduces each band (low and high) in separate runs. Data inspection and flagging of spurs in the frequency domain from accumulated scalar bandpass tables (generated with BPASS) and dropouts or amplitude jumps in the time domain are done interactively with the AIPS tasks BPEDT and EDITA. The flags are saved in output flag tables to use in non-interactive reruns of the pipeline. Standard amplitude normalization steps are performed with the AIPS task ACSCL. The field rotation angle corrections are performed with an EHT-specific receiver mount correction script (ehtutil.ehtpang, modifying the antenna table from the DiFX alt-az default to the proper receiver mounts of each station) using the AIPS task CLCOR before fringe fitting.

The fringe-fitting steps follow a similar framework to the HOPS pipeline but use KRING,112 a station-based fringe fitter that outperforms the standard FRING in terms of computational efficiency for large data sets, while maintaining an equivalent accuracy. The first step of the fringe search, commonly known as instrumental phase calibration, consists of solving for delay and phase offsets and fringe-rates using the full scan coherence and full 2 GHz bandwidth (combining spectral IFs). The second step solves for delay and phase offset residuals per individual spectral IF, again using the full scan coherence. The third step uses a fixed solution interval of 2 s to solve for fast phase rotations in time across the full bandwidth (combining IFs). The final stage is solving for scan-based residual delays and phases per individual spectral IF.

The AIPS pipeline particularly relies on ALMA being present to accurately solve for short interval solutions, as it uses ALMA as the reference station for the initial baseline-based FFT within KRING. Without ALMA, or in certain cases of a weak baseline to ALMA, KRING is unable to accumulate enough S/N in a single spectral IF or within a two-second segment to constrain a fringe solution. After applying all calibration steps, the data are frequency-averaged and exported in UVFITS format. A priori and network calibration are performed outside of AIPS in the common post-processing framework.
6. Flux Density Calibration

The flux density calibration for the EHT is done in two steps and is a common post-processing procedure for all three phase calibration pipelines, as it involves very little handling of the data themselves. In Section 6.1, we describe the a priori calibration process to calibrate visibility amplitudes to a common flux density scale across the array. In Section 6.2, we present the network calibration process, where we use array redundancy to absolutely calibrate stations with an intra-site companion.
6.1. A Priori Amplitude Calibration

A priori amplitude calibration serves to calibrate visibility amplitudes from correlation coefficients to flux density measurements, as in Equation (2). As the normalized correlation coefficients are in units of noise power, it is necessary to account for telescope sensitivities to convert to a uniform flux density scale across the array. The SEFD of a radio telescope is the total system noise represented in units of equivalent incident flux density above the atmosphere. It can be written as
Equation (3)

using the three measurable parameters :

1.
$T_\mathrmsys^* $ : the effective system noise temperature describes the total noise characterization of the system corrected for atmospheric attenuation (Equations (4) and (5)),
2.
DPFU : the degrees per flux density unit provides the conversion factor (K/Jy) from a temperature scale to a flux density scale, correcting for the aperture efficiency (Equation (6)),
3.
ηel : the gain curve is a modeled elevation dependence of the telescope's aperture efficiency (Equation (7)), factored out of the DPFU to track gain variation as the telescope moves across the sky.

The EHT is a heterogeneous array with telescopes of various sensitivities (ranging nearly three orders of magnitude, see Figure 8), operation schemes, and designs. A clear understanding of each station's metadata measurement and delivery is required for an accurate calibration of the measured visibilities. We determine the SEFDs of the individual stations and their uncertainties under idealized conditions, assuming adequate pointing and focus (see Sections 6.1.1, 6.1.3, and 6.1.4). Further losses and uncertainty in the SEFDs, particularly those induced by focus or pointing errors, are difficult to quantify using available metadata, but are qualitatively explained in Section 6.1.5. A more quantitative assessment of station behavior can be done via derived residual station gains from self-calibration methods in imaging or model fitting (Papers IV, VI).

Figure 8. Example of SEFD values during a single night of the 2017 EHT observations (April 11, low-band RCP). Values for 3C 279 are marked with full circles, values for M87 are marked with empty diamonds. ALMA SEFDs have been multiplied by 10 in this plot. The SPT is observing 3C 279 at an elevation of just 5fdg8, resulting in an uncharacteristically high SEFD due to the large airmass

6.1.1. Quantifying Station Performance

In order to determine the sensitivity of a single-dish station at a given time, measurements of the effective system temperature, the DPFU, and the gain curve are required. Here we provide details on how these parameters are measured for the EHT array.

The EHT operates in the millimeter-wave radio regime, where observations are very sensitive to atmospheric absorption and water vapor content. In contrast with centimeter-wave interferometers (e.g., VLBA/JVLA), millimeter-wave telescopes typically measure $T_\mathrmsys^* $ via the "chopper" (or hot-load) method : an ambient temperature load $T_\mathrmhot$ with known blackbody properties is placed in front of the receiver, blocking everything but the receiver noise, and the resulting noise power is compared to the same measurement on cold sky. Assuming $T_\mathrmhot\sim T_\mathrmatm$ (the hot load is at a temperature comparable to the radiating atmosphere), this method automatically compensates for atmospheric absorption to first order, essentially transferring the incident flux density reference point to above the atmosphere (e.g., Penzias & Burrus 1973 ; Ulich & Haas 1976) :
Equation (4)

where $T_\mathrmrx$ is the receiver noise temperature, and τ is the sky opacity in the line of sight. Details on the chopper techniques adopted for the EHT are provided in a technical memo113 (Issaoun et al. 2017a).

Three stations in the EHT array have double-sideband (DSB) receivers in 2017 (SMA, JCMT, and LMT), where both upper and lower sidebands on either side of the oscillator frequency are folded together in the recorded signal (e.g., Iguchi 2005, Paper II). Because only one 4 GHz sideband is correlated across the array, we correct $T_\mathrmsys^* $ for the excess noise contribution from the uncorrelated sideband
Equation (5)

where the sideband ratio rsb is the ratio of source signal power in the uncorrelated sideband to that in the correlated sideband. A sideband ratio of unity, for an ideal DSB system, is assumed for the SMA and LMT based on known receiver performance. A measured sideband ratio of 1.25 is used for the JCMT.114 The remaining stations use sideband-separating receiver systems and do not need this adjustment. The SPT, although sideband-separating, is believed to have suffered from a degree of incomplete sideband separation in 2017, giving it some amount of (uncharacterized) effective rsb.

In addition to the noise characterization, the efficiency of the telescope must also be quantified. The DPFU relates flux density units incident onto the dish to equivalent degrees of thermal noise power through the following equation :
Equation (6)

where kB is the Boltzmann constant ($k_\rmB=1.38\times 10^3$ Jy/K), Ageom is the geometric area of the dish, and $\eta _\rmA$ is the aperture efficiency of the telescope. For an idealized telescope with a uniform illumination (no blockage or surface errors), the full area would be available to collect the incoming signal and the aperture efficiency would be unity. Real radio telescopes intentionally taper their illumination to minimize spillover past the primary mirror, most have secondary mirror support legs that block part of the primary aperture, and generally the surface accuracy produces a non-negligible degradation in efficiency. To determine $\eta _\rmA$, well-focused and well-pointed observations are made of calibrator sources of known brightness, usually planets (e.g., Kutner & Ulich 1981 ; Mangum 1993 ; Baars 2007). The planet brightness temperature models from the GILDAS115 software package were used for this calibration. For each single-dish EHT station, we determine a single DPFU value per polarization/band, except for JCMT, which has measurable temporal variations from solar heating during daytime observations. A more detailed overview of the methodology for $\eta _\rmA$ is presented in Issaoun et al. (2017a).

We separately determine the elevation-dependent efficiency factor $\eta _\mathrmel$ (or gain curve) due primarily to gravitational deformation of each parabolic dish. The characterization of the telescope's geometric gain curve is particularly important for the EHT, which often observes science targets at extreme elevations in order to maximize (u, v) coverage. The elevation-dependent gain curve is estimated by fitting a second-order polynomial to measurements of bright calibrator sources continuously tracked over a wide range of elevation (see Figure 9 and the technical memo by Issaoun et al. 2017b). In the EHT array, SMT, PV, and APEX have characterized gain curves. The gain curve is parameterized as a second-order polynomial about the elevation at maximum efficiency :
Equation (7)

The JCMT has no elevation dependence at 230 GHz as it is operating at the lower end of its frequency range. The LMT has an adaptive surface that is able to actively correct for surface deformation as a function of elevation. Through observations of planets, the LMT was determined to have a flat 1.3 mm gain between 25° and 80° to within 10% uncertainty. At the SPT, the elevation of extra-solar sources is constant, and therefore possible elevation-dependent efficiency losses remain uncharacterized.

Figure 9. Example of a gain curve fit to single-dish normalized flux density measurements of calibrators at the SMT (Issaoun et al. 2017b).

We also mitigate a number of pathological issues uncovered in the 2017 data affecting the visibility amplitudes in a priori calibration. Additional loss of coherence in the signal chain at PV due to impurities in the LO, an excess noise contribution at APEX due to the inclusion of a timing signal, and the partial SMA channel dropouts were identified during data processing. Correction factors for the visibility amplitudes on baselines to these sites were estimated, as explained in the Appendix. These correction factors translate to a square multiplicative effect on the station-based SEFDs, as shown in Table 2. In the a priori calibration metadata, the multiplicative factors were folded into the DPFUs for PV and APEX and into the $T_\mathrmsys^* $ measurements for SMA (due to its time dependence). Representative median values for the aperture efficiency, DPFU, effective system temperature, and SEFD on EHT primary targets (M87 and Sgr A*) for each station participating in the EHT 2017 observations are shown in Table 2. A site-by-site overview of the derivation of a priori calibration quantities is given in a technical memo (Janssen et al. 2019b).

Table 2. Median EHT Station Sensitivities on Primary Targets during the 2017 Campaign, Assuming Nominal Pointing and Focus
aNighttime value for the DPFU. The daytime DPFU includes a Gaussian component dip as function of local Hawai'i time. bSPT has a 10 m dish diameter, with 6 m illuminated by receiver optics in 2017. cThe diameter for phased arrays reflects the sum total collecting area. dDPFUs for phased arrays are determined for the full collecting areas. eApplied when 6.25% and 18.75% of the SMA bandwidth was corrupted, respectively.

6.1.2. Calibrating Visibility Amplitudes

The $T_\mathrmsys^* $, DPFU, and elevation gain data for all stations are aggregated in ANTAB format text files. They are subsequently matched with observed visibilities for a given source using linear interpolation. Visibility amplitudes are calibrated in units of flux density by multiplying the normalized visibility amplitudes by the geometric mean of the derived SEFDs of the two stations across a baseline i–j :
Equation (8)

where $| V_\mathrmij| $ is then the calibrated visibility amplitude in Jy on that baseline, as in Equation (2).

Figure 10 shows the scan-averaged S/N on individual baselines, which is proportional to the phase-calibrated correlated signal, as a function of the projected baseline length (top panel), and the equivalent correlated flux density after a priori calibration (center panel) for observations of M87 (left) and 3C 279 (right) on April 11. The split in the S/N distributions is due to the difference in sensitivity between the co-located sites ALMA and APEX, leading to simultaneous baselines with two levels of sensitivity. The a priori calibration process puts all points on the same flux density scale (via Equation (8)), and the resulting data variations can thus be attributed to source structure, no longer dominated by sensitivity differences between baselines.

Figure 10. Stages of visibility amplitude calibration illustrated with the April 11 HOPS data set on M87 (left) and 3C 279 (right), as a function of projected baseline length. The two frequency bands are coherently scan-averaged separately and the final amplitudes are averaged incoherently across bands. Top : S/N of the correlated flux density component after phase calibration, both RCP and LCP. Middle : flux-density calibrated RCP and LCP values. Bottom : final, network-calibrated Stokes I flux densities. Error bars denote ±1σ uncertainty from thermal noise.

6.1.3. Single-dish Error Budget

The SEFD error budget, assuming nominal pointing and focus, is dominated by the measurement uncertainty for the DPFU (see Table 3). Depending on the source elevation, the uncertainty contribution for the elevation gain may also be non-trivial (particularly for the LMT) and adds in quadrature to the DPFU error to give the SEFD error budget. The gain curve error budget is obtained from the propagation of errors on the polynomial fit parameters in Equation (7), and is also itself elevation-dependent. We assume that the uncertainty in $T_\mathrmsys^* $ is negligible as it is the variable measured closest to the individual VLBI scans and the accuracy of the chopper method is well studied (see Section 6.1.5, Kutner 1978 ; Mangum 2002). The measurement uncertainties associated with pointing or focus errors are not folded into these error budget estimates as they are not easily quantifiable a priori

Table 3. Station-based SEFD Percentage Error Budget during the 2017 Campaign, Assuming Stable Weather Conditions and Nominal Pointing and Focus (Subdominant Effects from $T_\mathrmsys^* $ Measurements and Sideband Ratios are not Shown

aThe range in the budget at the JCMT is the result of a larger uncertainty in the calibration during daytime observing, due to its aperture efficiency time dependence. bThe error budget for SPT and LMT are lower limits due to uncharacterized losses, see Section 6.1.5. cThe range in the budget at the SMA is due to a larger uncertainty in the phasing for weaker sources. dALMA uncertainty is a lower limit from systematics caused by the assumed source flux density during QA2 calibration.

For all single-dish stations, the DPFU uncertainty is estimated by the standard deviation in $\eta _\rmA$ from a distribution of planet measurements added in quadrature to the uncertainty in the model brightness temperatures assumed for the planets. The scatter in planet measurements reflects changes in telescope performance with varying weather conditions, and thus it encompasses possible fluctuations in the mean value assumed during the observing window. An exception is the JCMT during daytime observing, where $\eta _\rmA$ has a time dependence parametrized by a fit of a Gaussian component dip as a function of local time, described in a technical memo (Issaoun et al. 2018). The uncertainty in $\eta _\rmA(t)$ is determined through the propagation of the errors on the fit parameters via least-squares fitting. Individual uncertainty contributions of the various components and the resulting percentage SEFD error budget for each EHT station during the 2017 April observations are listed in Table 3. Site-by-site derivations of flux density calibration uncertainties during the EHT 2017 campaign are given in Janssen et al. (2019b).
6.1.4. Phased-array Calibration

The phased arrays combine the total collecting area of all their dishes into one virtual telescope. This depends on precise phase alignment of the signals, with an accuracy that is captured by the phasing efficiency $\eta _\mathrmph$ (see Appendix in Paper II)
Equation (9)

The phasing efficiency contributes to the aperture efficiency of the phased array, and reflects the ratio of source signal power116 observed by the phased array, versus that observed by a perfectly phased array. The complex gains γi (as in Equation (2)) are taken over all the dishes in the phased array, and have zero relative phase in the case of ideal phasing (ηph = 1).

The phasing efficiency as defined above is valid when the signals being combined are optimally weighted by the effective collecting area of each antenna, $A_i,\mathrmeff\sim 1/\mathrmSEFD_i$. Then the SEFD of the phased array is
Equation (10)

Both SMA and ALMA use equal weights for the formation of the sum signal. Due to their homogeneity, Equations (9) and (10) are excellent approximations.

At the SMA, the phasing efficiency ηph is estimated from self-calibrated phases to a point-source model (Young et al. 2016). Phases for each dish of the connected-element array are calculated online once per integration period, which varies in the range of 6–20 s depending on the observing conditions, and the same phases are fed back as corrective phases for beamforming the phased array. The DPFU for the individual antennas that comprise the SMA are well characterized at 0.0077 K/Jy, with ηA = 0.75, and the 6 m dishes have a flat gain curve at 230 GHz, which is near the lower end of their operating frequency range (Matsushita et al. 2006). An SEFD for each antenna is calculated from DSB $T_\mathrmsys^* $ measurements taken regularly at the time of observing. The overall SEFD for the SMA phased array is then estimated via Equation (10).

For ALMA, both amplitude and phase gain for each dish are solved during the offline QA2 processing of interferometric ALMA data, under an assumed point-source model with known total flux. The SEFDs of individual antennas are thus determined through amplitude self-calibration, automatically accounting for system noise and efficiency factors but sensitive to errors in the source model. Because ALMA data has the additional complication of linear-to-circular conversion, the phased-sum signal SEFD is determined via the full-Stokes Jones matrix of the phased array, as computed by PolConvert (Equation (15) of Martí-Vidal et al. 2016). By convention, QA2 sensitivity tables place all phasing-related factors into the $T_\mathrmsys^* $ component of Equation (3), allowing DPFU to assume a constant value corresponding to a single ALMA antenna. Further details are provided in Section 6.2.1 of Goddi et al. (2019).

During the EHT 2017 observations, ηph was above 0.8 for 80% (ALMA) and 90% (SMA) of the time. Poorer efficiency at both sites is associated with low elevation and increased atmospheric turbulence. At ALMA, phase corrections are calculated online by the telescope calibration system and applied to the array with a loop time of 18 s (Goddi et al. 2019). At the SMA, integration times at the correlator can be as short as 6 s, but longer intervals are used if needed to build S/N. The corrective phases are passed through a stabilization filter before being applied, resulting in an effective loop time of 12–40 s for the SMA. Phasing at both sites suffers when the atmospheric coherence timescale becomes short with respect to the loop time. To minimize the impact, both arrays are arranged in tight configurations during phased array operations.

The uncertainty on the ηph measurement at the SMA is estimated to be 5%–15%, and depends primarily on the S/N of the gain solutions. The SMA (usually with six 6 m dishes phased) has considerably less collecting area than ALMA (usually with 37 12 m dishes phased) to use for solving phase gains. For weaker sources, the uncertainty in estimating corrective phases at the SMA and in calculating the phasing efficiency can be considerable. The assumed flux of the point-source model used to self-calibrate ALMA during QA2 has a quoted 10% systematic uncertainty in Goddi et al. (2019). The uncertainties from self-calibration and phasing are uncharacterized, therefore the uncertainty of 10% for the derived SEFD of the ALMA phased array is considered a lower limit. Errors from the use of a point-source model for M87 and 3C 279 during gain calibration are expected to be small in comparison to these values. The individual uncertainties and error budget for the phased arrays are shown in Table 3.
6.1.5. Limitations of a Priori Calibration

Although the DPFU is typically represented as a single value measured under good performance conditions, a station's efficiency is expected to vary with temperature, sunlight, and quality of pointing and focus. We have attempted to characterize specific time-dependent trends such as daytime dependence for the JCMT, but other factors are very difficult to decouple from the overall station behavior and associate with individual scans. Specific efficiency losses during scans, in particular due to lack of pointing/focus accuracy, are not included in the a priori amplitude calibration information for single-dish sites and remain in the underlying correlated visibilities. Therefore, the a priori error budget in Table 3 is only representative of global station performance and cannot be estimated for individual scans. In addition to a priori calibration, a list of problematic scans, where the station performance is known to be poor and the error budget is thus assumed to be undetermined, is passed on to analysis groups. These losses can be corrected in imaging and model fitting via self-calibration methods and amplitude gain modeling (Papers IV, VI).

The uncertainty in the chopper calibration is also difficult to quantify, as we do not know the true coupling of the hot load to the receiver (including spillover and reflection) and thus its effective temperature is uncertain (Kutner 1978 ; Jewell 2002). One of the key assumptions of the chopper method is the equivalence (to first order) of the hot load, ambient, and atmospheric temperatures, which allows for the correction of the atmospheric attenuation in the signal chain. Any deviation from this assumption in the $T_\mathrmsys^* $ measurements may introduce systematic biases. This can be partly mitigated by frequent measurements and monitoring of the DPFU under stable weather conditions and nominal telescope performance, to offset any significant scaling from temperature assumptions. The majority of stations in the EHT use a two-load (hot and cold loads) chopper method, with temperature refinement from atmospheric modeling, to measure the receiver noise temperature, and have radiometers to monitor the atmospheric opacity, which typically reduces uncertainty in the chopper calibration down to the 1% level (Jewell 2002 ; Mangum 2002). In contrast, the LMT and SPT used a single-load chopper method in 2017, leading to a larger error contribution estimated at the 5%–10% level minimum (Jewell 2002 ; Mangum 2002) ; with an error that grows rapidly at high line-of-sight opacity.

Limitations in accuracy of the a priori calibration may also come from the cadence of DPFU and $T_\mathrmsys^* $ measurements, typically performed between scheduled VLBI scans or outside VLBI observing altogether. The changing dish performance during the VLBI observations and intra-scan atmospheric variations are not typically captured by these measurements, although frequent pointing and focus calibration is done during the observations to keep an optimal performance. Furthermore, the time cadence varies across participating stations due to different chopper calibration setups, pointing, and focus needs, and allocated time for the EHT observing campaign. It is therefore not atypical for self-calibration corrections in downstream analysis to slightly deviate from the attributed amplitude error budget. To maximize mutual coverage, many stations are pushed past their nominal operating conditions during EHT observations, such as the LMT or the JCMT in the early evening local time due to surface heating and instability, and the SPT at extremely low elevation and high winds. For those stations and conditions, we expect residual gains to deviate significantly from the a priori amplitude error budget. A more detailed discussion of a priori calibration uncertainties and limitations is given in Issaoun et al. (2017a).
6.2. Network Calibration

Network calibration is a framework to estimate visibility amplitude corrections at some sites by utilizing array redundancy and supplemental measurements of the total flux density of a source (Fish et al. 2011 ; Johnson et al. 2015 ; Blackburn et al. 2019). It allows for absolute amplitude calibration of intra-site baselines and tightens consistency between simultaneous baselines to co-located sites when both sites are observing (see the bottom panels of Figure 10). It makes fewer assumptions than other techniques such as self-calibration and does not assume a specific compact source model.

Network calibration makes two related assumptions. The first is that redundant baselines in the EHT array (e.g., ALMA–SMA and APEX–JCMT) share the same model visibility. The second is that co-located sites provide a zero-baseline interferometer (e.g., ALMA–APEX), with a corresponding visibility that is a positive real number equal to the total flux density V0. We express the measured visibility Vij on a baseline between sites i and j as
Equation (11)

where $ \mathcal V _ij$ is the true visibility on that baseline, and gi and gj are the station-based residual gains assuming no thermal noise (the latter introduces uncertainty in the estimated gains).

Given two co-located sites i and j, we can solve for the amplitudes of their gains using a third remote site, using the assumptions above, $ \mathcal V _ik= \mathcal V _jk$ and $ \mathcal V _ij=V_0$. In the absence of thermal noise,
Equation (12)

Note that network calibration only provides gain estimates for those sites with a co-located partner.

In practice, thermal noise affects the accuracy of gains estimated using Equation (12). To optimize network calibration, we use all sets of baselines between co-located sites and distant sites and solve for the set of unknown model visibilities $ \mathcal V _ij$ and station gains gj by minimizing an associated χ2. Specifically, for each solution interval, we minimize
Equation (13)

where σij is the thermal uncertainty on Vij. We implemented network calibration via this minimization procedure within the eht-imaging library (Chael et al. 2016, 2018).

For the EHT 2017 April observations, network calibration is performed on frequency-averaged visibility UVFITS data coherently time-averaged over 10 s solution intervals. Both parallel-hand visibility components (further referred to as RCP/LCP or RR/LL) are network-calibrated with shared gain coefficients, using the total intensity measured by the ALMA array as V0 (Goddi et al. 2019). The assumed flux density values per band on each observing day are reported in Table 4 for both M87 and 3C 279. For each source, a constant flux density is adopted per day, as both sources vary by <5% within an observation, well within the 10% flux density calibration error budget of ALMA measurements.

Table 4. Total Flux Density Estimates used for Network Calibration
Note. The flux density values used for network calibration in SR1 come from the initial ALMA QA2 data release (2017 October), with a quoted uncertainty of 10%. Updated values are reported in Appendix B of Goddi et al. (2019) and are approximately 10% higher than shown here.

Network calibration enables absolute amplitude calibration of sites with a co-located partner (ALMA and APEX, SMA and JCMT) when both sites are operating, to the limit of thermal noise to the strongest remote stations. The remaining isolated sites (SMT, LMT, SPT, and PV) are unaffected by network calibration.

Following all calibration steps, Stokes I total intensity components correspond to
Equation (14)

For JCMT, which is a single polarization station, we use the available RCP or LCP component as a proxy for the Stokes I value. This corresponds to assuming zero contribution from Stokes V circular polarization.

Most assumptions in the network calibration procedure are valid for all targets observed by the EHT. However, the assumption that co-located sites act as a true zero-baseline interferometer may not hold for sources with extended structure, such as M87. The distance between the SMA and the JCMT is 160 m, giving a resolution on that baseline of 1farcs6. The distance between ALMA (phase center) and APEX is 2.6 km, giving a resolution on that baseline of 0farcs1. For very compact sources, such as the quasar 3C 279, these two baselines both see point-like sources. For sources with extended structure, such as M87 and its large-scale jet, these two baselines will see slightly different structure. For example HST-1, a bright feature in the jet of M87 at just 0farcs8 from the radio core (Chang et al. 2010), produces a different response on both intra-site baselines. However, HST-1 has ≤1% of the total core flux density of M87 as measured by ALMA (Table 4), so its effect on the network calibration gain solutions for ALMA and APEX is insignificant in comparison to the 10% uncertainty on the ALMA total flux density estimates.
7. Final Data Products
7.1. Data Release Specification

The SR1 data on M87 and 3C 279 represent a subset of a more comprehensive engineering release (ER) data production (ER5) for the EHT 2017 observations, after extensive internal validation and review. ER5 data are themselves derived from a fifth revision (Rev5) correlation data product. Information about accessing SR1 data and the software used for analysis can be found on the Event Horizon Telescope website's data portal.117

The sequence of correlation and engineering releases represents a year-long effort of identifying and mitigating data issues, and developing new software and procedures ; first on secondary targets for ER1–ER3 and then including EHT primary science targets for ER4–ER5. Each internal engineering data release was subject to an independent review by a panel of experts not involved in the data preparation, before being made available for downstream analysis, including imaging and model fitting. The HOPS data set was present in all engineering releases, receiving the most extensive review and internal validation. AIPS data were included in ER1 for an initial comparison to HOPS on EHT 2017 secondary targets, and in ER5 for comparisons with both HOPS and the newly added CASA data set.

The final data products at the end of the calibration and reduction pipelines provide a uniform and reliable data set for scientific analysis that has been reduced and simplified by the removal of bad data (failed observations), and after compensating for non-astrophysical systematics. The data reduction process is automated and makes only minimal assumptions about the source : (1) that the target is mostly compact, and (2) that it has known a priori large-scale structure and total flux density (e.g., from ALMA observations). The calibration of systematics is therefore limited by an inability to jointly fit source parameters along with gains, but this pathway avoids introducing any strong model assumptions during the data preparation.

In addition to the raw correlator output, three levels of successive data reduction are provided, representing the assumptions made during calibration. The first level (1) includes only the phase calibration provided during fringe fitting, after which data can be averaged. At this stage, the data represent correlation coefficients and are the most fundamental data product for the formation of closure phases and closure amplitudes. This is followed by (2) data that has been brought to a physical amplitude scale (Jy) through a priori flux density calibration, and then (3) network amplitude calibrated using a priori assumptions about large-scale source structure and total flux density. The time–frequency resolutions of the various data products are presented in Table 5, and generally exceed what is needed to capture source structure. This resolution is chosen to allow for a manageable data volume while still providing flexibility for downstream time–frequency averaging as well as the fitting of any residual systematics through additional model-dependent techniques such as self-calibration

Table 5. Data Products Available in SR1
Note. Integration time Δt and frequency averaging windows Δν are given, as well as total data volumes for low- and high-band subsets, which have slightly different coverage

The SR1 data release includes products of all three fringe-fitting pipelines. The HOPS pipeline data product is designated as the primary scientific EHT data set, given the degree of vetting it has received during an iterative process of five engineering releases and a current performance advantage at low S/N. The CASA and AIPS data sets are used for validation, including direct data cross-comparisons as well as validation of downstream analysis results. Each data product is provided in UVFITS format. The choice of format was motivated by the need for common output across all pipelines, and easy loading, inspection, and imaging in all software used in the downstream analysis efforts and via readily available Python modules. A suite of metadata accompany the release, such as the ANTAB tables used for a priori calibration, documentation and validation tests for each processing and calibration stage, assessment of derived calibration solutions, and suggested flagging information from investigations of station performance.

The first science release only provides calibrated Stokes I (total intensity) products for M87 and 3C 279. A summary of the data set content and S/N statistics is shown in Table 6, and a cumulative histogram of the Stokes I component S/N in the fully averaged data set is shown in Figure 11. A median reported thermal uncertainty is about 7 mJy on non-ALMA baselines and, remarkably, only about 0.7 mJy on baselines to ALMA for Stokes I single-band scan-averaged visibilities. In this first science release, the issue of polarimetric leakage calibration and correction is not addressed. Leakage has a relatively small influence on the total intensity and it is sufficient to parameterize the effects of leakage as a systematic source of non-closing errors (see Section 8). Future EHT results concerning polarimetry and other Stokes components will necessarily involve leakage calibration.

Figure 11. Cumulative histogram of Stokes I S/N in the HOPS data set for all observations of M87 and 3C 279, using fully averaged data. Solid curves represent baselines to ALMA, while the dashed curves show all other baselines

Table 6. Content of the SR1 Data Set

Note. Data products in the fully averaged SR1 data set. The shared data set is composed of only those detections that are reported by all three pipelines. The max data set is a theoretical maximum calculated assuming perfect realization of the observation schedules. The full set of all closure quantities is shown, which is used to estimate systematics in Section 8 ; as well as the non-redundant set, which reflects the actual number of unique phase and amplitude degrees of freedom measured by the (uncalibrated) array.

7.2. Closure Quantities

While the data release consists of reduced complex visibilities, derivative closure data products are particularly important for downstream data analysis, as well as for the description of data uncertainties. Unlike complex visibilities, closure quantities are robust against station-based gain errors. They are, however, susceptible to systematic non-closing errors, discussed in Section 8. For the needs of this Letter, we only provide brief definitions and description of conventions.

We define a closure phase formed from baseline visibilities on a closed triangle ijk as
Equation (15)

with a corresponding uncertainty
Equation (16)

where Sij is the estimated S/N, associated with the Vij visibility, that is
Equation (17)

Formation of closure phase cancels the station-based gain factors that appear in Equation (2). In the case of visibility amplitudes, the gain factors can be similarly canceled by the formation of the log closure amplitude, defined as
Equation (18)

for a quadrangle ijkℓ, where "ln" is a natural logarithm and Aij represents debiased amplitude
Equation (19)

The associated uncertainty of log closure amplitude is
Equation (20)

Uncertainties reported in Equations (16) and (20) are calculated based on propagation of thermal visibility errors and are strictly correct in a high S/N limit, where distributions of both types of closure quantities are well approximated with a normal distribution. The number of closure quantities that can be derived from SR1 visibilities is given in Table 6. The numbers describe a fully averaged (i.e., scan and 4 GHz band-averaged) data set. We give the number of all closure quantities, corresponding to the full (or maximal) set formed from all possible loops over three or four stations in every scan. The full set has a balanced representation of baselines, and is used to estimate systematic errors in Section 8.4. Elements of a maximal set are, however, not independent (the set is highly redundant). We also provide the number of closure products in the non-redundant (or minimal) set. This is a reduced subset that captures all the available information in the closure quantities. Selection of a particular non-redundant data set is not unique and in general non-trivial (L. Blackburn et al. 2019, in preparation).

When intra-site baselines are present in the array, a special set of trivial closure quantities can be formed. Such closure phases and log closure amplitudes are zero by construction, within statistical uncertainties. While they do not carry any direct information about the source compact structure, they are useful for network calibration (Section 6.2) and the characterization of uncertainties, presented in Section 8.
7.3. Data Features

Certain properties of the reduced data can be directly observed in the behavior of visibilities and closure quantities. The data indicate remarkable persistent features in the structure of the M87 compact emission, as well as source structural variability on a timescale of days. In this section we give a rudimentary interpretation of these features. The implications of these basic features for the imaging, modeling, and scientific interpretation of the source structure are explored in companion Letters (Papers I, IV, V, VI).

Figure 12 shows the aggregate baseline coverage for EHT 2017 observations of M87 and 3C 279 via the HOPS pipeline. The coverage and data properties via the other two pipelines are comparable. Our shortest baselines are between co-located sites (SMA–JCMT and ALMA–APEX). These baselines are sensitive to arcsecond-scale structure, while our longest baselines are sensitive to microarcsecond-scale structure. For M87, the highest resolution (fringe spacing of 25 μas) is achieved in the east–west direction on baselines joining the Hawaiʻi stations to PV, while for 3C 279 the highest resolution (fringe spacing of 24 μas) is achieved in the north–south direction, on PV and SMT baselines to the SPT.

Figure 12. Aggregate (u, v) coverage for M87 (top panel) and 3C 279 (bottom panel) for the 2017 April observations, comparable for all three pipelines. Co-located sites (SMA/JCMT and ALMA/APEX) result in redundant baselines. The dashed circles show baseline lengths corresponding to fringe spacings of 25 and 50 μas.

The 2017 observations led to detections on all baselines for M87. A longer averaging time (up to scan duration) is enabled by the atmospheric phase corrections performed by all three pipelines. Figure 10 (top-left panel) shows the S/N as a function of projected baseline length for M87 on April 11, for fully averaged data. A similar distribution is also shown for 3C 279 in Figure 10 (top-right panel), with around an order of magnitude difference due to the higher total flux density of 3C 279 compared to M87 (Table 4).

The correlated flux density for M87 on April 11 after amplitude and network calibration is shown in Figure 10 (bottom left panel). There is a pronounced secondary peak in the visibility amplitudes with two minima on either side, interpreted as visibility nulls. The first of these nulls occurs at 3.4 Gλ. It is steep on the east–west oriented LMT and SMT baselines to the Hawaiʻi stations, and shallower on the north–south oriented ALMA and APEX baselines to LMT at the same baseline length. The second null in amplitude is observed at 8.3 Gλ, on the east–west oriented PV baselines to the Hawaiʻi stations. The correlated flux density for 3C 279 on April 11 after amplitude and network calibration is also shown in Figure 10 (bottom right panel). The trend in the visibility amplitudes is clearly different from the trend seen in M87. 3C 279 appears to have more complex structure on long baselines, and the structure varies with baseline position angle.
7.3.1. Persistent Structural Features

Figure 13 shows the correlated flux density after amplitude and network calibration as a function of baseline length for all four days of observations of M87 via the HOPS pipeline. The network-calibrated amplitudes show broad consistency over different days, and are consistent between pipelines (Section 8.5). The majority of notable low-amplitude outliers across days are due to reduced efficiency of the JCMT or the LMT on a select number of scans (caused by, e.g., telescope pointing issues or surface instability). Although the amplitudes of these data points are low, closure information remains stable and is unaffected by station gain. This is shown by comparing the erratic amplitudes on the LMT–SMT baseline in Figure 13 (cluster of points at about 1 Gλ) with the smooth trends in closure phase for the ALMA–LMT–SMT triangle (Figure 14, top left) and in closure amplitude for the ALMA–LMT–APEX–SMT quadrangle (Figure 14, top right).

Figure 13. Correlated flux density of M87 as a function of projected baseline length for all four days of observations, from HOPS data that has been fully averaged. Outliers are due to reduced performance of the LMT or the JCMT. Error bars denote ±1σ uncertainty from thermal noise

Figure 14. Selection of M87 closure phases (left and middle columns) and log closure amplitudes (right column) as a function of Greenwich Mean Sidereal Time (GMST) for all four observed nights from the HOPS data set. Plotted uncertainties denote ±1σ ranges from thermal noise in the fully averaged data

The secondary peak in amplitude and the location of the two nulls are persistent for all four days. These signatures in the visibility amplitudes suggest that the source is not changing dramatically over several days, is compact with a characteristic spatial scale of lesssim50 μas, and exhibits similar structure over a range of baseline position angle. Long baselines with various orientations lie in a stable trend along the second peak, and a minimum in amplitude at 3.4 Gλ is seen on both the east–west and north–south oriented baselines.

While the overall trend may indicate a compact and nearly circularly symmetric structure that is stable in time, a more detailed inspection of the data set suggests the presence of a slight anisotropy, also made evident by multiple measurements of non-zero closure phase. This can be seen comparing the ALMA/APEX–LMT and SMA/JCMT–LMT amplitudes in Figure 10 (bottom left). Both baselines probe a (u, v) distance of about 3.4 Gλ, but they have a very different, nearly perpendicular orientation (Figure 12). Flux density measured on the north–south oriented ALMA–LMT baseline is a few times larger than that for the east–west oriented SMA–LMT baseline. These properties translate to striking source features in imaging and model fitting, presented in Papers IV and VI, respectively.
7.3.2. Time Variability

M87 was observed on the two consecutive nights of April 5/6 and again four nights later for the two consecutive nights of April 10/11. We observe clear indications of modest source evolution between the two pairs of nights, and broad consistency within each pair. The evolution can be seen particularly well in the behavior of robust closure quantities.

Across the full set of closure quantities, some closure phases formed by wide and open triangles (e.g., ALMA–LMT–SMA, Figure 14, bottom left) show different closure phase trends between the first pair of days and the second pair. Additionally, the east–west oriented LMT–SMA–SMT triangle shows different closure phase trends between the two pairs of days (Figure 14, bottom center), but the equivalent triangle in the opposite orientation, LMT–PV–SMT, shows no such trend (Figure 14, top middle).

Strong night-to-night variability of closure phases is associated with baselines probing (u, v) components close to the first visibility amplitude null, where visibility phases are particularly sensitive to small structural changes. The LMT–Hawaiʻi baselines are particularly affected. Rapid swings of closure phase, as large as 200° in 2 hr, are found for the LMT–SMA–SMT triangle, but exclusively for the latter pair of nights on April 10/11. Triangles that do not probe the 3.4 Gλ null location indicate less variability, e.g., ALMA–LMT–SMT or LMT–PV–SMT. Despite larger uncertainties, similar trends are seen in log closure amplitudes (right column of Figure 14). In particular, significant differences between the two pairs of nights can be seen on the ALMA–LMT–APEX–SMA quadrangle, while the ALMA–LMT–APEX–SMT quadrangle gives more consistent values.
8. Data Validation and Systematics

In this section, we summarize data set validation tests, performed using diagnostic tools developed in the eat library framework and focusing on the properties of the final network-calibrated data products. The section is structured as follows. In Section 8.1, we discuss internal consistency tests performed during the fringe-fitting stage. In Section 8.2, the accuracy of reported thermal uncertainties is tested. In Section 8.3 we investigate the robustness of data products against decoherence with increased coherent averaging time. Section 8.4 presents internal consistency tests in each pipeline and provides estimates for the magnitude of non-closing systematic errors, which become important considerations in the error budget for high S/N measurements. Finally, in Section 8.5, direct comparisons between the three pipelines are given. A more comprehensive discussion of these automated data validation procedures is given in a technical memo (Wielgus et al. 2019).
8.1. Fringe Validation

During fringe detection, a number of basic tests are performed on the data that check for data integrity, false fringes, and the overall self-consistency of the detected fringe solutions and measured correlation coefficients. These fringe validation tests reflect the internal validation of each pipeline, as opposed to the overall statistical validation and cross-comparisons presented in the following subsections. In addition to identifying issues with the fringe-fitting pipelines themselves, consistent review of data products throughout engineering data production played an important role in characterizing upstream issues with the data and their correlation.

Figures 15 and 16 show two fringe solution consistency tests that are run as part of an automated test suite at each stage of the HOPS pipeline (Section 5.1, with details in Blackburn et al. 2019). In Figure 16, as well as in subsequent plots of distributions, the number of 3σ outliers and the size of the tested sample for each source are provided. The dashed black curve indicates a standard normal distribution with zero mean and unity variance.

Figure 15. Measured residual relative delays for selected M87 baselines on April 11, reported by the HOPS pipeline (Section 5.1) prior to explicit fringe closure. The top panel shows smooth delay trends over the night for both parallel hands, LL (dots) and RR (crosses). The bottom panel shows the sum of the delays on this closed triangle, which is consistent with the expected value of zero to within statistical errors. After fringe closure, RR and LL are set to the same delay, and closure delay is zero by construction

Figure 16. Delay and delay-rate differences between RR and LL parallel-hand fringe detections ($\rmS/\rmN\gt 7$) from the HOPS pipeline in units of thermal measurement uncertainty, along with the fraction of 3σ outliers. A small amount of systematic error is added in quadrature to delay (1 ps) and delay-rate (0.1 fs/s). The RR−LL differences are formed before fringe closure (after which they are zero by construction). These small differences demonstrate that there are no false fringes and that the relative difference between RCP and LCP feeds is stable at each site. Combined errors $\sigma ^2=\sigma _\mathrmRR^2+\sigma _\mathrmLL^2$ are used.

The HOPS pipeline baseline-based fringe solutions (prior to the global enforcement of fringe closure) show smooth evolution across each observing night and consistency across four polarization products, which are independently fit. Delay calibration assumes a constant RCP versus LCP delay offset per night at each station, which is verified by the stability of RR−LL delays to within thermal measurement error. Independently measured delay-rates between polarizations are also consistent to within thermal error. The lack of large-deviation outliers in these fringe solution consistency tests is a strong indication that there are no false fringes or corrupted measurements above the detection threshold.
8.2. Thermal Error Consistency

Thermal error plays an essential role in the VLBI uncertainties, both for the visibilities as well as for the derivative closure quantities, for which uncertainties are simply propagated from the visibility errors (Section 7.2). An accurate accounting of thermal noise is essential for deriving faithful model-fitting uncertainties, and for correct noise debiasing in the case of incoherently averaged amplitudes (Rogers et al. 1995). Fundamentally, thermal uncertainty σth in the real and imaginary components of the dimensionless complex correlation coefficient rij (Equation (1)) can be estimated from first principles. Under the assumption of a stationary white noise process at each antenna
Equation (21)

where Δt is the integration time, Δν is the averaged bandwidth, and ηQ is the factor that accounts for quantization efficiency. The thermal uncertainties reported by each pipeline depend on the self-consistent tracking of scale factors through data conversion and calibration, as well as accounting for the data weights and bandpass response over the averaging windows in Equation (21).

The UVFITS file format formally associates a weight w for each visibility measurement, with associated reported uncertainty $\sigma _\mathrmrep\equiv 1/\sqrtw$. In the ideal case, σrep properly represents thermal uncertainties, σrep = σth. For the HOPS and CASA pipelines, the thermal uncertainty is determined from first principles. However, the weights for the AIPS pipeline require a large scaling factor to be applied for their final output to ensure that σrep = σth.118 We derive this correction factor using the scatter from differences in adjacent high-S/N closure phases. For CASA, the direct interpretation of reported weights as $1/\sigma _\mathrmth^2$ also leads to a small bias, resulting in underestimation of σth by approximately 5%, as estimated by the closure phase-differencing technique.

We test the scan-by-scan accuracy of σrep via a comparison with an empirical estimator σemp, fitting the moments of visibility amplitudes distribution. We estimate σemp for each scan, baseline, band, and polarization combination, by using moment matching of the visibility amplitude distribution over the scan duration (Wielgus et al. 2019). Each ensemble is composed of, on average, 900 individual visibility amplitude measurements. Figure 17 shows distributions of (σrep − σemp)/σrep for all three SR1 processing pipelines, using the 5399 ensembles shared by the pipelines. The median of each distribution (med) is given in the legend of Figure 17, and shows ensemble values that are roughly consistent with the alternative closure phase differencing test. The distributions have large tails at negative values, where the empirical uncertainty exceeds the reported uncertainty. These tails are predominantly from high S/N scans with significant true intra-scan amplitude gain variation, which inflates σemp and biases the median slightly downward. The amplitude distribution test provides a scan-by-scan estimate of the thermal error and is most reliable at low S/N ; while the closure phase differencing test is appropriate at high S/N, longer integrations, and under the assumption of a constant scaling factor for σrep/σemp. The median absolute deviation (mad) is given as a measure of the associated uncertainties on σrep, and is fundamentally limited by the finite sample size of the estimator. From these metrics, the HOPS data set provides the most accurate accounting of thermal uncertainty.

Figure 17. Joint M87 and 3C 279 histograms of differences between reported thermal uncertainties σrep, and empirically estimated uncertainties σemp. The dashed black histogram shows the limiting accuracy (high S/N, zero variance of σrep) of the empirical estimator from the finite number of 0.4 s measurements available per scan. Median (med) and median absolute deviation (mad) of each distribution are given

8.3. Temporal Coherence after Calibration

All three data pipelines correct for changing visibility phase over scans, both in the correction for a linear drift via the delay-rate and in corrections for stochastic, station-dependent wander from atmospheric contributions (see Section 5). Although these corrections do not provide absolutely calibrated visibility phase, they eliminate differential wander on short timescales, allowing the visibilities to be coherently averaged for longer intervals than the atmospheric coherence time. An imperfect phase correction will lead to decoherence in the averages, which, in severe cases, may introduce non-closing amplitude errors.

To evaluate the performance of the phase correction algorithms, we compute two quantities for each scan : the amplitude Ascan resulting from coherent averaging visibilities over the full scan (3–7 minutes) and subsequent debiasing (Equation (19)), and the amplitude $A_2\rms$ obtained from 2 s coherently averaged visibility segments that were subsequently incoherently averaged over the full scan (Rogers et al. 1995 ; Johnson et al. 2015). The ratio $A_\mathrmscan/A_2\rms$ then quantifies the loss in amplitude from uncorrected phase fluctuations within scans.

Figure 18 shows cumulative histograms of $A_\mathrmscan/A_2\rms$ for a common subset of 4688 ensembles (subsets of unique scan, baseline, band, and polarization) shared between pipelines, with an $\rmS/\rmN\gt 7$ threshold. While small errors in the estimated thermal noise have little effect on the S/N of coherent averages, they can significantly affect the outcome of incoherent averaging. Thus, only for this particular test, we applied a fixed correction factor of 1.05 to CASA thermal noise estimates σrep before incoherent averaging, to account for the small bias in this pipeline discussed in Section 8.2. For all three pipelines, the coherence of the phase-corrected data is significantly better than that of data with no atmospheric phase correction (the gray curve in Figure 18 ; see also Figure 2 of Paper II), with over 90% of the calibrated data experiencing an amplitude loss of under 10%. These results demonstrate that coherent averaging over scans is admissible for the SR1 data set, particularly in case of the HOPS data products.

Figure 18. Joint M87 and 3C 279 cumulative histograms of amplitude ratios between coherent averaging for entire scans (Ascan), and coherent averaging for 2 s before incoherent averaging over scans ($A_2\rms$). The gray histogram shows the results from the HOPS pipeline with no atmospheric phase correction applied. For each pipeline, the fraction of data with coherence above 90% is indicated

8.4. Intra-pipeline Validation

In this subsection we perform internal data consistency tests for each pipeline, in order to estimate the magnitude of systematic non-closing errors, e.g., related to the uncalibrated polarimetric leakage. For that purpose, we inspect closure phases and log closure amplitudes derived from the SR1 data set and evaluate consistency between (1) RR and LL components, (2) low- and high-frequency bands, and (3) trivial closure quantities. For each test, we derive a magnitude of residual errors, in excess to the reported thermal uncertainties. These values are then used to characterize the magnitude of non-closing errors in the data set, utilized in the downstream analysis.
8.4.1. Quantifying Residual Errors

We evaluate the characteristic magnitude of systematic errors in the SR1 data set based on tests of distributions of closure quantities. In this approach we rely on the following modified median absolute deviation statistic :
Equation (22)

where "med" denotes median, the subscript zero indicates that the raw distribution moment is estimated, and the normalization factor of 1.4826 scales the result so that it acts as a robust estimator of standard deviation for a normally distributed random variable Y with zero mean. We assume total uncertainties σ associated with closure quantities to be well approximated by
Equation (23)

such that the total uncertainty consists of the known a priori thermal component σth and a constant systematic non-closing error s, of unknown magnitude, added in quadrature. We then solve for the characteristic value of s that enforces
Equation (24)

where σ is the total uncertainty associated with X. As an example, for RR–LL consistency of closure phases we have
Equation (25)

We exclude low S/N data (S/N < 7), for which the normal distribution approximation does not hold well.
8.4.2. RR–LL Consistency

Consistency of closure quantities derived from RR and LL visibilities, matched for the same scan, baseline, and band, are expected to be dominated by effects related to polarimetric leakage, which remains uncalibrated in SR1 data. Assuming that some amount of leaked polarized signal mixes randomly into the parallel-hand visibilities, the degree of systematic error can be crudely approximated as
Equation (26)

where the number of baselines n is 3 for closure phases and 4 for closure amplitudes, $| D| \lt 0.1$ is a leakage D-term magnitude, and $| \brevem| $ is a typical fractional interferometric baseline polarization (i.e., fractional linearly polarized correlated flux density relative to total intensity) ; see Johnson et al. (2015). If a characteristic $| \brevem| \lt 0.2$ is assumed, these upper bounds translate under Equation (26) to <2fdg8 for the closure phase systematic uncertainty and <5.7% for the closure amplitude uncertainty. The results of the SR1 errors estimation by normalizing $\mathrmmad_0$ are summarized in Table 7. The estimated errors are consistent with the simple upper limit given by Equation (26) and roughly consistent between all data reduction pipelines. While for the high S/N source 3C 279 the leakage related errors may dominate over the thermal errors, they remain strongly subthermal for M87

Table 7. Systematic Errors in SR1 Data Set

Note. Characteristic magnitudes of systematic errors, estimated using the subset of data shared by all three pipelines. Scan-averaged single-band data. Numbers in parentheses represent characteristic systematic errors in units of thermal noise.

8.4.3. Frequency Bands Consistency

Comparisons between low-/high-frequency bands may reveal the presence of band-specific systematics, including frequency-dependent polarimetric leakage. Apart from those, source spatial structure and spectral index both may add a small contribution. The estimated magnitudes of systematic errors found for closure phases and log closure amplitudes are given in Table 7. For all pipelines, the magnitude of characteristic closure phase inconsistency was found to be about 0.5 times the thermal uncertainty for M87 and about 1.5 times the thermal uncertainty for 3C 279 (scan-average, single-band/polarization). For 3C 279 systematic uncertainties strongly dominate over the thermal scatter, and this should be taken into account before the direct averaging of frequency bands.
8.4.4. Trivial Closure Quantities

The intra-site baselines ALMA–APEX and JCMT–SMA provide the EHT array with multiple "trivial" closure triangles and quadrangles. Ideally, these trivial closure phases and trivial log closure amplitudes should be equal to zero, but this is not precisely true in the presence of polarimetric leakage. Furthermore, the small but finite length of intra-site baselines leads to measurements that are susceptible to contamination from large-scale structure, breaking the assumptions of a trivial closure quantity. This particular aspect is a concern for M87 and its large-scale jet. The estimated characteristic magnitude of systematic errors in trivial closure phases is given in Table 7. While for 3C 279 the magnitude of about 1° can be fully explained by polarimetric leakage, M87 systematics are inconsistent with limits given by Equation (26), suggesting the presence of an additional source of error. We illustrate the systematic-error fitting procedure in Figure 19, in which 3C 279 trivial closure phase distribution is shown, before and after adding the systematics, and is estimated to be about 1° consistently for all processing pipelines.

Figure 19. Normalized distributions of trivial closure phases for 3C 279 in three data reduction pipelines, before (blue) and after (red) accounting for the residual systematic uncertainties. Numbers indicate the fraction of 3σ outliers

8.4.5. Systematic Error Budget

Based on values reported in Table 7, we conclude that, for a single band, systematic errors of 3C 279 measurements are dominated by polarimetric leakage and its contribution can be approximated with characteristic values of about 1fdg5 for closure phases and 0.03 for log closure amplitudes. For M87, leakage is not nearly as important, and other subtle effects like polarimetric calibration uncertainties may influence the total systematic error budget. Suggested systematics are 2° for closure phases and 0.04 for log closure amplitudes. For each test of closure phases and log closure amplitudes summarized in Table 7, we show related distributions in Figure 20. Errors in Figure 20 were inflated according to the above recommendation for systematic errors. A standard (zero mean, unit variance) normal distribution is shown with a dashed line. The match between the empirical distributions and the normal distribution indicates that the addition of the systematic uncertainties allows for the approximate capture of the total data uncertainty. Under the assumption of independent baseline errors, the closure uncertainties given in this section can be translated to 2% non-closing systematic uncertainties in visibility amplitudes and 1° of non-closing systematic uncertainties in visibility phases.

Figure 20. Closure statistics distributions after inflating errors by the amount of non-closing systematics recommended in Section 8.4.5. The plots follow the same order as the tests reported in Table 7. The dashed lines represent a standard normal distribution, and numbers show the fraction of 3σ outliers. Combined errors are used where appropriate

8.5. Inter-pipeline Consistency

Direct comparisons between corresponding data products delivered by separate pipelines allow us to quantify the degree of confidence that we may have in their properties and their dependence on specific choices in calibration procedure. Figure 21 (top) shows the distribution of visibility amplitude differences betwen the reduction pipelines, in units of their thermal uncertainty. Thermal errors represent a particular scale of interest ; however, visibilities reduced by separate pipelines are not independent variables and share the same thermal noise realization. Another useful quantity is the relative absolute amplitude difference. As indicated in Table 8, the median relative difference between the most consistent pair of pipelines, HOPS–CASA, is 3.8%, well within the budget of a priori flux density calibration (Section 6). While for 3C 279 all three pairs represent a similar level of consistency, for M87 the HOPS–CASA pair is by far the most consistent one, as indicated in Table 8. This result is consistent with known difficulties in the processing of low S/N data with the AIPS pipeline, originating from the lack of S/N to constrain a fringe solution in the two-second intervals used for fringe fitting (Section 5.3). Distributions of differences between amplitude data products are unbiased ; however, significant tails are present, with 10% of the M87 visibility amplitude data inconsistent by more than 22.8% for the most consistent pair, HOPS–CASA

Figure 21. Consistency of visibility amplitudes (top), closure phases (middle), and log closure amplitudes (bottom) between the three reduction pipelines. Scan-averaged single-band Stokes I data are used.

Table 8. Inter-pipeline Consistency of the SR1 Data Set

Note. Results given for scan-averaged single-band Stokes I data. Numbers in parentheses are given in thermal error units. The subset of data shared by all pipelines was used.

In Figure 22 we show HOPS–CASA and HOPS–AIPS scatter plots of correlation coefficient amplitude $| r_ij| $. The three pipelines demonstrate increasing levels of consistency at high S/N. AIPS shows a tendency to occasionally overestimate amplitude at low S/N, sometimes by a large factor, indicating a degree of over-tuning and acceptance of possible false fringes.

Figure 22. Scatter plots of complex correlation coefficient amplitudes for HOPS–CASA and HOPS–AIPS pairs of pipelines. Data are fully averaged, with an S/N > 1 threshold applied. For each detection, the mean rij of available RCP and LCP components in the low and high band is given. Detections only present in one of the pipelines are shown with a fixed value of 5 × 10−7 for the missing pipeline, and in some cases represent differences in the construction of a priori flags and fringe rejection strategies.

Contrary to visibility amplitudes, the distributions of closure phase and closure amplitude differences, shown in Figure 21, generally exhibit a spread at or below the level of thermal uncertainty, particularly for the HOPS–CASA pair. No significant tails are present and 90% of the M87 data remain consistent to within 0.9 standard deviations of the combined thermal error budget for HOPS–CASA (Table 8). This highlights the robustness of the closure quantities, independent of station-based gains.

Examples of closure phases for all three pipelines, for some of the triangles discussed in Section 7, are shown in Figure 23. While there is a broad consistency, HOPS is unique in reconstructing well-behaved closure phases on triangles including the LMT–SMA baseline over the full range of observations on April 11. To corroborate smooth trends and large closure phase evolution for these data, in two panels in Figure 23 we show data from a redundant JCMT triangle (JCMT and SMA are collocated). The redundant JCMT triangles show closure phases consistent with their SMA counterparts, and are more consistently reconstructed across the pipelines.

Figure 23. Comparison of M87 closure phases between the three fringe-fitting pipelines for selected triangles. April 6 is shown in the top row, April 11 in the bottom row. The pipelines are offset slightly in time for clarity (HOPS −3 minutes, CASA at the original timestamp, AIPS +3 minutes). Plotted uncertainties denote ±1σ ranges from thermal noise in the fully averaged data set. For the two Hawaiʻi triangles that demonstrate pronounced evolution on April 11 (see also Figure 14, bottom panels), we also include the corresponding redundant triangles with JCMT (which joined the array two scans earlier) as light crosses.

A bias toward zero closure phase can be seen when data are averaged in time, particularly for the AIPS data set. This is due to use of a point-source model during global fringe fitting on short time intervals (2 s for AIPS). While the individual fringe solution phases are station-based and separately close, the process biases baseline phases to zero, and closure phases generated from baseline phases averaged over multiple segments will be biased toward the point-source model. This bias is not expected in HOPS products, as HOPS fringe solutions are baseline-based and assume no structure phase for the coherent stacking of data from multiple baselines. The median bias toward zero closure phase, estimated from high S/N data at least 3σ away from zero, is about 1° for AIPS and CASA with respect to unbiased HOPS. However, while 90% of CASA data are biased by less than 4fdg9, 10% of AIPS data are biased by more than 8fdg7. See Wielgus et al. (2019) for an additional discussion of pipeline comparisons and associated systematics.

The HOPS pipeline benefited from a long period of development, extensive review, and internal validation through the suite of five engineering releases spanning a year-long data processing and calibration effort. In contrast, the AIPS pipeline has been used in two data releases as a secondary data set and the CASA pipeline, which is under active development, has recently been brought to maturity and included in ER5. Nonetheless, inter-pipeline comparisons of HOPS, CASA, and AIPS show a high degree of general consistency. The HOPS pipeline product was chosen as the primary scientific data set for SR1, based on the long validation history, level of calibration quality presented in this section, and to select a single data set for the preparation of scientific results. The other two pipelines are included in SR1 as supporting data sets for calibration, direct data comparisons, and as an independent pathway for validating the products of downstream analysis.

9. Conclusions

Observations from the EHT's 2017 April campaign are the first ever to have the necessary sensitivity, coverage, and resolution for horizon-scale imaging of black hole candidates M87 and Sgr A*. We have presented the complete data processing pathway that led to the first science release data set from the campaign, which includes the primary science target M87 and the secondary target 3C 279. The 2017 observations reflected a dramatic expansion of the EHT from previous years to a total of eight sites, and include for the first time ALMA as a phased array. While much more powerful, the expanded network represented a unique analysis challenge in terms of the heterogeneous nature of the array : basic telescope characteristics, weather, sensitivity, site-specific data issues, sampling rate, and channelization ; and a challenge in terms of raw data volume and the needs for a homogeneous and systematized calibration strategy.

The development of processing pipelines and characterization of the data occurred over a series of five internal engineering releases, during which site-specific data issues were identified and mitigated in correlation and post-processing. SR1 is the first science release of calibrated data products arising from the mature reduction pipelines, following a series of independent internal reviews. The science data were produced without making assumptions about the detailed compact structure of the targets, and thus provide an unbiased data set for downstream imaging and modeling.

We have developed three independent processing pipelines for the initial fringe detection, phase calibration, and reduction of EHT data. The pipelines used HOPS, which has been continually developed and used for early EHT analysis over the previous decade ; AIPS, the standard calibration environment for VLBI data from major facilities such as the VLBA ; and CASA, a modern environment for radio interferometer calibration and analysis that has recently been augmented with VLBI capabilities. The output from each pipeline was subjected to a suite of validation tests covering self-consistency over bands and polarizations, and consistency of trivial closure quantities.

From these tests, we estimated the residual non-closing systematic errors after calibration. For M87 such errors remain smaller than Stokes I data thermal uncertainties even after full scan and frequency band averaging. Non-closing errors are no larger than 2° for closure phases and 4% for closure amplitudes. For 3C 279, systematics are small in an absolute sense, but they dominate the total uncertainties of the averaged data set due to the high S/N. Differences between pipelines, particularly for the robust closure quantities, were found to be largely within the total budget of uncertainties. The HOPS data were selected as the primary data set for the scientific conclusions presented in companion Letters (Papers I, IV, V, VI) with the remaining two data sets available for direct data comparisons and the cross-validation of downstream analysis.

At EHT frequencies, absolute flux density calibration is particularly challenging due to the large and time-varying 1.3 mm opacity from atmospheric water vapor, and difficulties maintaining pointing and surface accuracy particularly at the larger dishes. We have outlined the gathering and unified interpretation of auxiliary calibration data from the various sites for the purposes of a priori flux density calibration, and a strategy for estimating the residual flux density error budget within the limitations of single-dish calibration. Where available, we have made use of network redundancy to further constrain flux density calibration given generic model-independent assumptions about the source.

A number of salient features became apparent in the M87 data set after processing and calibration. The visibility amplitudes as a function of projected baseline length persistently show a prominent secondary peak bracketed by two nulls, the first at 3.4 Gλ and the second at 8.3 Gλ, across all four observed days. The visibility amplitudes exhibit characteristics of a compact source with a spatial scale lesssim50 μas, and broad circular symmetry broken on baselines probing the first null. This spatial scale corresponds to only a few Schwarzschild radii for a 6.5 × 109 M⊙ black hole (Paper VI) at the distance of M87 (Blakeslee et al. 2009 ; Gebhardt et al. 2011 ; Cantiello et al. 2018). M87 closure phases on select triangles show clear time evolution between the two pairs of days, April 5/6 and April 10/11, providing evidence for intrinsic evolution of the source. The triangles with the largest closure phase variations between the two pairs of days have a baseline probing the (u, v) plane region about the first minimum in visibility amplitude. Analysis and interpretation of these features are presented in companion Letters (Paper I, IV, V, VI).

Although previous observations of M87 from early EHT campaigns (in 2009 and 2012) probed scales of a few tens of microarcseconds, the visibility amplitude behavior on the few baselines present remained consistent with a Gaussian source, showing no apparent finer structure (Doeleman et al. 2012 ; Akiyama et al. 2015). The first M87 closure phases at 1.3 mm reported in Akiyama et al. (2015) were consistent with zero to within 2 σ. In addition to a first reported measurement of 1.3 mm closure amplitudes, the 2017 observations of M87 are the first to show non-Gaussian structure in the compact source and significantly non-zero closure phases.

The SR1 data provide the first opportunity for total intensity imaging of M87 (Paper IV). Efforts to characterize and remove polarization leakage are ongoing and will enable studies of the linear polarization structure of M87 and other EHT targets. Additional work to better calibrate in the presence of intrinsic source variability, as well as increased amplitude gain variability, is necessary for Sgr A* and other low-elevation targets.

For 2018, the EHT was joined by the Greenland Telescope, greatly expanding the coverage for northern sources such as M87. In the near future, the array will also be joined by the Kitt Peak 12 m telescope in Arizona and the Northern Extended Millimeter Array (NOEMA) at the Plateau de Bure observatory in France. In addition to generally improved baseline coverage, both sites provide short baselines and associated redundancy (with SMT and PV, respectively) for the array—which is particularly beneficial for amplitude calibration. The EHT doubled recorded bandwidth to a rate of 64 Gbps in 2018 as well, over four 2 GHz bands. Additional development to enable coherent fringe fitting and atmospheric phase correction across all four bands will allow the EHT to better resolve features on long baselines, short timescales, and near visibility nulls, and it will increase robustness of the array against poor weather and the potential loss of sensitive central anchor stations.

While continuous development of the instrument and the data reduction pipeline will yield future observations with improved (u, v) coverage, higher S/N, and sharper resolution, the observations carried out in 2017 already deliver data of unprecedented scientific quality. The dramatic difference between the 2017 observations and early EHT campaigns in number of participating stations, S/N, coverage, and weather conditions make the EHT 2017 data set an exceptional opportunity for scientific discoveries via, e.g., imaging and model fitting well beyond previous EHT capabilities.

Appendix : Site and Data Issues

A.1. Issues Requiring Mitigation

The JCMT and SMA are located within hundreds of meters of each other on Maunakea. The small natural fringe rate is insufficient to wash out unwanted signals on the JCMT–SMA baselines (to phased and single-dish SMA). The JCMT and the SMA used identical frequency setups in 2017, resulting in two types of spurious correlations. For correlations between JCMT and the SMA single-dish reference antenna (not used directly for science analysis), two narrowband terrestrial signals required special handling : one from the 1024 MHz spur tone of the R2DBEs, and a second one from the YIG oscillator tone (which is part of the LO chain) locally generated at the SMA. These signals were mitigated by flagging the affected frequency channels in post-processing.

Broadband celestial signals in the lower sideband with respect to the 220.1 GHz first LO used at the JCMT and SMA also contaminated the signal in the upper-sideband data. The differential fringe rate between upper and lower sidebands is of O(Hz) ; thus, the lower-sideband contamination averages out to zero over sufficiently long integration times. The contamination only affects the reference antenna contribution to the phased array, as other antennas are subject to 90°/270° Walsh switching (Thompson et al. 2017, Section 7.5) that removes on average the lower sideband signal over a Walsh cycle of 0.65 s. Correlations between the JCMT and SMA single-dish reference antenna thus get the full lower sideband contribution, but correlations between JCMT and SMA phased array only get 1/N contribution, where N is the number of telescopes being phased. To avoid phase steering toward this spurious 17% contribution to the signal, neither the SMA nor the JCMT is ever used as the reference station during atmospheric phase calibration. For scans with very small fringe-rates, there may be a small residual contribution after the 10 s averages used for network calibration (Section 6.2). This adds to the intra-site baseline amplitude error budget that propagates into gain solutions for that procedure, as well as for closure amplitudes that use the baseline on comparable timescales.

Data from PV were subject to substantial amplitude loss due to instabilities in the signal chain, attributed to excess phase noise in the maser frequency reference (which has since been replaced). Examination of the data on the ALMA–PV baseline with progressively shorter APs demonstrated a pattern of frequency spikes off the main signal with evidence that the full correlated amplitude could be recovered with an AP of 2.048 ms. Further examination of a variety of scans showed that the pattern of frequency spikes was stable across scans, sources, and days, and the amplitude loss was constant. The effect was mitigated by continuing to use the data with a 0.4 s AP and multiplying the visibility amplitudes on baselines to PV by a constant derived multiplicative factor of 1.914 during a priori flux density calibration, which is equivalent to multiplying the effective SEFD for PV by 3.663.

Misconfigured Mark 6 recorders at APEX caused substantial data loss on many scans. The first 20–30 s of recording on a particular scan (sometimes much longer) were generally good, but partial or complete data dropouts could occur thereafter. DiFX accounts for the amount of valid data and automatically corrects averaged amplitudes and data weights for partial data loss to within 1% accuracy. The remaining data from long-duration dropouts were manually flagged to avoid introducing bad APEX data into the processed data. The consequence is that ALMA–APEX coverage is inconsistent, and this complicates the strategy for network calibration and closure amplitude analysis, which makes use of intra-site baseline coverage. It also means that for the 2017 observations, APEX cannot be consistently used to help calibrate ALMA amplitude variation during poor weather when ALMA phasing efficiency is unstable.

A separate unrelated small correction factor is applied to APEX baselines to account for reduction in amplitude from the introduction of a 1 pulse-per-second (PPS) signal in the APEX data. The factor is estimated by measuring amplitudes with and without the PPS signal flagged. It is valid for multi-second averages of visibility amplitudes.

Isolated groups of frequency channels in the beamformer system at the SMA were occasionally corrupted, causing a small fraction of the bandwidth (in the high band) to be lost during the first three days of the observation. Processing of a single band within the SMA beamformer is divided across eight hardware units, each of which processes one-eighth of the total bandwidth, distributed across 128 channels of 2.234375 MHz each (Primiani et al. 2016), so that the exact pattern of lost channels, once identified, is predictable. The times when the data corruption occurred and the amount of bandwidth affected were identified using the strong noise correlation signal between the SMA (beamformed) phased array and the SMA single-dish reference (recorded on a standard EHT backend). The pattern of lost bandwidth is evenly distributed throughout the band, and we derive SEFD corrections to account for the effective relative signal power lost upon frequency average (Table 2).

The LMT data are contaminated by polarization leakage, which is delayed from the primary signal by 1.5 ns. This occurs in both polarizations, and is attributed to reflections in the optical setup of the LMT receiver used in 2017 (1.5 ns corresponds to 45 cm). The level of polarization leakage is 10%, but for an unpolarized source it will dominate the correlated signal power of cross-hand VLBI products, therefore causing a false fringe at the delayed location. During fringe closure with the HOPS pipeline, an additional 1.5 ns delay systematic is added in quadrature to LMT baselines, so that any such false fringes will not bias the global station delays. A future polarization leakage correction will need to accommodate leakage at non-zero delay to properly account for the contamination. For 2018 and beyond, the special-purpose interim receiver used at LMT was replaced by a dual-polarization sideband-separating 1.3 mm receiver with better stability and full 64 Gbps coverage with the rest of the EHT (Paper II).

A.2. Issues not Addressed during Processing

The failure of a hard drive in one of the JCMT modules caused one-sixteenth of the data in the low band to be lost. The lost data affects all scans on the module approximately equally, as packets are scattered onto all hard drives at record time. This issue required no special handling because DiFX automatically adjusts data weights based on the amount of data in each AP.

Due to a small glitch in the ALMA correlator, the correlation coefficients on ALMA baselines are observed to undergo a slight dip every 18.192 s. The effective amplitude loss on scan-averaged quantities, less than 0.1%, is well within the error budget and therefore unmitigated.

No corrections were made for losses due to finite fast Fourier transform (FFT) lengths, which are required to be long in order to align ALMA 32 × 58.59375 MHz data in the frequency domain with the wideband 2048 MHz single-channel data from most EHT stations. A small loss is introduced due to the changing delay over the 64 μs of time corresponding to the FFT length used. The loss is zero at the DC edge of the channel and increases linearly with frequency. This effect is baseline-dependent and greatest on the baselines with the greatest east–west extent, especially when the source is rising at one location and setting at the other. Across all fringes on all sources on all baselines on all five days, the median signal loss is 0.67%, with the worst case (on a scan on the Hawaiʻi–PV baseline) about an order of magnitude larger. FFT losses are negligible on baselines to ALMA because the delay error accumulates over a maximum of 58.59375 MHz in frequency rather than 2048 MHz.

The LMT faces significant challenges in maintaining an accurate surface for 1.3 mm as the temperature fluctuates over the course of the evening. Pointing was also a challenge for scans at low or high elevation. These issues result in large residual gain trends obtained via amplitude self-calibration beyond the nominal error budget (Paper IV). However, the station-based amplitude gain issues do not influence robust interferometric closure quantities.

The SPT, participating for the first time in the VLBI observations, suffered from pointing problems early in the campaign. 3C 279 observing time was used to diagnose and resolve these issues, resulting in missing a majority of 3C 279 scans on April 5 and 6. The pointing issues were known and captured in observing logs during the run. The non-detections do not appear in the 3C 279 data set (Figure 2), and their absence is expected.

A.3. Issues at Correlation

Two unanticipated issues with the ALMA data were discovered and fixed in a seventh revision (Rev7) correlation. First, the tuning of one of the ALMA LO generators was specified to insufficient precision, resulting in an undocumented 50 mHz LO offset. In most VLBI experiments, such a small LO offset might be transparently compensated by a small change in fitted delay-rate. However for the wide EHT bandwidths, the inability for a single delay-rate to model the effect over the entire 2 GHz band is noticed, where the result of imperfect correction is to imprint a small rate slope with frequency, or, equivalently, a small delay drift with time. For this reason, the effect is separately corrected for prior to fringe fitting when post-processing Rev5 data, which is possible for sufficiently small LO offsets.

Second, it was discovered that the ALMA delay system automatically removes the bulk atmospheric delay from above the array. By default, DiFX tries to remove the bulk atmospheric delay from above each station, resulting in a double correction for ALMA. This was most noticeable at low elevation, where the double correction imprinted a large and rapidly (but monotonically) changing delay-rate. The large residual delay-rate is not large enough to cause decoherence over the duration of a correlation AP (0.4 s). The changing delay-rate causes substantial decoherence over a several-minute scan if only a first-order fringe solution is used. Because EHT data reduction already includes a mechanism to measure and correct for nonlinear phase due to atmospheric turbulence, it can also compensate for this drift in delay-rate imprinted on the data in the initial correlation. So long as signal-to-noise is sufficient to measure phase over short timescales, the impact on calibrated data is negligible.

Both of these issues were ultimately corrected in a final Rev7 correlation release. This included the LO adjustment for ALMA as well as special scripting for the geometric model preparation that allows the normal atmospheric correction at all sites other than ALMA to be merged with a no-atmospheric correction at ALMA. Comparison of SR1 results with comparable processing of Rev7 shows no significant difference, showing that the effects were sufficiently mitigated in post-processing for SR1.

M87-4 Imaging the Central Supermassive Black Hole

Footnotes

103

https://science.nrao.edu/facilities/vlba

104

http://www.atnf.csiro.au/vlbi

105

https://radio.kasi.re.kr/eavn

106

http://www.evlbi.org

107

Free-format parsable text file containing flux density calibration information and keywords as defined for AIPS : http://www.aips.nrao.edu/cgi-bin/ZXHLP2.PL?ANTAB.

108

https://www.haystack.mit.edu/tech/vlbi/hops.html

109

http://github.com/sao-eht/eat

110

https://www3.mpifr-bonn.mpg.de/div/vlbi/globalmm

111

http://www.aips.nrao.edu/cook.html

112

See AIPS MEMOS 101 and 107 for details ; http://www.aips.nrao.edu/aipsmemo.html.

113

EHT Memo Series : https://eventhorizontelescope.org/for-astronomers/memos.

114

https://www.eaobservatory.org/jcmt/instrumentation/heterodyne/rxa/

115

http://www.iram.fr/IRAMFR/GILDAS

116

It is common to see $\eta _\mathrmph^1/2$ defined as the phasing efficiency (e.g., Matthews et al. 2018), which scales with signal amplitude.

117

https://eventhorizontelescope.org/for-astronomers/data

118

See AIPS Memo 103 ; http://www.aips.nrao.edu/aipsmemo.html.

M87-2 Array et Instrumentation

bruno — 2019-04-15T02:46:28Z

II. Array and Instrumentation

The Event Horizon Telescope (EHT) is a very long baseline interferometry (VLBI) array that comprises millimeter- and submillimeter-wavelength telescopes separated by distances comparable to the diameter of the Earth. At a nominal operating wavelength of 1.3 mm, EHT angular resolution (λ/D) is 25 μas, which is sufficient to resolve nearby supermassive black hole candidates on spatial and temporal scales that correspond to their event horizons. With this capability, the EHT scientific goals are to probe general relativistic effects in the strong-field regime and to study accretion and relativistic jet formation near the black hole boundary. In this Letter we describe the system design of the EHT, detail the technology and instrumentation that enable observations, and provide measures of its performance. Meeting the EHT science objectives has required several key developments that have facilitated the robust extension of the VLBI technique to EHT observing wavelengths and the production of instrumentation that can be deployed on a heterogeneous array of existing telescopes and facilities. To meet sensitivity requirements, high-bandwidth digital systems were developed that process data at rates of 64 gigabit s−1, exceeding those of currently operating cm-wavelength VLBI arrays by more than an order of magnitude. Associated improvements include the development of phasing systems at array facilities, new receiver installation at several sites, and the deployment of hydrogen maser frequency standards to ensure coherent data capture across the array. These efforts led to the coordination and execution of the first Global EHT observations in 2017 April, and to event-horizon-scale imaging of the supermassive black hole candidate in M87.

1. Introduction
It is generally accepted that active galactic nuclei (AGNs) are powered by accretion onto supermassive black holes (SMBHs ; Heckman & Best 2014). These central engines are powerful actors on the cosmic stage, with roles in galactic evolution, star formation, mergers, and particle acceleration as evidenced by relativistic jets that both dynamically influence and redistribute matter on galactic scales (Blandford et al. 2018). Inflowing material typically obscures the event horizons of these black hole candidates, but it is in this extreme environment of the black hole boundary that strong-field effects of general relativity become evident and the accretion and outflow processes that govern black hole feedback on galactic scales originate (Ho 2008). Imaging black holes on scales that resolve these effects and processes would enable new tests of general relativity and the extraordinarily detailed study of core AGN physics. Realization of this goal requires a specialized instrument that does two things. It must have the ultra-high angular resolution required to resolve the nearest SMBH candidates, and it must operate in a range of the electromagnetic spectrum where light streams unimpeded from the innermost accretion region to telescopes on Earth. Achieving these specifications is the primary objective of the Event Horizon Telescope (EHT) : a very long baseline interferometry (VLBI) array of millimeter (mm) and submillimeter (submm) wavelength facilities that span the globe, creating a telescope with an effective Earth-sized aperture (Doeleman et al. 2009a).

While the EHT is uniquely designed for the imaging of SMBHs, other pioneering instruments are capable of probing similar angular scales for other purposes. Operating in the infrared, the GRAVITY interferometer delivers relative astrometry at the 10 micro-arcsecond (μas) level and has provided evidence for relativistic motion of material in close proximity to Sgr A* (GRAVITY Collaboration et al. 2018a). These infrared observations are an important and parallel probe of the spacetime surrounding Sgr A*, but cannot be used to make spatially resolved images of the black hole candidate because the interferometer intrinsic resolution is only 3 mas. The RadioAstron satellite, used as an orbiting element of combined Earth-Space VLBI arrays, is also capable of 10 μas angular resolution (Kardashev et al. 2013), but it operates at longer radio wavelengths that cannot penetrate the self-absorbed synchrotron plasma that surrounds the event horizon. In many ways the EHT is complementary to the Laser Interferometer Gravitational-Wave Observatory (LIGO) facility, which has detected the gravitational wave signatures from merging stellar-mass black holes (Abbott et al. 2016). LIGO and the EHT observe black holes that differ in mass by factors of $10^4\mbox—10^7$ ; LIGO events are transient, while the EHT carries out long-term studies of its main targets.

This Letter is one in a sequence of manuscripts that describes the first EHT results. The full sequence includes an abstract Letter with a summary of results (EHT Collaboration et al. 2019a, hereafter Paper I), this Letter with a description of the array and instrumentation (Paper II), a description of the data pipeline and processing (EHT Collaboration et al. 2019b, hereafter Paper III), a description of imaging techniques (EHT Collaboration et al. 2019c, hereafter Paper IV), and theoretical analyses of astrophysical and physics results (EHT Collaboration et al. 2019d, hereafter Paper V ; EHT Collaboration et al. 2019e, hereafter Paper VI, respectively).
1.1. EHT Science Goals

The scientific goals of the EHT array are to resolve and detect strong general relativistic signatures expected to arise on event-horizon scales. The best-known effect is that a black hole, surrounded by an optically thin luminous plasma, should exhibit a ''silhouette'' or ''shadow'' morphology : a dim central region delineated by the lensed photon orbit (Falcke et al. 2000). The apparent size of the photon orbit, described not long after Schwarzschild's initial solution was published (Hilbert 1917 ; von Laue 1921), defines a bright ring or crescent shape that was calculated for arbitrary spin by Bardeen (1973), first imaged through simulations by Luminet 1979, and subsequently studied extensively (Chandrasekhar 1983 ; Takahashi 2004 ; Broderick & Loeb 2006). The size and shape of the resulting shadow depends primarily on the mass of the black hole, and only very weakly on its spin and the observing orientation. For a non-spinning black hole, the shadow diameter is equal to $\sqrt27$ Schwarzschild radii (Rs = 2GM/c2). Over all black hole spins and orientations, the shadow diameter ranges from 4.8 to 5.2 Rs (Bardeen 1973 ; Johannsen & Psaltis 2010). Because any light that crosses the photon orbit from outside will eventually reach the event horizon, use of the term ''horizon scale'' will hereafter be understood to mean the size of the shadow and the lensed photon orbit. Detection of the shadow via lensed electromagnetic radiation would provide new evidence for the existence of SMBHs by confining the masses of EHT targets to within their expected photon orbits. A more detailed study of the precise shape of the photon orbit can be used to test the validity of general relativity on horizon scales (Johannsen & Psaltis 2010). Full polarimetric imaging can similarly be used to map magnetic field structure near the event horizon, placing important constraints on modes of accretion and the launching of relativistic jets (Broderick & Loeb 2009 ; Johnson et al. 2015 ; Chael et al. 2016 ; Akiyama et al. 2017 ; Gold et al. 2017).

Separate signatures, potentially offering a more sensitive probe of black hole spin, are the timescales of dynamical processes at horizon scales. A characteristic timescale for such processes is given by the orbital period of test particles at the innermost stable circular orbit (ISCO), which depends sensitively on the black hole spin (Bardeen et al. 1972). Monitoring VLBI observables to track the orbital dynamics of inhomogeneities in the accretion flow can thus be used to probe the spacetime, and potentially spin, of the black hole (Broderick & Loeb 2006 ; Doeleman et al. 2009b ; Fish et al. 2009 ; Fraga-Encinas et al. 2016 ; Medeiros et al. 2017 ; Roelofs et al. 2017).

1.2. Target Sources and Confirmation of Horizon-scale Structure
The bright radio core of M87 and Sgr A* (Table 1) are the primary EHT targets, as the combination of their estimated mass and proximity make them the two most suitable sources for studying SMBH candidates at horizon-scale resolution (Narayan & McClintock 2008 ; Johannsen et al. 2012). With bolometric luminosities well below the Eddington limit (Di Matteo et al. 2000 ; Baganoff et al. 2003), both the nucleus of M87 and Sgr A* are representative of the broad and populous class of low-luminosity AGN (LLAGN). AGN spend most of their time in this low state after prior periods of high accretion (Ho 2008), and LLAGN share many characteristics of stellar black hole emission in X-ray binaries, which exhibit episodic emission and jet production (Narayan & McClintock 2008). Thus, the prospects for applying results from horizon-scale observations of the central region of M87 and Sgr A* across a broad range of astrophysical contexts are excellent.

table1
aSgr A* : $\alpha _\rmJ2000.0=17^\rmh

45^\rmm
40\buildrel\rms\over. 0409,\,\delta _\rmJ2000.0=-29^\circ 00^\prime 28\buildrel\prime\prime\over. 118$ (10) ; M87 : $\alpha _\rmJ2000.0=12^\rmh

30^\rmm
49\buildrel\rms\over. 4234,\,\delta _\rmJ2000.0=12^\circ 23^\prime 28\buildrel\prime\prime\over. 044$ (11). bThe shadow diameter is within the range 4.8–5.2 Rs depending on black hole spin and orientation to the observer's line of sight (Johannsen & Psaltis 2010). cBrightness temperatures are reported for an observing frequency of 230 GHz. d $P_\mathrmISCO$ range is given in the case of maximum spin for both prograde (shortest) and retrograde (longest) orbits (Bardeen et al. 1972). eMass accretion rates $\dotM$ are estimated from measurements of Faraday rotation imparted by material in the accretion flow around the black hole.

References. (1) GRAVITY Collaboration et al. (2018a), (2) Reid et al. (2014), (3) Lu et al. (2018), (4) Marrone et al. (2007), (5) Walsh et al. (2013), (6) Gebhardt et al. (2011), (7) Blakeslee et al. (2009), EHT Collaboration et al. (2019e), (8) Akiyama et al. (2015), (9) Kuo et al. (2014), (10) Reid & Brunthaler (2004), (11) Lambert & Gontier (2009).

Within the past decade, VLBI observations at a wavelength of 1.3 mm have confirmed the existence of structure on the scale of the shadow in both the nucleus of M87 and Sgr A*. M87 (Virgo A) is thought to harbor a black hole in the range of $3.3\mbox—6.2\times 10^9$ solar mass (M⊙) (Gebhardt et al. 2011 ; Walsh et al. 2013), when scaled to a distance of 16.8 Mpc (Paper VI). Structure in M87 measuring 40 μas in extent has been resolved with 1.3 mm VLBI, corresponding to a total extent of 5.5 Schwarzschild radii at the upper end of the mass range (Doeleman et al. 2012 ; Akiyama et al. 2015). For Sgr A*, the black hole candidate at the Galactic center with a presumed mass of $4\times 10^6\,M_\odot $ (Balick & Brown 1974 ; Ghez et al. 2008 ; Genzel et al. 2010 ; GRAVITY Collaboration et al. 2018a), the 1.3 mm emission has been measured to have a size of 3.7 Rs (Doeleman et al. 2008 ; Fish et al. 2011). More recently, full polarimetric VLBI observations at 1.3 mm wavelength have revealed ordered and time-variable magnetic fields within Sgr A* on horizon scales (Johnson et al. 2015), and extension to longer baselines has confirmed compact structure on 3 Rs scales (Lu et al. 2018). These results, obtained with three- and four-site VLBI arrays consisting of the former Combined Array for Research in Millimeter-wave Astronomy (CARMA) in California, the Submillimeter Telescope (SMT) in Arizona, the James Clerk Maxwell Telescope (JCMT) and Submillimeter Array (SMA) facilities on Maunakea in Hawaii, and the Atacama Pathfinder Experiment (APEX) telescope in Chile, demonstrated that direct imaging of emission structures near the event horizon of SMBH candidates is possible in principle. For comparison and perspective, the closest approach of the orbiting stars used to determine the mass of Sgr A* is 1400 Rs (Gravity Collaboration et al. 2018b).

1.3. Array Architecture and Context
To realize these fundamental science goals, our international collaboration has engineered the EHT to move beyond the detection of horizon-scale structure and achieve the required imaging and time-domain sampling capability.

One of the key enabling technologies behind the EHT observations has been the development of high-bandwidth (wideband) VLBI systems that compensate to some degree for the generally smaller telescope apertures at millimeter and submillimeter wavelengths. The first detections of horizon-scale structure followed directly from deployment of new digital VLBI backend and recording instrumentation, custom-built for mm-wavelength observations that achieved a recording rate of 4 gigabit s−1 ( Gbps)136 (Doeleman et al. 2008). Continued development led to an increased recording rate of 16 Gbps (Whitney et al. 2013). Adoption of industry-standard high-speed data protocols, increased hard disk storage capacity, and flexible field programmable gate array (FPGA) computational fabric have enabled the EHT to reach data throughputs of 64 Gbps (Vertatschitsch et al. 2015), or 32 times the maximum recording rate and corresponding bandwidth, offered by open access VLBI facilities at longer wavelengths (e.g., the NRAO Very Long Baseline Array ; Napier et al. 1994).

In addition to the increased sensitivity provided by such large data recording rates, several factors, some engineered and some serendipitous, have converged to enable spatially and temporally resolved observations of black hole candidates by the EHT. By temporal resolution we mean that increased resolution, sensitivity, and baseline coverage allows the EHT to detect and spatially resolve horizon-scale time-variable structures, which would otherwise only be studied through light-curve analysis and light-crossing time assumptions. A list of the key enabling factors is as follows.

1.
Angular resolution : the angular resolution of Earth-diameter VLBI baselines at wavelengths of 1.3 mm can resolve the lensed photon orbits of Sgr A* and M87 (Table 1 : about 50 μas and 38 μas, respectively).
2.
Fourier coverage : using Earth-rotation aperture synthesis, the number of existing and planned mm/submm wavelength telescopes provides a sufficient sampling of VLBI baseline lengths and orientations to produce images with horizon-scale resolution (Fish et al. 2014 ; Honma et al. 2014 ; Lu et al. 2014 ; Ricarte & Dexter 2015 ; Bouman et al. 2016 ; Chael et al. 2016).
3.
Atmospheric transparency : at the required mm/submm observing wavelengths, the Earth's atmosphere at high-altitude sites is reliably transparent enough that global VLBI arrays can be formed for long-duration observations (Thompson et al. 2017).
4.
Optically thin accretion : for both Sgr A* and M87 the spectral energy density of the accretion flow begins to turn over at mm wavelengths, allowing photons from deep within the gravitational potential well to escape, presuming a synchrotron emission mechanism (see Broderick & Loeb 2009 ; Genzel et al. 2010, for M87 and Sgr A*, respectively).
5.
Interstellar scattering : radio images of Sgr A* are blurred due to interstellar scattering by free electrons (Lo et al. 1998 ; Shen et al. 2005 ; Bower et al. 2006 ; Lu et al. 2011 ; Bower et al. 2015 ; Johnson et al. 2018 ; Psaltis et al. 2018). This blurring decreases with wavelength as λ2 and becomes sub-dominant for wavelengths of 1.3 mm and shorter, where observations enable direct access to intrinsic structures in close proximity to the event horizon (Doeleman et al. 2008 ; Issaoun et al. 2019).

1.4. Current EHT Array
Figure 1 shows a map of the EHT array. In 2017 April, the EHT carried out global observations with an array of eight telescopes (see Table 2) that included the Atacama Large Millimeter/submillimeter Array (ALMA) for the first time. A purpose-built system electronically combined the collecting area of 37 × 12 m diameter ALMA dishes (see Appendix A.1) : the equivalent of adding a 70 m dish to the EHT array. Other participating telescopes were APEX, JCMT, SMA, SMT, the Large Millimeter Telescope Alfonso Serrano (LMT), the Pico Veleta 30 m telescope (PV), and the South Pole Telescope (SPT). Operating in the 1.3 mm window in full polarimetric mode and with an aggregate bandwidth of 8 GHz, the resulting increase in sensitivity above the first horizon-scale detections was nearly an order of magnitude (e.g., Section 3.8). For observations with phased-ALMA in 2018, the EHT added an additional facility (the 12 m diameter Greenland Telescope (GLT)) and doubled the aggregate bandwidth to its nominal target of 16 GHz.

figure1
Map of the EHT. Stations active in 2017 and 2018 are shown with connecting lines and labeled in yellow, sites in commission are labeled in green, and legacy sites are labeled in red. Nearly redundant baselines are overlaying each other, i.e., to ALMA/APEX and SMA/JCMT. Such redundancy allows improvement in determining the amplitude calibration of the array (Paper III).

Table 2. EHT Station Information
aGeocentric coordinates with X pointing to the Greenwich meridian, Y pointing 90° away in the equatorial plane (eastern longitudes have positive Y), and positive Z pointing in the direction of the North Pole. This is a left-handed coordinate system. Elevations are relative to the GRS 80 ellipsoid (Moritz 2000). bArray coordinates indicate the phasing center used in 2017. c2017 April position : the ice sheet at the South Pole moves at a rate of about 10 m yr−1. Effects of this slow drift are removed during VLBI correlation. dNOEMA : Northern Extended Millimeter Array ; KP 12 m : Kitt Peak 12 m. These stations have not participated in global EHT observations and their coordinates are approximate.

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First M87 Event Horizon Telescope Results. II. Array and Instrumentation

The Event Horizon Telescope Collaboration, Kazunori Akiyama1,2,3,4, Antxon Alberdi5, Walter Alef6, Keiichi Asada7, Rebecca Azulay8,9,6, Anne-Kathrin Baczko6, David Ball10, Mislav Baloković4,11, John Barrett2Show full author list

Published 2019 April 10 • © 2019. The American Astronomical Society.
The Astrophysical Journal Letters, Volume 875, Number 1
Focus on the First Event Horizon Telescope Results
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Abstract

The Event Horizon Telescope (EHT) is a very long baseline interferometry (VLBI) array that comprises millimeter- and submillimeter-wavelength telescopes separated by distances comparable to the diameter of the Earth. At a nominal operating wavelength of 1.3 mm, EHT angular resolution (λ/D) is 25 μas, which is sufficient to resolve nearby supermassive black hole candidates on spatial and temporal scales that correspond to their event horizons. With this capability, the EHT scientific goals are to probe general relativistic effects in the strong-field regime and to study accretion and relativistic jet formation near the black hole boundary. In this Letter we describe the system design of the EHT, detail the technology and instrumentation that enable observations, and provide measures of its performance. Meeting the EHT science objectives has required several key developments that have facilitated the robust extension of the VLBI technique to EHT observing wavelengths and the production of instrumentation that can be deployed on a heterogeneous array of existing telescopes and facilities. To meet sensitivity requirements, high-bandwidth digital systems were developed that process data at rates of 64 gigabit s−1, exceeding those of currently operating cm-wavelength VLBI arrays by more than an order of magnitude. Associated improvements include the development of phasing systems at array facilities, new receiver installation at several sites, and the deployment of hydrogen maser frequency standards to ensure coherent data capture across the array. These efforts led to the coordination and execution of the first Global EHT observations in 2017 April, and to event-horizon-scale imaging of the supermassive black hole candidate in M87.

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1. Introduction

It is generally accepted that active galactic nuclei (AGNs) are powered by accretion onto supermassive black holes (SMBHs ; Heckman & Best 2014). These central engines are powerful actors on the cosmic stage, with roles in galactic evolution, star formation, mergers, and particle acceleration as evidenced by relativistic jets that both dynamically influence and redistribute matter on galactic scales (Blandford et al. 2018). Inflowing material typically obscures the event horizons of these black hole candidates, but it is in this extreme environment of the black hole boundary that strong-field effects of general relativity become evident and the accretion and outflow processes that govern black hole feedback on galactic scales originate (Ho 2008). Imaging black holes on scales that resolve these effects and processes would enable new tests of general relativity and the extraordinarily detailed study of core AGN physics. Realization of this goal requires a specialized instrument that does two things. It must have the ultra-high angular resolution required to resolve the nearest SMBH candidates, and it must operate in a range of the electromagnetic spectrum where light streams unimpeded from the innermost accretion region to telescopes on Earth. Achieving these specifications is the primary objective of the Event Horizon Telescope (EHT) : a very long baseline interferometry (VLBI) array of millimeter (mm) and submillimeter (submm) wavelength facilities that span the globe, creating a telescope with an effective Earth-sized aperture (Doeleman et al. 2009a).

While the EHT is uniquely designed for the imaging of SMBHs, other pioneering instruments are capable of probing similar angular scales for other purposes. Operating in the infrared, the GRAVITY interferometer delivers relative astrometry at the 10 micro-arcsecond (μas) level and has provided evidence for relativistic motion of material in close proximity to Sgr A* (GRAVITY Collaboration et al. 2018a). These infrared observations are an important and parallel probe of the spacetime surrounding Sgr A*, but cannot be used to make spatially resolved images of the black hole candidate because the interferometer intrinsic resolution is only 3 mas. The RadioAstron satellite, used as an orbiting element of combined Earth-Space VLBI arrays, is also capable of 10 μas angular resolution (Kardashev et al. 2013), but it operates at longer radio wavelengths that cannot penetrate the self-absorbed synchrotron plasma that surrounds the event horizon. In many ways the EHT is complementary to the Laser Interferometer Gravitational-Wave Observatory (LIGO) facility, which has detected the gravitational wave signatures from merging stellar-mass black holes (Abbott et al. 2016). LIGO and the EHT observe black holes that differ in mass by factors of $10^4\mbox—10^7$ ; LIGO events are transient, while the EHT carries out long-term studies of its main targets.

This Letter is one in a sequence of manuscripts that describes the first EHT results. The full sequence includes an abstract Letter with a summary of results (EHT Collaboration et al. 2019a, hereafter Paper I), this Letter with a description of the array and instrumentation (Paper II), a description of the data pipeline and processing (EHT Collaboration et al. 2019b, hereafter Paper III), a description of imaging techniques (EHT Collaboration et al. 2019c, hereafter Paper IV), and theoretical analyses of astrophysical and physics results (EHT Collaboration et al. 2019d, hereafter Paper V ; EHT Collaboration et al. 2019e, hereafter Paper VI, respectively).
1.1. EHT Science Goals

The scientific goals of the EHT array are to resolve and detect strong general relativistic signatures expected to arise on event-horizon scales. The best-known effect is that a black hole, surrounded by an optically thin luminous plasma, should exhibit a ''silhouette'' or ''shadow'' morphology : a dim central region delineated by the lensed photon orbit (Falcke et al. 2000). The apparent size of the photon orbit, described not long after Schwarzschild's initial solution was published (Hilbert 1917 ; von Laue 1921), defines a bright ring or crescent shape that was calculated for arbitrary spin by Bardeen (1973), first imaged through simulations by Luminet 1979, and subsequently studied extensively (Chandrasekhar 1983 ; Takahashi 2004 ; Broderick & Loeb 2006). The size and shape of the resulting shadow depends primarily on the mass of the black hole, and only very weakly on its spin and the observing orientation. For a non-spinning black hole, the shadow diameter is equal to $\sqrt27$ Schwarzschild radii (Rs = 2GM/c2). Over all black hole spins and orientations, the shadow diameter ranges from 4.8 to 5.2 Rs (Bardeen 1973 ; Johannsen & Psaltis 2010). Because any light that crosses the photon orbit from outside will eventually reach the event horizon, use of the term ''horizon scale'' will hereafter be understood to mean the size of the shadow and the lensed photon orbit. Detection of the shadow via lensed electromagnetic radiation would provide new evidence for the existence of SMBHs by confining the masses of EHT targets to within their expected photon orbits. A more detailed study of the precise shape of the photon orbit can be used to test the validity of general relativity on horizon scales (Johannsen & Psaltis 2010). Full polarimetric imaging can similarly be used to map magnetic field structure near the event horizon, placing important constraints on modes of accretion and the launching of relativistic jets (Broderick & Loeb 2009 ; Johnson et al. 2015 ; Chael et al. 2016 ; Akiyama et al. 2017 ; Gold et al. 2017).

Separate signatures, potentially offering a more sensitive probe of black hole spin, are the timescales of dynamical processes at horizon scales. A characteristic timescale for such processes is given by the orbital period of test particles at the innermost stable circular orbit (ISCO), which depends sensitively on the black hole spin (Bardeen et al. 1972). Monitoring VLBI observables to track the orbital dynamics of inhomogeneities in the accretion flow can thus be used to probe the spacetime, and potentially spin, of the black hole (Broderick & Loeb 2006 ; Doeleman et al. 2009b ; Fish et al. 2009 ; Fraga-Encinas et al. 2016 ; Medeiros et al. 2017 ; Roelofs et al. 2017).
1.2. Target Sources and Confirmation of Horizon-scale Structure

The bright radio core of M87 and Sgr A* (Table 1) are the primary EHT targets, as the combination of their estimated mass and proximity make them the two most suitable sources for studying SMBH candidates at horizon-scale resolution (Narayan & McClintock 2008 ; Johannsen et al. 2012). With bolometric luminosities well below the Eddington limit (Di Matteo et al. 2000 ; Baganoff et al. 2003), both the nucleus of M87 and Sgr A* are representative of the broad and populous class of low-luminosity AGN (LLAGN). AGN spend most of their time in this low state after prior periods of high accretion (Ho 2008), and LLAGN share many characteristics of stellar black hole emission in X-ray binaries, which exhibit episodic emission and jet production (Narayan & McClintock 2008). Thus, the prospects for applying results from horizon-scale observations of the central region of M87 and Sgr A* across a broad range of astrophysical contexts are excellent.

Table 1. Assumed Physical Properties of Sgr A* and M87 Used to Establish Technical Goalsa
Sgr A* M87
Black Hole Mass M (M⊙) $4.1\times 10^6$ (1) (3.3–$6.2)\times 10^9$ (5), (6)
Distance D (pc) $8.34\times 10^3$ (2) $16.8\times 10^6$ (7)
Schwarzschild Radius Rs (μas) 9.7 3.9–7.3
Shadow Diameterb $D_\mathrmsh$ (μas) 47–50 19–38
Brightness Temperaturec TB (K) $3\times 10^9$ (3) 1010 (8)
Period ISCOd $P_\mathrmISCO$ 4–54 minutes 2.4–57.7 days
Mass Accretion Ratee $\dotM$ (M⊙ yr−1) 10−9–10−7 (4) $\lt 10^-3$ (9)

Notes.
aSgr A* : $\alpha _\rmJ2000.0=17^\rmh

45^\rmm
40\buildrel\rms\over. 0409,\,\delta _\rmJ2000.0=-29^\circ 00^\prime 28\buildrel\prime\prime\over. 118$ (10) ; M87 : $\alpha _\rmJ2000.0=12^\rmh

30^\rmm
49\buildrel\rms\over. 4234,\,\delta _\rmJ2000.0=12^\circ 23^\prime 28\buildrel\prime\prime\over. 044$ (11). bThe shadow diameter is within the range 4.8–5.2 Rs depending on black hole spin and orientation to the observer's line of sight (Johannsen & Psaltis 2010). cBrightness temperatures are reported for an observing frequency of 230 GHz. d $P_\mathrmISCO$ range is given in the case of maximum spin for both prograde (shortest) and retrograde (longest) orbits (Bardeen et al. 1972). eMass accretion rates $\dotM$ are estimated from measurements of Faraday rotation imparted by material in the accretion flow around the black hole.

References. (1) GRAVITY Collaboration et al. (2018a), (2) Reid et al. (2014), (3) Lu et al. (2018), (4) Marrone et al. (2007), (5) Walsh et al. (2013), (6) Gebhardt et al. (2011), (7) Blakeslee et al. (2009), EHT Collaboration et al. (2019e), (8) Akiyama et al. (2015), (9) Kuo et al. (2014), (10) Reid & Brunthaler (2004), (11) Lambert & Gontier (2009).

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Within the past decade, VLBI observations at a wavelength of 1.3 mm have confirmed the existence of structure on the scale of the shadow in both the nucleus of M87 and Sgr A*. M87 (Virgo A) is thought to harbor a black hole in the range of $3.3\mbox—6.2\times 10^9$ solar mass (M⊙) (Gebhardt et al. 2011 ; Walsh et al. 2013), when scaled to a distance of 16.8 Mpc (Paper VI). Structure in M87 measuring 40 μas in extent has been resolved with 1.3 mm VLBI, corresponding to a total extent of 5.5 Schwarzschild radii at the upper end of the mass range (Doeleman et al. 2012 ; Akiyama et al. 2015). For Sgr A*, the black hole candidate at the Galactic center with a presumed mass of $4\times 10^6\,M_\odot $ (Balick & Brown 1974 ; Ghez et al. 2008 ; Genzel et al. 2010 ; GRAVITY Collaboration et al. 2018a), the 1.3 mm emission has been measured to have a size of 3.7 Rs (Doeleman et al. 2008 ; Fish et al. 2011). More recently, full polarimetric VLBI observations at 1.3 mm wavelength have revealed ordered and time-variable magnetic fields within Sgr A* on horizon scales (Johnson et al. 2015), and extension to longer baselines has confirmed compact structure on 3 Rs scales (Lu et al. 2018). These results, obtained with three- and four-site VLBI arrays consisting of the former Combined Array for Research in Millimeter-wave Astronomy (CARMA) in California, the Submillimeter Telescope (SMT) in Arizona, the James Clerk Maxwell Telescope (JCMT) and Submillimeter Array (SMA) facilities on Maunakea in Hawaii, and the Atacama Pathfinder Experiment (APEX) telescope in Chile, demonstrated that direct imaging of emission structures near the event horizon of SMBH candidates is possible in principle. For comparison and perspective, the closest approach of the orbiting stars used to determine the mass of Sgr A* is 1400 Rs (Gravity Collaboration et al. 2018b).
1.3. Array Architecture and Context

To realize these fundamental science goals, our international collaboration has engineered the EHT to move beyond the detection of horizon-scale structure and achieve the required imaging and time-domain sampling capability.

One of the key enabling technologies behind the EHT observations has been the development of high-bandwidth (wideband) VLBI systems that compensate to some degree for the generally smaller telescope apertures at millimeter and submillimeter wavelengths. The first detections of horizon-scale structure followed directly from deployment of new digital VLBI backend and recording instrumentation, custom-built for mm-wavelength observations that achieved a recording rate of 4 gigabit s−1 ( Gbps)136 (Doeleman et al. 2008). Continued development led to an increased recording rate of 16 Gbps (Whitney et al. 2013). Adoption of industry-standard high-speed data protocols, increased hard disk storage capacity, and flexible field programmable gate array (FPGA) computational fabric have enabled the EHT to reach data throughputs of 64 Gbps (Vertatschitsch et al. 2015), or 32 times the maximum recording rate and corresponding bandwidth, offered by open access VLBI facilities at longer wavelengths (e.g., the NRAO Very Long Baseline Array ; Napier et al. 1994).

In addition to the increased sensitivity provided by such large data recording rates, several factors, some engineered and some serendipitous, have converged to enable spatially and temporally resolved observations of black hole candidates by the EHT. By temporal resolution we mean that increased resolution, sensitivity, and baseline coverage allows the EHT to detect and spatially resolve horizon-scale time-variable structures, which would otherwise only be studied through light-curve analysis and light-crossing time assumptions. A list of the key enabling factors is as follows.

1.
Angular resolution : the angular resolution of Earth-diameter VLBI baselines at wavelengths of 1.3 mm can resolve the lensed photon orbits of Sgr A* and M87 (Table 1 : about 50 μas and 38 μas, respectively).
2.
Fourier coverage : using Earth-rotation aperture synthesis, the number of existing and planned mm/submm wavelength telescopes provides a sufficient sampling of VLBI baseline lengths and orientations to produce images with horizon-scale resolution (Fish et al. 2014 ; Honma et al. 2014 ; Lu et al. 2014 ; Ricarte & Dexter 2015 ; Bouman et al. 2016 ; Chael et al. 2016).
3.
Atmospheric transparency : at the required mm/submm observing wavelengths, the Earth's atmosphere at high-altitude sites is reliably transparent enough that global VLBI arrays can be formed for long-duration observations (Thompson et al. 2017).
4.
Optically thin accretion : for both Sgr A* and M87 the spectral energy density of the accretion flow begins to turn over at mm wavelengths, allowing photons from deep within the gravitational potential well to escape, presuming a synchrotron emission mechanism (see Broderick & Loeb 2009 ; Genzel et al. 2010, for M87 and Sgr A*, respectively).
5.
Interstellar scattering : radio images of Sgr A* are blurred due to interstellar scattering by free electrons (Lo et al. 1998 ; Shen et al. 2005 ; Bower et al. 2006 ; Lu et al. 2011 ; Bower et al. 2015 ; Johnson et al. 2018 ; Psaltis et al. 2018). This blurring decreases with wavelength as λ2 and becomes sub-dominant for wavelengths of 1.3 mm and shorter, where observations enable direct access to intrinsic structures in close proximity to the event horizon (Doeleman et al. 2008 ; Issaoun et al. 2019).

1.4. Current EHT Array

Figure 1 shows a map of the EHT array. In 2017 April, the EHT carried out global observations with an array of eight telescopes (see Table 2) that included the Atacama Large Millimeter/submillimeter Array (ALMA) for the first time. A purpose-built system electronically combined the collecting area of 37 × 12 m diameter ALMA dishes (see Appendix A.1) : the equivalent of adding a 70 m dish to the EHT array. Other participating telescopes were APEX, JCMT, SMA, SMT, the Large Millimeter Telescope Alfonso Serrano (LMT), the Pico Veleta 30 m telescope (PV), and the South Pole Telescope (SPT). Operating in the 1.3 mm window in full polarimetric mode and with an aggregate bandwidth of 8 GHz, the resulting increase in sensitivity above the first horizon-scale detections was nearly an order of magnitude (e.g., Section 3.8). For observations with phased-ALMA in 2018, the EHT added an additional facility (the 12 m diameter Greenland Telescope (GLT)) and doubled the aggregate bandwidth to its nominal target of 16 GHz.
Figure 1.

Figure 1. Map of the EHT. Stations active in 2017 and 2018 are shown with connecting lines and labeled in yellow, sites in commission are labeled in green, and legacy sites are labeled in red. Nearly redundant baselines are overlaying each other, i.e., to ALMA/APEX and SMA/JCMT. Such redundancy allows improvement in determining the amplitude calibration of the array (Paper III).

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Table 2. EHT Station Information
Facility Diameter Location Xa Ya Za Latitude Longitude Elevationa
(m) (m) (m) (m) (m)
Facilities that Participated in the 2017 Observations
ALMAb 12 ($\times 54$) and 7 ($\times 12$) Chile $2225061.3$ $-5440061.7$ $-2481681.2$ $-23^\circ 01^\prime 45\buildrel\prime\prime\over. 1$ $-67^\circ 45^\prime 17\buildrel\prime\prime\over. 1$ 5074.1
APEX 12 Chile $2225039.5$ $-5441197.6$ $-2479303.4$ $-23^\circ 00^\prime 20\buildrel\prime\prime\over. 8$ $-67^\circ 45^\prime 32\buildrel\prime\prime\over. 9$ 5104.5
JCMT 15 Hawaii, USA $-5464584.7$ $-2493001.2$ $2150654.0$ $+19^\circ 49^\prime 22\buildrel\prime\prime\over. 2$ $-155^\circ 28^\prime 37\buildrel\prime\prime\over. 3$ 4120.1
LMT 50 Mexico $-768715.6$ $-5988507.1$ $2063354.9$ $+18^\circ 59^\prime 08\buildrel\prime\prime\over. 8$ $-97^\circ 18^\prime 53\buildrel\prime\prime\over. 2$ 4593.3
PV 30 m 30 Spain $5088967.8$ $-301681.2$ $3825012.2$ $+37^\circ 03^\prime 58\buildrel\prime\prime\over. 1$ $-3^\circ 23^\prime 33\buildrel\prime\prime\over. 4$ 2919.5
SMAb 6 ($\times 8$) Hawaii, USA $-5464555.5$ $-2492928.0$ $2150797.2$ $+19^\circ 49^\prime 27\buildrel\prime\prime\over. 2$ $-155^\circ 28^\prime 39\buildrel\prime\prime\over. 1$ 4115.1
SMT 10 Arizona, USA $-1828796.2$ $-5054406.8$ $3427865.2$ $+32^\circ 42^\prime 05\buildrel\prime\prime\over. 8$ $-109^\circ 53^\prime 28\buildrel\prime\prime\over. 5$ 3158.7
SPTc 10 Antarctica 809.8 −816.9 $-6359568.7$ $-89^\circ 59^\prime 22\buildrel\prime\prime\over. 9$ $-45^\circ 15^\prime 00\buildrel\prime\prime\over. 3$ 2816.5
Facilities Joining EHT Observations in 2018 and Later
GLT 12 Greenland $541547.0$ $-1387978.6$ $6180982.0$ $+76^\circ 32^\prime 06\buildrel\prime\prime\over. 6$ $-68^\circ 41^\prime 08\buildrel\prime\prime\over. 8$ 89.4
NOEMAd 15 ($\times 12$) France 4524000.4 468042.1 4460309.8 $+44^\circ 38^\prime 01\buildrel\prime\prime\over. 2$ $+5^\circ 54^\prime 24\buildrel\prime\prime\over. 0$ 2617.6
KP 12 md 12 Arizona, USA $-1995954.4$ $-5037389.4$ $3357044.3$ $+31^\circ 57^\prime 12\buildrel\prime\prime\over. 0$ $-111^\circ 36^\prime 53\buildrel\prime\prime\over. 5$ 1894.5
Facilities Formerly Participating in EHT Observations
CARMA 10.4, 6.1 $(\times 8)$ California, USA $-2397378.6$ $-4482048.7$ $3843513.2$ $+37^\circ 16^\prime 49\buildrel\prime\prime\over. 4$ $-118^\circ 08^\prime 29\buildrel\prime\prime\over. 9$ 2168.9
CSO 10 Hawaii, USA $-5464520.9$ $-2493145.6$ $2150610.6$ $+19^\circ 49^\prime 20\buildrel\prime\prime\over. 9$ $-155^\circ 28^\prime 31\buildrel\prime\prime\over. 9$ 4107.2

Notes.
aGeocentric coordinates with X pointing to the Greenwich meridian, Y pointing 90° away in the equatorial plane (eastern longitudes have positive Y), and positive Z pointing in the direction of the North Pole. This is a left-handed coordinate system. Elevations are relative to the GRS 80 ellipsoid (Moritz 2000). bArray coordinates indicate the phasing center used in 2017. c2017 April position : the ice sheet at the South Pole moves at a rate of about 10 m yr−1. Effects of this slow drift are removed during VLBI correlation. dNOEMA : Northern Extended Millimeter Array ; KP 12 m : Kitt Peak 12 m. These stations have not participated in global EHT observations and their coordinates are approximate.

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The sections that follow describe the specifications and characteristics of the array (Section 2), the EHT instrumentation deployed (Section 3), the observing strategy (Section 4), correlation, calibration, and detection (Section 5), and future enhancements (Section 6).

2. EHT Specifications and Characteristics
Extending the VLBI technique to wavelengths of 1.3 mm presents technical challenges. Heterodyne receivers exhibit greater noise, and the required stability of atomic frequency standards is higher than that typically specified for VLBI at longer wavelengths. Early 1.3 mm wavelength VLBI experiments and observations in the 1990s succeeded in making first detections of AGNs and Sgr A* on modest-length baselines (≤1100 km ; Padin et al. 1990 ; Greve et al. 1995 ; Krichbaum et al. 1998). Following this pioneering work (see Doeleman & Krichbaum 1999 ; Boccardi et al. 2017, for summaries), 1.3 mm VLBI efforts over the next decade focused on order-of-magnitude bandwidth expansion as a means to boost sensitivity. This development led to observations in 2007 with enough resolution to resolve emission on the scale of the event horizon of Sgr A* by using a three-station array with telescopes in Hawaii, California, and Arizona. Motivated by this detection, an EHT array capable of imaging strong general relativistic features was planned based on organizing coordinated observations on a network of mm-wavelength observatories (Doeleman et al. 2009a). These sites and their general characteristics are given in Table 2, which lists current and planned EHT sites as well as now-decommissioned observatories used in prior experiments. For the most part, the EHT consists of pre-existing telescopes that perform single-dish or connected-element astronomy observations during most of the year, but which required modifications or upgrades (in some cases significant ones) to carry out VLBI. The GLT, for example, was commissioned primarily to image M87 (Inoue et al. 2014), and a heterodyne receiver for the SPT was built specifically for EHT observations (Kim et al. 2018a). Details of how each site was modified for EHT work are given in the Appendix.

Technical specifications for the EHT were adopted to unify VLBI recordings across the heterogeneous array by establishing a common frequency configuration, polarization configuration, and sampling rate (Tilanus et al. 2013 ; Marrone et al. 2014). When ALMA participates in EHT observations, it is by far the most sensitive site, so the overall sensitivity of the EHT array is optimized on a per-bandwidth basis when all other sites can match the recorded frequency bands at ALMA. The EHT converged on a scheme that matches ALMA specifications : two 4 GHz sidebands in each of two polarizations for the 1.3 and 0.87 mm receiver bands, which could be realized through feasible modifications and enhancements at most sites. The resulting global array geometry and sensitivity is well matched to the science goals.
2.1. Angular Resolution

Imaging a black hole shadow requires several resolution elements in each direction across the lensed innermost photon orbit, in addition to field-of-view coverage that extends beyond the feature. The longest baselines of the EHT (e.g., South Pole to Arizona, Hawaii, or Spain) provide nominal angular resolutions of $\lambda /D\simeq 25\ $μas in the 1.3 mm wavelength band. Regularized maximum likelihood (RML) imaging methods (see Paper IV) typically achieve angular resolutions that are better than the nominal figure by factors of 2–3 (Narayan & Nityananda 1986). For the EHT case in particular, RML methods have been extensively tested using realistic and synthetic interferometric data to set the optimal resolution of the array (Honma et al. 2014 ; Bouman et al. 2016 ; Chael et al. 2016 ; Akiyama et al. 2017 ; Chael et al. 2018 ; Kuramochi et al. 2018). This results in an anticipated effective EHT angular resolution at 1.3 mm of 20 μas, yielding between about 36 resolution elements across a 120 × 120 μas field of view. For Sgr A* and M87 this field of view is expected to encompass the dim interior, bright annulus of the photon orbit, and sufficient spatial extent to extract the shadow feature (e.g., Mościbrodzka et al. 2009 ; Dexter et al. 2010). These considerations, and the expectation based on simulations that the EHT instrument and array could achieve such resolution, were important factors in specifying the EHT architecture. Further tests using EHT observations of quasar calibrator sources (e.g., 3C 279) obtained in the 2017 April observations demonstrate robust structural agreement between RML methods and more traditional CLEAN-based radio imaging techniques. Similar comparisons and results on M87, one of the EHT primary targets, can be found in Paper IV.
2.2. Sensitivity

Maximizing detections across sparse Fourier coverage is essential for high-fidelity image reconstruction. This is especially true for Sgr A* because its structure is scatter broadened by interstellar effects resulting in reduced VLBI visibility amplitudes on the longest baselines.

To maximize the number of interferometric detections across the array, the EHT uses a two-stage approach to fringe detection. First, detections are found on baselines from all stations to ALMA within the atmospheric coherence time. Next, these ALMA detections are used to remove the effects of phase fluctuations (due to atmospheric turbulence) above the non-ALMA stations, allowing coherent integration on non-ALMA baselines for intervals up to many minutes, thereby boosting the signal-to-noise ratio (S/N) to recover the full baseline coverage of the array (Paper III). Thus, the EHT sensitivity specification corresponds to the requirement that for baselines connecting each EHT site to ALMA, Sgr A* and M87 are detected with a typical signal-to-noise that enables this atmospheric phase correction with acceptable loss. In the usual case where the VLBI observing scan duration greatly exceeds the atmospheric coherence time, the loss due to noise in the phase-correction algorithm is $\sim e^

\rm-(S/N)

^2/2$, where the S/N is the signal-to-noise on the ALMA baselines. To ensure negligible loss, we specify S/N > 3 for EHT baselines to ALMA within an integration time, $T_\rmint

$, where Tint is less than the atmospheric coherence time. We note that the expected change in interferometric phase due to source structure over the imaged field of view (Section 2.1) would be less than a few degrees over typical VLBI scan lengths of a few minutes.

The S/N of a VLBI signal on a single baseline between stations is
Equation (1)
where ηQ is the digital loss due to sampling the received signal at each antenna with finite precision ($\eta _Q=0.88$ for 2-bit samples), $\rm\Delta \nu $ is the bandwidth of the recording, SEFDi is the system equivalent flux density (SEFD)137 for station i, and $S_\rmcor

$ is the expected correlated flux on the baseline between stations 1 and 2. $T_\rmint

$ is the integration interval of the VLBI signal. It is typically much less than the atmospheric coherence time (Tcoh), or the coherent integration time beyond which the VLBI visibility138 signal decreases by 10 % due to phase fluctuations imposed by turbulence in the troposphere (typically from a few to 20 s). On the weakest baseline involving ALMA, ALMA–SPT, with an estimated flux for Sgr A* of 0.1 Jy (see APEX-CARMA baseline in Lu et al. 2018) and with Δν = 4 GHz, an integration time of 3 s yields an S/N of about 12 (see Table 3 for parameters), which far exceeds the EHT S/N specification for detections on ALMA baselines. Figure 2 shows that more than 75% of scans on baselines in the 2017 array that include ALMA had Tcoh greater than 10 s.

Figure 2. Atmospheric coherence time for EHT ALMA baselines. VLBI observations consist of scans, each 3–7 minutes long (see Figure 12). Each scan in the 2017 EHT observation campaign was divided into sequential coherent integration intervals, which were then incoherently averaged to obtain an estimate of VLBI signal amplitude per scan. As the duration of the coherent interval decreases, the loss in amplitude due to atmospheric phase fluctuations decreases. Solid lines represent the 25th percentile of the coherence distribution for each baseline : 75% of the data exhibit higher time coherence than indicated by the line. The heavy black dashed line shows the 25th percentile of the coherence distribution for all baselines. The light dashed and dotted lines show the 95 % and 90 % coherence limits for the baseline with lowest coherence, which is from PV to ALMA (largely due to low-elevation PV scans on Sgr A* during the observations). The number of scans used to compute the coherence curves are shown next to each station in parenthesis.

Table 3. EHT Station Sensitivities
aSEFD = 2k$T_\rmsys

^* $/$\eta _\rmA

A_\rmgeom

$ with $T_\rmsys

^* $ the effective system temperature and $A_\rmgeom

$ the geometric collecting area of the telescope. The effective system temperature lists representative values for the 2017 Sgr A* and M87 observations, i.e., for median elevations of the sources and typical atmospheric opacities at each facility. It includes effects from elevation-dependent gains and phasing efficiency relevant for some of the telescopes. bWith σrms-ALMA the thermal noise for the station's baseline with ALMA using Equation (1) for a bandwidth of 4 GHz and integration time of 10 s (see Figure 2). cThe median number of phased antennas in 2017 for the SMA was 6 × 6 m antennas and for ALMA was 37 × 12 m antennas. If all ALMA antennas are phased that would be equivalent to a single 88 m antenna. dThe LMT was upgraded from 32.5 m to a full 50 m diameter telescope in early 2018. At SPT the aperture was under-illuminated in 2017 with an effective diameter of 6 m.

2.3. Fourier Coverage

An interferometer like the EHT samples the Fourier transform of the image on the sky. By correlating the data obtained from N stations, $N(N-1)/2$ spatial frequencies are measured. As the Earth rotates, those spatial frequencies form tracks in the Fourier plane (i.e., the (u, v) plane) to produce a sparsely sampled Fourier transform of the sky image. With the sensitivity requirements established, one can estimate the baseline coverage that results after the two-stage detection process above (Section 2.2) is followed. Figure 3 shows that the measured spatial frequencies that satisfy the EHT signal-to-noise specification when ALMA is included in the array result in near-full coverage on all baselines in the array, thereby maximizing imaging potential. At the outset of EHT build-out, this full coverage goal served as a design goal based on imaging simulations of synthetic data (see Section 2.1). Subsequent observations in 2017 April confirm that this (u, v) coverage is sufficient to image horizon-scale features (Paper IV).

Figure 3. Expected EHT Fourier space coverage on Sgr A*. The left panel shows both detections (red) and non-detections (gray) of Sgr A* in the 2013 EHT campaign. Participating telescopes were : APEX, CARMA, JCMT, SMA, and SMT. The dashed circles mark baselines with a fringe spacing equal to 50 μas (approximately the diameter of the shadow of the SMBH candidate Sgr A*) and 25 μas. The two remaining panels show simulated EHT observations in 2020 : (1) without ALMA and (2) with ALMA. Specifications to determine baseline detections shown are those detailed in Section 2.2. These figures emphasize the benefit of including ALMA in the array : its high sensitivity allows detections for SgrA* on all observed baselines. Because each EHT site requires at least one strong baseline to identify an interferometric fringe and to correct for residual delays, rates, and phase wander, ALMA significantly extends the Fourier coverage and sensitivity even for non-ALMA baselines. Coverage shown in the two right panels corresponds to an array including Chile (APEX, ALMA), Mexico (LMT), France (NOEMA), Spain (PV), Hawaii (SMA, JCMT), Arizona (SMT), and South Pole (SPT). The corresponding baseline coverage of the 2017 observations is shown in Figure 11.

2.4. Time Resolution

Characteristic timescales that affect the evolution of structures in horizon-scale images include the light-crossing time ($T_\rmlight

=GM/c^3$) and the period of the ISCO (PISCO), both of which scale with mass. With an assumed mass of $4.1\times 10^6M_\odot $ for Sgr A*, $T_\rmlight
=20\,\rms$ and PISCO ranges from 4 minutes for a prograde orbit around a maximally spinning black hole to 54 minutes for a retrograde orbit around a maximally spinning black hole. If a mass of $6.2\times 10^9M_\odot $ is assumed for M87, $T_\rmlight
=8.5\,\rmh$ and PISCO ranges from 4.5 to 58 days for the same orbits. All of these timescales, while important for imaging and modeling time-variable structures, far exceed the coherence times of the atmosphere, which set the integration intervals and sensitivity requirements for the EHT. Hence, the EHT must already track VLBI observables on considerably finer timescales than Tlight or PISCO for the primary cosmic targets, M87 and Sgr A*.
2.5. Frequency Configuration

The instrumentation at EHT sites is designed to match ALMA's bandwidth and intermediate frequency (IF) ranges. ALMA antennas are equipped with dual-polarization, sideband-separating receivers with four IF outputs (Section 3.1). The total bandwidth that can be transported back from each ALMA antenna is 16 GHz, thus resulting in a maximum IF bandwidth of 4 GHz per output. The sky frequencies for both the lower- and upper-sideband must overlap perfectly from station to station, which fixes both the local oscillator (LO) frequency and IF frequency ranges at each observatory (Tilanus et al. 2013). Table 4 shows the frequency configurations of the EHT in both atmospheric transmission windows around 230 and 345 GHz.

Table 4. EHT Frequency Configurations

The main considerations for selecting the chosen LO frequencies are (Marrone et al. 2014) as follows.

1.
The tuning range of the receivers at participating facilities.
2.
Atmospheric transmission.
3.
The avoidance of Galactic 12CO : $\nu \,\sim $ 230.3–230.8 GHz and $\nu \,\sim $ 345.4–346.1 GHz within the VLBI observing bands.
4.
To a lesser degree : avoidance of Galactic 13CO : $\nu \,\sim $ 220.2–220.6 GHz and $\nu \,\sim $ 330.3–330.9 GHz within the VLBI observing bands.
5.
Access to 12CO spectral lines in an extended tuning range of the receivers above 9 GHz when observing in the 1.3 mm band, or below 4 GHz when observing in the 0.87 mm band.
6.
Access to maser lines within the VLBI band, e.g., the SiO maser line at 215.596 GHz ($v=1,\,J=5\to \,4$).
7.
Performance of existing quarter-wave plates used to observe circular polarization.

For ALMA's 230 GHz band, the IF band previously was restricted to a lower limit of 5 GHz (now 4.5 GHz), which resulted in a common IF range across the telescopes of 5–9 GHz, whereas the common IF range for the 345 GHz band is 4–8 GHz.
3. Instrumentation

A schematic of the EHT's VLBI signal chain at single-dish telescopes is shown in Figure 4. The front end is typically a dual-polarization sideband-separating receiver in the 1.3 mm or 0.87 mm bands, often the product of a joint development project between the EHT and the telescope facility. These efforts are described in the Appendix. A hydrogen maser provides a frequency reference standard of sufficient stability for mm-VLBI (Section 3.2), and is used to phase lock all analog systems as well as digital sampling clocks throughout the signal chain.

Figure 4. System diagram at a single-dish EHT site with 64 Gbps capability. Dual-polarization (left and right circular polarization (LCP and RCP)) and upper- and lower-sideband (USB and LSB) analog IF signals are sent from the receiver. The receiver local oscillator is locked to the station hydrogen maser 10 MHz reference. Block downconverters (BDCs) mix these signals to baseband. R2DBEs sample the analog signals and distribute packetized data to Mark 6 recorders over a 10 GbE network. All timing is locked to a 10 MHz maser reference and synchronized with a pulse-per-second (PPS) Global Positioning System (GPS) signal. The components are controlled through a 1 GbE network. See Figure 8 for a photograph.

Dedicated block downconverters (BDCs ; Section 3.3) mix IF bands coming from the receivers to baseband. Each 4 GHz wide IF band is split and downconverted into two 2 GHz wide sections at baseband. High-bandwidth digital backends (DBEs ; Section 3.4) are used to sample two 2 GHz baseband signals each. The sampled data are put into the VLBI Data Interchange Format (VDIF ; Whitney et al. 2009) and transmitted to a Mark 6 recorder (Section 3.5) via two 10 Gbps Ethernet (GbE) small form-factor pluggable (SFP+) interfaces.139 The 16 Gbps output from each DBE matches the recording rate of a single Mark 6 VLBI recorder that records in parallel to 32 hard drives (Whitney et al. 2013). Four DBE—Mark 6 systems are used to sample and record the four 4 GHz wide IF bands coming from the two receiver sidebands and dual polarizations for an aggregate data rate of 64 Gbps.

For operations at high-altitude, helium-filled hermetically sealed hard drives are used, avoiding the need to build pressure chambers around the recorders. The hard drives collectively accumulated over 10,000 hr of recording at up to 5100 m altitude without a disk failure during the 2017 observations. The full 64 Gbps signal chain thus uses 128 hard drives in parallel, each with a capacity of 6–10 TB for a total storage capacity of about 1 PB. For the stations on the periphery of the network that cannot participate in all scans, 1 PB supports a typical VLBI observing campaign of about 6 days, while stations in the center need a double set of modules, or about 2 PB. Across the array, an EHT observing campaign involving all stations in Table 3 would require a total of about 15 PB of data storage.

Connected-element (sub)millimeter interferometers have more complex systems that use phased-array processors to sum signals from multiple telescopes into a single signal with much greater sensitivity. These processors are integrated with their digital correlators and output the summed signal as VDIF data packets to Mark 6 recorders as at single-dish stations.

The following sections describe each subsystem in more detail.
3.1. Receivers

The past three decades have seen the development and widespread use of heterodyne receivers in the millimeter and submillimeter bands based on superconductor–insulator–superconductor (SIS) junctions (e.g., Phillips et al. 1981 ; Maier 2009 ; Carter et al. 2012 ; Tong et al. 2013 ; Kerr et al. 2014). Over this period, instantaneous bandwidths increased by more than a factor of 30, while noise temperatures decreased by an order of magnitude. Improvements in receiver and antenna reflector technology have combined with the increased recording rates to lay the foundations for a millimeter wavelength VLBI array that is capable of observing targets with a flux density below 1 Jy. In the receivers, high-frequency radiation from the sky is mixed with a pure tone (an LO signal derived from a high-stability frequency reference) and downconverted to an IF using photon-assisted tunneling to transport current across the SIS junction's energy gap. Presently installed SIS-based receivers at observatories typically support IF bandwidths of 4–12 GHz, with higher bandwidth systems becoming available at selected sites.

Heterodyne receivers have two observing bands with sky frequencies centered at $\nu _\mathrmLO-\nu _\mathrmIF$ (LSB) and $\nu _\mathrmLO+\nu _\mathrmIF$ (USB), respectively, from which the signals are folded on top of one another (double-sideband (DSB) receiver). With the use of an RF 90° hybrid, two mixers, and an IF 90° hybrid, modern millimeter receivers can separate the sidebands into two distinct IF channels (sideband-separating (2SB) receiver). The SIS mixers employed at these wavelengths use single-polarization rectangular waveguides that couple to a single polarization of the incident radiation through planar antennas mounted in rectangular waveguides. Dual-polarization receivers employ two independent orthogonal signal chains. Polarizations are split using a wire grid or a waveguide-based orthomode transducer (OMT). The latter can be inserted in front of the mixer blocks and cryogenically cooled, resulting in reduced ohmic losses. Some of the EHT stations use OMTs with circular polarizers, but the majority use quarter-wave plates in front of the receivers. ALMA records in dual orthogonal linear polarization, which is converted to circular polarization in post-processing as described in Section 5.
3.2. Hydrogen Maser Frequency Standards

As with connected-element arrays, VLBI relies on the fundamental ability of radio band receivers to accurately preserve the phase of detected cosmic radiation. For connected-element arrays, a common LO, derived from a station frequency reference, is used for all antenna receivers. On long VLBI baselines, sharing a common frequency reference is currently not technically feasible, and each VLBI site must use its own clock. This practice imposes a strict requirement on the stability of the frequency standards used for VLBI. Generally, one requires $\omega \tau \sigma _y(\tau )\ll 1$, where ω is the observing frequency in rad s−1, $\sigma _y(\tau )$ is the square root of the Allan variance (the Allan standard deviation), and τ is the integration time. This limit keeps rms phase fluctuations well below 1 rad (Rogers & Moran 1981).

Because of their excellent stability on timescales that match VLBI integrations (about 10 s, Figure 5), hydrogen masers are used almost without exception as VLBI frequency references worldwide. At $\sigma _y(10\,\rms)=1.5\times 10^-14$, VLBI observations at wavelengths down to 0.87 mm can be carried out with coherence losses ($\mathrmLoss\simeq 1-e^-(\omega \tau \sigma _y(\tau ))^2$) limited to $\lt 5$ % on a baseline where stations at either end are equipped with similarly stable masers (Doeleman et al. 2011). The use of hydrogen masers ensures that phase fluctuations in the VLBI signal due to atmospheric turbulence are typically the dominant source of coherence loss in EHT observations (Rogers et al. 1984 ; see also Figure 2).

Figure 5. Top panel : measured Allan standard deviation, $\sigma _y(\tau )$, of the hydrogen maser at the LMT compared to a precision quartz oscillator. The open red points are the manufacturer specifications of the hydrogen maser when compared to another maser. At a 1 s integration time, the quartz oscillator and maser have similar stability, so the measurements indicate that the maser is meeting its specifications as installed at a coherence time of 1 s. The flattening of the $\sigma _y(\tau )$ curve beyond 10 s is due to the decreased stability of the quartz crystal. The extrapolation of Allan deviation from short integration times to 10 s indicates that the maser meets the stability goal of $\sigma _y(10\,\rms)=1.5\times 10^-14$. Bottom panel : the long-term drift of the maser at the SMA compared to GPS, measured by differencing the 1 PPS ticks from the maser and local GPS receiver. The vertical width of the trace is due to variable ionospheric and tropospheric delays of the GPS signal (including the excursion near hour 200), while the long-term trend represents the frequency error of the maser. The drift measured from this plot, and its effects on the fringe visibility, are removed during VLBI correlation.

The hydrogen masers used in the EHT are monitored for stability using two tests. The first compares the stability of the 10 MHz frequency reference output of the maser with that of a high-precision quartz oscillator, known to have a similar performance as a maser on 1 s timescales. This in situ measurement confirms nominal maser operation at 1 s integration times, and extrapolation then yields an estimate of maser performance at 10 s (see Figure 5). A second test is to routinely monitor the offset between 1 PPS signals derived from the maser and a GPS receiver. GPS stability on 1 s timescales is poor due to variations induced by the ionosphere, but on longer timescales ($\gt 10^4$ s) GPS precision, which is referenced to the average of many atomic clocks, will exceed that of any single maser at an EHT location. An observed linear drift (Figure 5) over month to year timescales confirms long-term maser stability and also provides an instrumental delay-rate that is required for later interferometric detection (see Section 5).
3.3. Block Downconverters

A BDC design was developed to mix selected pieces of the incoming IF band from the receiver (in the range 4–9 GHz) down to baseband (0–2 GHz) for sampling. For observing at 1.3 mm, bandpass filters select 5–7 GHz and 7–9 GHz bands that are mixed against a LO at 7 GHz to convert to baseband. Similarly, for observing at 0.87 mm, 4–6 GHz and 6–8 GHz bands are mixed against an LO at 6 GHz to convert to baseband. The LO is phase locked to a 10 MHz reference from the station frequency standard. Coaxial relays in the output stage select which set of baseband outputs is connected to the data acquisition system, and the LO of the unused set is muted to avoid interference. The downconverter has two duplicate chains of filters and mixers for processing two of the four receiver IF channels, and two such downconverters are used in a complete system. A simplified schematic of a BDC is shown in Figure 6.

Figure 6. Simplified schematic diagram of the BDC. Only one of the two (identical) polarization channels is shown, and several intermediate amplification stages are omitted. Two local oscillators maser-locked and tuned to 6 GHz and 7 GHz are used to mix all the filtered IF bands between 4 and 9 GHz to baseband (0–2 GHz). For 230 GHz operation, a 5–9 GHz IF band is split with output of 5–7 GHz (''low-band'') and 7–9 GHz (''high-band''). For 345 GHz operation, a 4–8 GHz IF band is split with an output of 4–6 GHz (''low-band'') and 6–8 GHz (''high-band''). The 6 and 7 GHz local oscillator signals are also sent to the other polarization channel. The attenuation and band selection can be set using a control panel or remotely via an Ethernet connection.

The maximum conversion gain of each channel is about 23 dB, and it can be adjusted downward to about −8 dB in 0.5 dB steps to match the output power of the BDC with the input dynamic range of the digitizers. At a nominal output power of −7 dBm, the BDC operates in the linear regime over the entire programmable range of the attenuators. An 8-bit controller provides control of the synthesizers, digital attenuators, and coaxial relays, and interfaces to a keypad and display unit for manual operation, as well as to an Ethernet port for remote control.

3.4. Wideband VLBI Digital Backend

Coherent received station data in modern VLBI systems are recorded digitally. The VLBI instrument that digitizes and formats the analog received signal for recording is termed the digital backend (DBE). The high bandwidths that enhance the EHT sensitivity require proportionately fast digital sampling speeds. The timing of the samples is an implicit time stamping of the data, so the sampler clock must be timed with maser stability and precision.

For several generations of instrumentation the EHT has based its digital hardware on open-source technology shared by the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER ;140 Hickish et al. 2016). The open-source hardware currently in use includes five gigasample-per-second (Gsps) analog-to-digital converter (ADC) boards, based on an integrated circuit that interleaves four cores, each with a maximum sample rate of 1.25 Gsps. The ADC circuit design and hardware testing is documented in Jiang et al. (2014). The compute hardware platform is the CASPER second-generation Reconfigurable Open Access Computing Hardware (ROACH2). The ROACH2 uses an FPGA as its digital signal processing engine.141

The current EHT DBE instrument was developed in 2014, and is called the ROACH2 Digital Back End (R2DBE ; Vertatschitsch et al. 2015). The R2DBE samples two analog channels at 4.096 Gsps, each with 8-bit resolution, i.e., two 2.048 GHz wide bands, before re-quantizing the samples with 2-bit resolution, packing the data in VDIF format, and then transmitting it over two 10 GbE connections to the Mark 6 recorder.142 Each R2DBE transmits two 8 Gbps data streams to a Mark 6 for recording. Accurate timing and synchronization is achieved by referencing the ROACH2 clocks to the maser via an external EHT-developed 2.048 GHz synthesizer.

The per-channel signal processing flow within the R2DBE is shown in Figure 7. Gain, offset, and sampler clock phase mismatches between the cores of the ADC produce spurious artifacts in the spectrum of the digitized signal, most prominently a spur at one quarter of the sample rate frequency that is caused by interleaving imperfection of the quad-core ADC. A calibration routine is performed at the start of each observation to tune the distribution of 8-bit samples for each core in offset, gain, and phase, removing these artifacts (Patel et al. 2014). A digital power meter is implemented in the firmware to calculate input power every millisecond, which is useful for pointing and calibration measurements.

Figure 7. Functional diagram of the R2DBE. A pair of ADCs sample two channels of 2.048 GHz Nyquist bandwidth IF bands, typically representing two antenna polarizations. After requantization of the samples to 2 bits, the data are distributed in VDIF packets over a 10 GbE network to Mark 6 recorders. The maximum FPGA clock speed is too slow to process the ADC output stream rate of 4096 megasamples per second in series, so 16 ADC samples are transferred from the sampler in parallel on each FPGA clock cycle and are processed in parallel though the FPGA, which is clocked at a sixteenth of the sample clock, or 256 MHz. The FPGA and sampler clocks are locked to the maser reference frequency. In addition to the sample clock and dual IF inputs, each ADC circuit board is also equipped with a low-frequency synchronization input. On one of the ADC boards, the synchronization input is connected to GPS PPS. An internal PPS for VDIF time stamping is synthesized from the 2.048 GHz maser-referenced clock and synchronized to the GPS real-time PPS time-tick once at the beginning of an observation. The internal PPS drift relative to GPS real-time PPS (Figure 5) is measured by a counter and is available to be read from a register over Ethernet, as well as copied into the VDIF data-header, as it is a prior parameter for VLBI correlation.

An important design consideration is the optimal number of bits per sample recorded onto storage media at the telescopes. This is determined by trading off the sensitivity increase realized through sampling more bandwidth at higher precision (see Equation (1)) with the cost of media required to store the data (for a detailed explanation, see Thompson et al. 2017). For the EHT, a maximum aggregate bandwidth of 16 GHz is set by the characteristics of ALMA receivers. When bandwidth is limited in this way, one examines the increase in sensitivity per additional unit media. For 1-bit recording (two-level sampling), the digital efficiency (ηQ in Equation (1)) is 0.64. Moving to 2-bit recording (four-level sampling) increases ηQ to 0.88 at the expense of doubling the required recording media, for a 38 % sensitivity increase per additional unit media—this is approximately equivalent to doubling the front-end bandwidth and keeping 1-bit sampling. Tripling the media cost and recording 3 bits (eight-level sampling) delivers only a 25.5 % increase in sensitivity per additional unit media. The 2-bit sampling scheme was chosen as it ensures ample margin for sensitivity requirements while minimizing recording media, which dominates the cost of VLBI correlation (Deller et al. 2011).

In a 2-bit system, the noise voltage thresholds of the four sampling levels should be properly set to maximize digital processing efficiency. A proper setting ensures that all four levels are optimally populated for a given input voltage signal from the telescope receiver system (Cooper 1970 ; Thompson et al. 2017). The processing efficiency is not a sensitive function of these thresholds, but the statistics of the level populations can vary significantly as elevation and weather condition changes cause fluctuations in the receiver power arriving at the sampler. For this reason, a calibration of the sampler threshold setting are performed periodically during calibration scans to maintain optimal settings.
3.5. High-speed Data Recorders

The Mark 6 VLBI Data System (Whitney et al. 2013) is a packet recording system used to store the R2DBE output streams to hard drives. The recorder captures the two 8 Gbps streams from the R2DBE using commercial 10 Gbps Ethernet network interface cards. It strips the internet packet headers and stores the payload containing VDIF data frames. For sustained recording at 16 Gbps, each Mark 6 recorder writes the data in time slices across 32 hard drives with a round-robin algorithm. The disks are mounted in groups of eight in four removable modules for ease of handling and shipping. For the EHT, four such recorders are configured in parallel to achieve an aggregate data capture rate of 64 Gbps.

Mark 6 recorders and modules are commercially available and in use in other VLBI applications. Several modifications were required for EHT use at high altitude, as hardware specifications typically state 10,000 ft as the maximum operating altitude. The low ambient air density necessitates sealed, helium-filled hard drives, both for the system disk for recorders and also in all modules onto which data are recorded. In addition, the Mark 6 interior was modified to direct a high-volume airflow onto the CPU, network, and data interface cards, which were found to be sensitive to overheating at altitude.

A photograph of the EHT VLBI backend (BDCs, R2DBEs, and Mark 6s) at the PV 30 m telescope is shown in Figure 8. Recorders used for earlier EHT campaigns included the Mark 5C system, which was capable of capturing only a 4 Gbps data stream onto two modules. The bandwidth of the EHT backend since 2004 is plotted in Figure 9 and represents a 64-fold increase, corresponding to an eight-fold improvement in sensitivity.

Figure 8. EHT digital VLBI backend as installed at the Institut de Radioastronomie Millimétrique (IRAM) PV 30 m telescope in Spain. The upper portion of the right-hand side rack holds the four R2DBE units. Two block downconverters are installed near the middle. The VLBI backend computer is mounted on the bottom right. The rack on the left and the lower portion of the rack on the right hold the four Mark 6 recorders with four disk modules each, providing a total of about 1 PB in data storage.

Figure 9. Recording rate of EHT observations over time. As of 2018, EHT stations record at 64 Gbps, equivalent to a doubling of recorded bandwidth every two years for over a decade (blue curve). The high bandwidth, a result of linking EHT instrumentation to industry trends and commodity electronics, is a crucial component of the EHT's sensitivity, enabling detections on long baselines, providing resilience of the network against poor weather and low-elevation targets, and allowing detections from all stations to ALMA within short atmospheric coherence times (see Section 2.2).

3.6. Phased Arrays

To use the total collecting area available at connected-element interferometers that participate as single stations in the EHT VLBI network (ALMA, SMA, and, in the future, the Northern Extended Millimeter Array (NOEMA) these arrays coherently add the signal received from the target source by each antenna and record as if from a single antenna. Practical constraints on the maximum data rate that can be recorded at each site require that this summation be performed in real time.

Forming a coherent sum requires correcting for deterministic delays, such as geometric and known instrumental delays, as well as non-deterministic delays, which at EHT frequencies are significantly affected by the distribution of water vapor in the atmosphere. The atmospheric delay varies over time, antenna location, and direction so that accurate compensation can only be achieved through the use of in situ calibration methods.

Phasing systems were developed for the SMA and ALMA (see Appendix), and these observatories participated as phased arrays since 2011 and 2017, respectively. A phasing system for NOEMA is in the process of being implemented and commissioned for VLBI. Figure 10 shows the SMA phasing efficiency, i.e., the fraction of beamformed power compared to ideal phasing, estimated using Equation (2), achieved over the course of several scans during one night of the 2017 EHT campaign. For most of the scans, the efficiency is well above 0.9 (see inset). Typical phasing performance of the ALMA array can be found in Matthews et al. (2018).

Figure 10. Phasing efficiency of the SMA on various sources over the course of one observing schedule. The inset shows the cumulative distribution of phasing efficiency of the SMA over the entire 2017 EHT observing campaign.

3.7. Setup and Verification

As part of the integration of the new VLBI systems in 2015, most station backends were configured at Haystack Observatory prior to shipment to the telescopes. New equipment still typically passes through Haystack for initial inspection, check-out, and configuration. Each site takes responsibility for the installation of the equipment and ensuring that the connections to facility hardware work to specification and are not affected by factors such as telescope motion.

Before each observing campaign, each site goes through a comprehensive setup and verification procedure, which includes the completion of a checklist by site operational staff. The procedure verifies operation of the BDC, R2DBE, and Mark 6 systems, and the exact frequency and lock status of LOs, which set the exact observed sky band, and the ADC clock that time stamps the data. The check also includes the coherence and drift of the hydrogen maser time standard as this clock rate measurement is needed during correlation for fringe-stopping.

Due to the remote nature of many of its sites and the large data volume recorded, the EHT lacks real-time verification of fringes. Shipping data from remote stations to the central correlator and processing takes several days at minimum, and many months in the worst case (from the South Pole ; see Appendix A.11). If a key system fails, it is possible for a site to take data that never result in fringes, making careful testing and retesting of subsystems throughout the observation absolutely crucial. Data from brief observations (10–30 s) can be transferred from sites with fast internet connections for near real-time fringe verification. While possible, this requires robust data transfer connections.

The most complete in situ full-system check consists of the injection of a test tone at a known frequency in front of the receiver. A short data segment is recorded, and the autocorrelations and zero-baseline cross-correlations are inspected to verify that the test tone appears at the correct frequency and with the correct profile. Further, the tone in the baseband is mixed down to 10 kHz using a third LO and compared to a 10 kHz tone derived from the maser 10 MHz reference. The two should be phase locked when examined on an oscilloscope, which verifies the phase stability of the whole system. This test is exquisitely sensitive to small disturbances in the system. At the JCMT an equivalent test is done by verification of local connected-element fringes with the SMA.

Results and logs from the setup and verification are centrally archived and available to the correlator centers for the interpretation of station issues and for fault diagnosis when data quality issues emerge.
3.8. The Array

The EHT included eight observing facilities in 2017. Three additional facilities have since joined (GLT) or will soon join (KP 12 m and NOEMA), and two facilities (CARMA and the CSO) have participated in past EHT observations but have now been decommissioned. Properties of these facilities are summarized in Tables 2 and 3, and the Appendix. The baseline Fourier coverage provided by the array in 2017 for M87 is shown in Figure 11. Table 5 shows the actual performance of the array on scans of M87 during the 2017 science observations. The scan-averaged thermal noise within one 2 GHz frequency band was significantly better than 1 mJy on most baselines to ALMA, and generally a few mJy on baselines excluding ALMA. These achieved sensitivities, combined with the realized (u, v) coverage in Figure 11, confirm that the EHT has met its essential specification in providing an array that can image features on the scale of an SMBH shadow.

Figure 11. Aggregate EHT baseline coverage for M87 over four nights of observing with the 2017 array. Only detections are shown. The dashed circles show baseline lengths corresponding to fringe spacings of 25 and 50 μas. See Paper III for details.

Table 5. Median Thermal Noise (mJy) for Observations in 2017

Note. Median scan-averaged thermal noise per baseline in mJy for all M87 detections in 2017 April. Entries for the SPT reflect the median thermal noise on 3C 279, since the SPT cannot observe M87 due to its geographic location. Scan durations were three to seven minutes. For more details, see Paper III.

4. Observing

EHT science observing campaigns are scheduled for March or April when Sgr A* and M87 are night-time sources and the weather tends to be best on average over all sites. In addition, ALMA tends to be in a more compact configuration with better prospects for including more antennas in a phased array for increased sensitivity. Test and commissioning runs are scheduled a few months prior to campaigns to ensure that VLBI equipment, which may be dormant for months at a time, is operational.
4.1. Weather

Weather is an important consideration for VLBI observations at millimeter wavelengths. Most of the EHT observatories are located in the northern hemisphere, and those stations have especially large weather variations between seasons. Opacity and turbulence are typically lowest at night and in winter and early spring. At many sites, and particularly the connected-element arrays, the reduced atmospheric turbulence during night-time hours is essentially required. To protect against inclement weather, the EHT uses flexible observing with windows that are about twice as long as the intended number of observing nights. Within the window, a few hours before the start of observing each night, weather conditions are reviewed at all sites and a decision is made whether or not to observe that night. When an EHT night is not triggered, it is often possible for the time to be used for other observing programs at an observatory.
4.2. Scheduling

The process of scheduling starts with the list of approved target sources, time allocations at EHT telescopes and ALMA, and the dates of the observing window (Section 4.1). Schedule construction has to satisfy multiple requirements :

1.
a high total on-source time for each target,
2.
a wide range of parallactic angles sampled for polarimetry,
3.
long baseline tracks on all sources within the limited number of observing days,
4.
randomized scan lengths and scan start times on Sgr A* for periodicity analysis,
5.
good baseline coverage in the (u, v) plane, and
6.
regular gaps for telescope pointing and calibration.

AGN sources are chosen as calibrators based on their brightness, compactness, and proximity to the target sources. The calibration sources are used for multiple purposes, including fringe finding, bandpass calibration, and polarization calibration.

Observing blocks are created for each of the sources, and these blocks are merged into tracks, each corresponding to a single night of observing. Depending on time allocations and Fourier-coverage needs, multiple blocks on the same source may appear in the same track or in different tracks. Each observatory has different needs for overhead because the EHT is an inhomogeneous array. Overhead accommodates time for pointing, focus, and primary and secondary flux observations at all sites, plus phase-up time and array-polarimetric calibrations at the phased arrays. A typical EHT schedule (Figure 12) records VLBI scans with a duty cycle of approximately 50%, with a substantial fraction of those scans on targets strong enough to use for array calibration.

Figure 12. EHT 2017 observing schedule for M87 and 3C 279, covering one day of observations (April 6). Empty rectangles represent scans that were scheduled, but were not observed successfully due to weather, insufficient sensitivity, or technical issues. The filled rectangles represent scans corresponding to detections available in the final data set. Scan durations vary between 3 and 7 minutes, as reflected by the width of each rectangle, and scans are separated by periods of time used at each site for local pointing adjustments and calibration measurements. For this schedule, 3C 279 was the calibrator source for the primary target, M87. For information on other observing days, see Paper III.

4.3. Monitoring and VLBI Backend Control

The EHT developed a centralized monitoring tool called VLBImonitor to visualize observing status, collect ancillary calibration and weather data from each site, and provide real-time and predicted weather information from meteorological services. The information collected, logged, and displayed includes atmospheric and local weather conditions, observatory metadata such as telescope coordinates and on-source status, system temperature measurements, opacity measurements, digital backend and recorder state information, and comments from on-site observers and operators. Communication with the metadata server (by the software clients at each site or via a web interface) uses the JSON-RPC (remote procedure call) protocol over HTTPS. A ''masterlist'' defines metadata parameters that are accepted (white-listed) by the server and all their properties (e.g., data type, measurement cadence, a function that evaluates if the current value is valid or invalid, and units).

The VLBImonitor software143 was introduced for the 2017 observations. In 2018, a VLBI backend computer and network were added at the sites to provide a common monitoring and control platform at each station. Both monitoring and control remain in active development. At present, the EHT deploys specialist teams at each station, which, in practice, limits the observing window to about 12 days. It is a long-term objective for the EHT to both increase the length of this window and to conduct VLBI observations without the need for on-site specialists, after an initial setup and verification by local and remote experts. A critical component toward this goal is the implementation of comprehensive remote monitoring of the stations and VLBI equipment, as well as remote control of the VLBI backend.
5. Correlation and Calibration

The recorded data modules at all sites are separated by frequency band, with the ''low-band'' shipped to the VLBI correlator at MIT Haystack Observatory in Westford, Massachusetts, USA, and the ''high-band'' to the correlator at Max-Planck-Institut für Radioastronomie (MPIfR) in Bonn, Germany. Correlation is performed using the Distributed FX (DiFX) software correlator (Deller et al. 2011) running on clusters of more than 1000 compute cores at each site, and is split between the two sites to speed processing and allow cross-checks. At least as many Mark 6 playback units are needed at each correlator as there are stations in the EHT. The Mark 6 playback units at the MIT correlator are connected via 40 Gbps data links. A 100 Gbps network switch then delivers data to the processing nodes using 25 Gbps links. At MPIfR the internode communication, which includes the Mark 6 playback units, is realized via 56 Gbps connections, exceeding the maximum playback rate of the Mark 6 units of 16 Gbps.

Each 2 GHz observing band is correlated independently, with multiple passes required to correlate the full 4 or 8 GHz in an experiment. The correlation coefficients between pairs of antennas are calculated after correcting for an a priori clock model (Earth rotation, instrumental delays, and clock offsets and drift rates). All sites except ALMA record left and right circular polarizations (L/R) producing cross-correlations in the standard circular basis (LL, LR, RL, RR). ALMA antennas, however, are natively dual-linear polarization (X/Y), so a linear-to-circular polarization conversion is performed on ALMA baselines after VLBI correlation. PolConvert (Martí-Vidal et al. 2016) is a software routine developed for this purpose as part of the program to phase the ALMA array for VLBI operation (Matthews et al. 2018 ; Goddi et al. 2019). This routine forms linear combinations of the cross-polarization-basis correlator products (XR, YR) and (XL, YL) with ±90° phase shifts introduced to the visibility phase to produce complex visibilities in the circular-polarization basis, for each integration time. The input correlator products to PolConvert are equalized in gain and phase, and the X–Y channel phase differences are removed before polarization conversion. This X–Y channel equalization is performed using standard calibration techniques for connected-element ALMA operation (for details see Paper III).

To reduce data volumes and increase S/N, the cross-products computed in the correlator are averaged both in time and frequency. These complex cross-products are then fitted for fringe-delay (linear change in phase versus frequency) and fringe-rate (linear change in phase versus time), which are then removed. Residual fringe-delay and fringe-rate are due to several factors. Largest among these are residual clock drifts, instrumental electronic delays, and atmospheric phase fluctuations that can result in rapidly varying fringe-rate residuals. For the compact, narrow-field EHT continuum targets, delay and rate variability due to intrinsic source structure is expected to produce much smaller residuals. The averaging time and bandwidth in the correlator is thus set to ensure that any coherence losses due to delay or rate variations are negligible, or equivalently that such variations can be tracked both in time and frequency. For EHT observations, the typical averaging bandwidth is 0.5 MHz and the averaging time is 0.4 s, allowing residual delays up to ±1 μs and residual rates up to ±2.5 Hz. These settings enable the isolation and identification of instrumental spectral features, and also the ability to track atmospheric phase variations. This averaging in both time and frequency, results in a decimation of data volumes by more than a factor of 1 million.

After the initial correlation, the data are further processed through a pipeline that results in final data products for use in imaging, time-domain analyses, and modeling (Blackburn et al. 2019 ; Janssen et al. 2019). During fringe detection, the excess in correlated signal power due to the source on a VLBI baseline is identified, and the complex Fourier component of source brightness distribution is measured. As outlined in Section 2.2, high signal-to-noise detections on baselines to ALMA can be used to remove atmospheric phase fluctuations on non-ALMA baselines. Phase stabilizing the array in this way allows coherent integration of the VLBI signal on non-ALMA baselines beyond the atmospheric coherence time. Figure 13 demonstrates the process on real EHT data during relatively poor weather conditions, confirming the general approach and basis for the specifications in Section 2. Precise estimates of the observed systematic errors during the 2017 April EHT campaign are detailed in Paper III.

Figure 13. Fringes detected on EHT baselines before and after phase steering using the ALMA phased array as a reference station. Shown here are residual fringe-rate spectra, where the peak occurs at a single fringe-rate that is consistent with linear clock drift over the entire scan. Stochastic atmospheric phase variations result in fringe-rate variation over time, spreading the signal in the plot on the left. To recover the total fringe amplitude, baselines to ALMA are used to phase reference the array at a short timescale. Data shown are from a VLBI scan on a quasar calibrator (3C 279) obtained during EHT observations in 2017 April. The data are taken at low elevation, and at several sites during the afternoon and early evening when the atmosphere is often unstable. Baselines to ALMA are able to phase steer the remaining sites in the array at an effective timescale of 1–3 s depending on S/N. At SMA due to the mid-afternoon local observation, phasing is particularly challenging. This leads to an amplitude efficiency of about 90 % on SMA baselines, as well as increased measurement thermal noise for the APEX-SMA spectrum with a full-scan S/N of only 10.

Subsequent calibration steps convert the correlation coefficients derived from fringe detection to correlated flux density (Jy). This is accomplished through use of a priori information about station sensitivities, and by the application of self-calibration techniques to correct for variations in telescope gain over time and frequency. In cases where two EHT telescopes are in close geographical proximity (e.g., ALMA-APEX and SMA-JCMT), additional calibration constraints can be derived from the resulting baseline redundancy and using only general assumptions about the observed source (Paper III).
6. Future Developments

The EHT array is continuing to develop. With the ability to image SMBHs on horizon scales now confirmed (Papers I ; III ; III ; V ; VI), the focus of EHT development will shift to enabling observations that can refine constraints on fundamental black hole properties, processes of black hole accretion and outflow, and tests of general relativity. This depends on achieving higher angular resolution, enhancing image fidelity, and enabling dynamic imaging of time-variable phenomena. Higher resolution will allow more detailed studies and modeling of sub-horizon structures as well as sensitive tests for asymmetries in shadow features. Greater image fidelity will bring fainter emission near the horizon into focus for the study of accretion and jet processes, and it will enable a sensitive comparison across imaging epochs, which is especially germane for M87 with its dynamical timescale of days to weeks. For Sgr A*, the light-crossing time of 20 s requires a dynamic approach to image reconstruction, with the potential of observing the near real-time evolution of a black hole.

The planned and in-progress addition of telescope facilities at new geographic sites will improve the (u, v), or Fourier, coverage, and thus imaging fidelity. Over the course of the next two years, the EHT expects to add two more facilities : a beamformed NOEMA in France, which, once completed, will be the equivalent of an approximately 50 m dish, and a 12 m diameter dish on Kitt Peak in Arizona. A newly realized and important consequence of designing high-bandwidth systems is that adding telescopes with modest diameters (sime6 m) creates VLBI baselines with sufficient sensitivity to detect the primary EHT targets. An expansion of the EHT can, therefore, include the possibility of deploying numerous smaller apertures, enabling not only improved image quality but also snapshot capability, which is a precursor to constructing black hole movies (Bouman et al. 2018 ; Johnson et al. 2018). Additional plans to enhance the data throughput of VLBI backend and phased array systems are underway, linked to new generations of wideband millimeter and submillimeter receivers and industry trends that will allow for rapid design and implementation. With the inclusion of more sites and wider bandwidths, the computational requirements for VLBI correlation will increase : linearly with bandwidth, and as the square of the number of stations. The exploration of scalable approaches to address future EHT correlation needs is underway (Gill et al. 2019). The combination of these efforts is aimed at the substantial expansion of aperture plane sampling of the EHT and improved imaging.

To significantly improve angular resolution requires development in different directions. Planned extension of the EHT to operation at 0.87 mm wavelength, a standard receiving band at many facilities, would increase the angular resolution of the array by 40%. VLBI tests at 0.87 mm are underway and this capability is expected at a subset of EHT sites over the next 3–5 yr (see Table 4). An alternate approach to increased angular resolution is to deploy EHT antennas in space where baseline length is not limited to the diameter of the Earth, potentially allowing horizon-scale imaging of additional SMBH candidates (Johannsen et al. 2012). Space platforms also offer the possibility of rapidly sampling the Fourier plane, thereby opening the potential for dynamical imaging of black hole accretion and outflow processes (D. Palumbo et al. 2019, in preparation ; F. Roelofs et al. 2019, in preparation ; M. Shea et al. 2019, in preparation).

EHT observation strategies continue to be refined. With further development of remote monitoring and control tools, the EHT can explore triggering observations during the best conditions throughout the year outside the current March–April window. One consequence of this flexibility would be that observations for Sgr A* and M87 could be optimized separately in a given observing cycle, instead of grouped together as they are currently. Distributing the observations over a larger portion of the year also increases the likelihood that the EHT would detect emission transients or flaring on intermediate timescales should they occur, and affords, in general, the opportunity to study M87 on timescales that correspond to the expected ISCO period of order one to several weeks (Table 1). Not all EHT sites may be able to participate in such flexible campaigns, but even a subset of the array, especially if augmented with many smaller dishes, could provide useful observations for variability studies.
7. Conclusion

The goal of the EHT project is to observe SMBHs with spatial and temporal resolution that permits imaging on the scale of the lensed photon orbit, and the study of dynamics on commensurate light-crossing timescales. Leading up to the detection of event-horizon-scale structure in Sgr A* in 2008, and now a decade afterward, the development of EHT instrumentation proceeded through a series of systems that supported increasingly ambitious observations. These observing campaigns led to precursor scientific results that motivated a strategy of building an imaging array : one with baselines long enough to resolve horizon-scale structure, that included enough geographical sites to sufficiently sample the Fourier plane, and had the sensitivity required to detect compact, low flux density targets. Technology maturation, fueled by industry-driven trends, was focused primarily on improving the bandwidth of observations by increasing digitization and recording rates. Over a period of 10 yr, EHT data capture rates increased from 4 to 64 Gbps, allowing for observations that take full advantage of the capabilities of modern millimeter receivers. The parallel development of phased array technologies and investment in site-specific infrastructure (see the Appendix) have now led to a global EHT array with the capability to address its science goals.

Had the EHT project needed to build a VLBI array from the ground up, the cost would have been prohibitive. By developing new systems and infrastructure that allowed for the use of existing telescopes and facilities, most of which were not originally conceived to operate as VLBI elements, the EHT has created a purpose-built array with unique capability at modest cost.

Appendix : Specific Details of Participating Facilities in EHT Observations

One of the technical challanges of the EHT array is that it is assembled from existing telescope facilities that differ to a greater or lesser extent in their technical characteristics and readiness for VLBI operations. As a result, EHT instrumentation installed at each site requires customization. This appendix provides information on the specifics of each site in turn, not general to the array overall.
A.1. ALMA (5100 m Altitude)

The ALMA, located on the Chajnantor plain in Chile, is an international partnership between Europe, the United States, Canada, Japan, South Korea, Taiwan, and Chile (Wootten & Thompson 2009). The connected-element interferometer consists of fifty 12 m and twelve 7 m antennas, and is supplemented with four 12 m total-power antennas. Reflector surface accuracy is better than 25 μm rms.

The ALMA Phasing Project (APP) was an international effort to produce an antenna phasing system leveraging the superb (sub)millimeter capabilities and large collecting area of ALMA for VLBI applications (Doeleman 2010 ; Matthews et al. 2018). The APP added to the hardware and software already available at the ALMA site for connected-element interferometry the additional components necessary for coherently summing the ALMA antennas and recording VLBI data products. The rubidium clock that was formerly used to generate the reference 5 MHz LO tone was replaced with a hydrogen maser. Phasing interface cards were added to the ALMA Baseline Correlator to serve as the VLBI backend. A fiber link system was built and deployed to transport the phased-sum signal from the ALMA high-elevation site to the ALMA Operations Support Facility at an elevation of about 2900 m, where a set of Mark 6 VLBI recorders was installed. Numerous software enhancements were also required, including the implementation of an ALMA VLBI Observing Mode (VOM) and a phase solver to calculate the phases needed to adjust each of the ALMA antennas to allow coherent summation of their signals. The ALMA phasing system treats the phased sum as another input to the Baseline Correlator, so the phased-sum signal can be correlated with individual antenna signals. Standard ALMA single-field interferometric data are generated as a matter of course during VOM operation, and ALMA-only data products are archived as usual. When all antennas are included in the phased sum, ALMA is equivalent to an effective 88 m diameter aperture for VLBI operations. Details are described in Matthews et al. (2018) and Goddi et al. (2019).
A.2. APEX (5100 m Altitude)

APEX is a 12 m antenna located on the Chajnantor plain in Chile about 2 km from the ALMA site (Güsten et al. 2006). It was built by VERTEX Antennentechnik from the ALMA prototype development and inaugurated in 2005. It was outfitted and operated by the Max-Planck-Institut für Radioastronomie in Bonn (50%), the Onsala Space Observatory (23%), and the European Southern Observatory (27%) as the first telescope on the Chajnantor plain. The first VLBI fringes were obtained with APEX in 2012 at 230 GHz (Wagner et al. 2015).

The reflector surface accuracy is 17 μm rms, which gives good efficiency at frequencies exceeding 1 THz, and the telescope is correspondingly equipped with receivers spanning 200 GHz–1.4 THz. The surface panels and subreflector were replaced in early 2018 to improve the surface to 10 μm rms and so further raise the efficiency at the highest frequencies. At 230 GHz the elevation gain curve is flat to about 3% due to the high structural rigidity of the antenna. Pointing accuracy is better than 2 arcsec rms, and tracking accuracy is typically below 1 arcsec rms depending on wind conditions. The beam FWHM is 27.1 arcsec at 228.1 GHz.

The maser 10 MHz reference is transported to the front-end synthesizers and backend equipment on four low temperature-coefficient, double-shielded 85 m length cables. The cables are wrapped in thermal insulation and firmly fixed to support structures in the receiver cabin to minimize phase instabilities resulting from temperature changes or telescope movement. No round-trip phase stabilization is used. The front-end synthesizers (first LO and tone generation) each have their own frequency reference cable from the maser. References for the backend equipment are supplied through a distributor because the frequencies generated are much lower than for the front-end. The R2DBE and another VLBI backend called the DBBC are located in the antenna close to the receiver (15 m cable length) for low loss transmission of the dual-polarization dual-sideband 4–12 GHz receiver IF output. The Mark 6 recorders are located in a control container about 50 m from the telescope. The backends transmit eight 8 Gbps VDIF-format data streams on fiber with short-range 10 GbE 850 nm SFP+ fiber transceivers to the recorders.
A.3. GLT (100 m Altitude Currently, 3200 m Altitude Planned)

The GLT (Inoue et al. 2014) was originally the 12 m ALMA-North America prototype antenna (Mangum et al. 2006) located at the Very Large Array (VLA) site near Socorro, New Mexico. The antenna was awarded to the Smithsonian Astrophysical Observatory (SAO) in 2011, representing the partnership of the SAO and Academia Sinica Institute of Astronomy (ASIAA). The antenna was retrofitted and rebuilt for operation in the extreme arctic conditions of northern Greenland. Presently located at a temporary site on Thule Air Base, Greenland, the telescope is equipped with a new set of submillimeter receivers operating at 86, 230, and 345 GHz. In 2018, the GLT dish surface underwent iterative adjustments to improve surface accuracy, eventually achieving better than 40 μm rms. The pointing accuracy is about 3−5 arcsec during 230 GHz observations. The telescope is planned to be relocated to Greenland Summit, where the atmosphere provides excellent transparency for submm and THz observations (Matsushita et al. 2017).

The GLT has a complete VLBI backend. In 2018 January, fringes were detected between the GLT and ALMA, and in 2018 April, the GLT participated in EHT observations (Chen et al. 2018). The maser and associated equipment are located in a dedicated trailer approximately 40 m from the telescope. The maser 10 MHz is fed through a phase-stable coaxial cable to an adjacent synthesizer that generates the first LO (18–31 GHz) reference for the receivers. This first LO reference along with a separate maser reference of 100 MHz are combined and transmitted to the antenna through a single-mode fiber and used to phase-lock all the associated instruments in the receiver cabin (Kubo et al. 2018). The BDCs and R2DBEs are located in the receiver cabin and are interconnected using short segments of phase-stable coaxial cables. The Mark 6 recorders are located in the VLBI trailer approximately 35 m from the telescope. Communications between the R2DBEs and the Mark 6 recorders are via a 10 GbE optical network. The current system supports a throughput of 64 Gbps to the recorders.
A.4. JCMT (4100 m Altitude)

The JCMT is located on Maunakea in Hawai'i. It was dedicated in 1987 and was operated by a consortium (the United Kingdom, Canada, and the Netherlands) until 2015. Since then, the East Asia Observatory has operated the JCMT with funding from Taiwan, China, Japan, Korea, the United Kingdom, and Canada. The reflector is a 15 m Cassegrain design and has a surface accuracy of about 25 μm rms. The telescope is enclosed in a co-rotating dome and is protected by a 0.3 mm thick GoreTexTM windblind that is not removed for observing. The atmospheric opacity is measured with a line-of-sight 183 GHz radiometer.

The telescope participated in the VLBI observations that in 2007 detected the horizon-scale emission in Sgr A* (Doeleman et al. 2008) and has successfully participated in all EHT observing since then. This was done in cooperation with the SMA, which generated the phase-stable frequency reference signals and recorded the IF, utilizing the extended SMA (eSMA) infrastructure that enables the JCMT to join the SMA array as a connected element. From the 2019 VLBI campaign the JCMT will use a locally installed VLBI backend for recording, and will be equipped with a new receiver outfitted with ALMA 230 and 345 GHz mixers at 1.3 and 0.87 mm built by ASIAA.
A.5. Institut de Radioastronomie Millimétrique : 30 m (PV, 2900 m Altitude)

The IRAM 30 m telescope is located on Pico Veleta in the Spanish Sierra Nevada near Granada. The telescope was built in the early 1980s (Baars et al. 1987). The first VLBI fringes at 1.3 mm were obtained in 1995 (Greve et al. 1995) with one antenna of the Plateau de Bure interferometer, and since 1996 the PV 30 m has participated in the regular 3 mm VLBI CMVA/GMVA biannual runs.

The telescope surface has been adjusted to an accuracy of about $55\,\mu \rmm$ rms using phase-coherent holography with geostationary satellites. This yields a 230 GHz aperture efficiency of 47% at the optimal elevation of 50°. The gain elevation curve drops to about 35 % at elevations of 20° and 80°. The blind pointing accuracy is about 3 arcsec. The tracking accuracy is better than 1 arcsec for wind speeds below about 10 m s−1. Active thermal control of the telescope backstructure allows for efficient operation around the clock, and a de-icing system enables quick startup after winter storms. A 225 GHz radiometer continuously monitors the sky opacity at a fixed azimuth. Since 2018 October, the 30 m telescope is connected via a 1 Gbps fiber link to IRAM/Granada and the Spanish research network RedIRIS.

The PV 30 m is currently equipped with two heterodyne receivers. One of these, the Eight MIxer Receiver (EMIR) installed in 2009, has eight sideband-separating (2SB) mixers. The EMIR has 8 GHz of bandwidth per sideband covering the atmospheric windows at 3, 2, 1.3, and 0.87 mm wavelengths in dual-polarization. The EHT uses the EMIR 1.3 and 0.87 mm bands. Conversion from linear to circular polarization is done by quarter-wave plates, which are installed in a carousel to quickly switch between non-VLBI and VLBI observations. The IF signal from the receiver cabin is transported to a temperature-controlled backend room over 100 m coaxial cables. A new hydrogen maser was installed in 2018 January and then used for the GMVA and EHT sessions in 2018 April. For the EHT, four R2DBEs deliver 64 Gbps (two polarizations, two sidebands) to four Mark 6 recorders (see Figure 8).
A.6. IRAM : NOEMA (2600 m Altitude)

NOEMA is located in the French Alps and is the largest millimeter-wave facility in the northern hemisphere. With twelve 15 meter antennas, 2SB receivers with 8 GHz IF per sideband and polarization, and baselines up to 1.7 km, NOEMA will operate at 10 times the sensitivity and 4 times the spatial resolution of its predecessor, the former Plateau de Bure Interferometer (Guilloteau et al. 1992).

The NOEMA Phase 1 extension program was completed in 2018 September with the delivery of four additional antennas to the existing six, each with a surface accuracy of 35 μm rms. The dual-polarization 2SB receivers operate in the 3, 2, and 1.3 mm wavelength bands, with noise temperatures of, respectively, 35 K, 40 K, and 50 K in each band. Signal processing is done using an FPGA-based FFX correlator with flexible configurations modes. Beginning in 2019, NOEMA will have a phased-array mode with an initial processing bandwidth of 2 × 2 GHz (16 Gbps), eventually growing to 128 Gbps. The NOEMA Phase 2 extension program (2019) includes the construction of two additional antennas, the delivery of a second correlator for dual-band operation (2 × 32 GHz), a receiver upgrade to perform full-array observations up to 373 GHz (0.8 mm), and a baseline extension to 1.7 km for high-fidelity imaging down to a spatial resolution of 0.1 arcsec.
A.7. Kitt Peak 12 m (KP, 1900 m Altitude)

The telescope on Kitt Peak was acquired by the University of Arizona in 2013 March. The 12 m dish was a prototype antenna (Mangum et al. 2006) made for the ALMA project by the Alcatel/European Industrial Engineering consortium. It was relocated from the VLA site in New Mexico to the enclosure of the previous NRAO 12 m telescope on Kitt Peak, Arizona, in 2013 November. The telescope is operated by the Arizona Radio Observatory (ARO), a division of the Steward Observatory of the University of Arizona. First light was observed in 2014 October. The surface was adjusted to an rms figure error of 16 μm in 2018 September using photogrammetry. A 225 GHz radiometer measures atmospheric opacity.

VLBI observations will make use of a newly developed multi-band receiver (1.3–4 mm), which incorporates ALMA Band 3 and Band 6 mixers for the 3 and 1.3 mm bands. All bands sample both polarizations, and the 1.3 mm band will be converted to circular polarizations through a quartz quarter-wave plate. The receiver is under commissioning and the telescope is scheduled to participate in the next scheduled EHT observations. The master reference for this site is located within the domed enclosure adjacent to the computer room that houses the VLBI backend electronics.
A.8. LMT (4600 m Altitude)

The LMT is situated at the summit of Volcán Sierra Negra in Central Mexico. It is jointly operated by the Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE) and the University of Massachusetts (UMass). In 2017, two additional rings of precision surface panels were installed to enlarge the LMT primary mirror from 32.5 to 50 m. The primary mirror is an active surface comprised of 180 segments steered by 720 actuators to correct thermal and mechanical distortions. The large collecting area and a central geographical location with respect to other EHT sites make the LMT particularly important for array sensitivity and imaging fidelity.

Initial technical work to develop 3 mm wavelength VLBI at the LMT was the product of a multi-year collaboration between UMass, INAOE, SAO, the Massachusetts Institute of Technology Haystack Observatory, the Universidad Nacional Autónoma de México (UNAM), and NRAO. The first 3 mm observations were carried out in 2013 April with the facility Redshift Search Receiver (Erickson et al. 2007), a broadband dual-polarization, dual-beam receiver that acted as the front end. Those observations were performed with a VLBI backend using a high-precision quartz oscillator frequency reference running at 2 Gbps recording rate. Subsequent integration of a hydrogen maser and further testing in 2014 led to first VLBI science observations at 3 mm wavelength in 2015 (Ortiz-León et al. 2016).

In 2014, an interim special-purpose VLBI 1.3 mm wavelength receiver was assembled using mixers from the CARMA observatory and resourced through a collaboration including the institutes above and the University of California, Berkeley. This receiver was a single-pixel, dual-polarization, double-sideband receiver. It was deployed in 2015 for commissioning along with a 32 Gbps VLBI system (Figure 4), both of which were used for the 2017 April EHT observations. In early 2018, a new dual-polarization, sideband-separating 230 GHz receiver, using ALMA mixers, was delivered by UMass and installed along with an upgrade of the VLBI system to 64 Gbps capability.

The hydrogen maser at the LMT is located in a temperature-stable environment deep in the apex cone. The maser reference is brought to a 10 MHz distribution system in the VLBI backend room. The backend room is located one level below the receiver cabin and houses the 2.048 GHz synthesizer, the 1 PPS distribution system, BDCs, R2DBEs, and the Mark 6 recorders.
A.9. SMA (4100 m Altitude)

The SMA is an eight-element radio interferometer located atop Maunakea operated by SAO and ASIAA (Ho et al. 2004). The 6 m dishes are configurable with baselines as long as 509 m, which produces a synthesized beam of about 1 arcsec width at 230 GHz, and sub-arcsec width at 345 GHz. The SMA has participated in EHT observations since 2006. In 2006 and 2007, the SMA provided a maser reference tuning signal to the Caltech Submillimeter Observatory and the JCMT, respectively. In 2009, the SMA contributed collecting area to the EHT through the Phased Array Recording Instrument for Galactic Event Horizon Studies (PhRInGES), a 4 Gbps phased-array system.

During EHT observations, the SMA uses its own correlator, known as the SMA Wideband Astronomical ROACH2 Machine (SWARM), instead of the R2DBE. SWARM is a combined correlator and phased array that was initially deployed in 2014 and built out to its full 32 GHz bandwidth by 2017 (Primiani et al. 2016). SWARM supports VLBI through a built-in beamformer based on a signal-noise decomposition of the correlator output while observing the target source (Young et al. 2016). Phasing the array requires tracking all sources of delay, including fluctuations in water vapor concentration in the atmosphere. The SWARM phasing system is equipped with a real-time phasing solver that continually updates the beamforming weights over the course of the observation to compensate for these variable delays, which manifest as variable phase errors in each antenna. Because the phased array capability is used to observe sources that are unresolved on baselines within the array, the corrective beamformer weights can be computed by extracting from the correlator output that contribution associated with a point-like source. Furthermore, as the weights are applied to the signal from each antenna before computing cross-correlations between antenna pairs, the solution obtained from the correlator output for a particular integration period can also be used to calculate the average phasing efficiency over that same period. In addition to solving and applying corrective phasing in real time, the system produces an estimate of the phasing efficiency, ηphgr,
Equation (2)

where wi is the complex-valued weight applied to antenna $\rmi$. See Young et al. (2016)144 for a more detailed discussion of the phased array and performance assessment thereof.

While the SWARM correlator architecture lends itself conveniently to phased-array processing, it also presents several challenges for integrating the instrument into a VLBI array. First, the beamformer processing of 2 GHz bands is spread across eight ROACH2 devices. These parallel data streams must be collected and formatted in real time in order to record to the Mark 6, which is done using a custom FPGA device called the SWARM Digital Backend (SDBE). The data are received on four of the eight 10 GbE ports on the SDBE. The packets are time-stamped, the frequency domain samples are quantized from 4-bit complex to 2-bit complex, the packets are formatted with VDIF headers, and then transported over Ethernet to the Mark 6. As the beamformer data packets are relatively small, several of these packets are bundled into each UDP packet to reduce the interrupt rate on the Mark 6 and prevent packet loss. The second complication to using SWARM in VLBI is that the data are in complex frequency domain representation as opposed to the time-domain format used by the majority of stations in the EHT, and the data are sampled at a different rate than the single-dish EHT stations : 4.576 Gsps compared to 4.096 Gsps at single-dish sites. Prior to the correlation of SWARM data with data from other sites, an offline inversion and resampling program known as the Adaptive Phased-array and Heterogeneous Interpolating Downsampler for SWARM (APHIDS) is used to preprocess the SMA data. Development of a real-time preprocessing system to be integrated into the SDBE is currently in progress. The SMA VLBI pipeline is illustrated in Figure 14.

Figure 14. Block diagram demonstrating the VLBI data pipeline, from SWARM to correlatable data in VDIF format. The SDBE is integrated with SWARM and does the real-time processing necessary to interface with the on-site Mark 6 during an observation. After observing, the data is preprocessed offline in APHIDS prior to correlation with data from other sites.

A.10. SMT (3200 m Altitude)

The SMT, located on Mount Graham, Arizona, was built by the Max-Planck-Institut für Radioastronomie in 1993, and is now operated and maintained by the ARO (Baars et al. 1999). Work to incorporate the telescope in mm-wavelength VLBI experiments began in the late 1990s (Doeleman et al. 2002 ; Krichbaum et al. 2002). In 2007, the SMT participated in the observations that detected horizon-scale emission in Sgr A* (Doeleman et al. 2008). The 10 m telescope is mounted in a co-rotating enclosure that minimizes the effects of insolation and wind during observations. The telescope surface accuracy is 15 μm rms and the telescope pointing is typically accurate to better than 1.5 arcsec rms. Due to weak diurnal variations in water vapor and the protection of the telescope enclosure, the SMT can observe 24 hr per day. Atmospheric opacity is monitored at this site with a tipping 225 GHz radiometer that is mounted to the rotating dome.

The SMT is equipped with dual-polarization heterodyne receivers covering the atmospheric windows from 200 to 700 GHz. For VLBI observations, the 1.3 mm receiver system uses prototype ALMA sideband-separating mixers, with polarization splitting achieved via a room-temperature wire grid, and circular polarization induced through a quartz quarter-wave plate. The SMT also has a double-sideband receiver for observations at 0.87 mm ; a replacement sideband-separating receiver for this band is in development at the University of Arizona. The 64 Gbps EHT backend hardware is mounted in the receiver cabin. The master reference for the SMT is a hydrogen maser mounted at the base of the telescope pier in a temperature-stabilized closet.
A.11. SPT (2800 m Altitude)

The SPT is a 10 m diameter mm-wavelength telescope located at the geographic South Pole (Carlstrom et al. 2011) and is operated by a collaboration led by the University of Chicago. The off-axis Gregorian design is optimized for observations of the cosmic microwave background with wide-field, multi-color bolometer cameras. The primary reflector surface accuracy is 20 μm rms.

EHT observations with the SPT are managed by the University of Arizona. The standard observing campaigns occur during the austral fall when the South Pole is inaccessible. VLBI setup and testing is performed by a two-person SPT winter-over team, with remote supervision from Arizona. EHT observing at the SPT employs a dual-frequency 230/345 GHz VLBI receiver (Kim et al. 2018a), which was constructed at the University of Arizona. The receiver was first installed in late 2014 and first operated in 2015 January (Kim et al. 2018b). The receiver was reinstalled in an upgraded receiver cabin in 2016 in preparation for the 2017 EHT campaign. To illuminate the VLBI receiver, an alternate secondary mirror is installed ahead of prime focus to form a Cassegrain telescope, which relays the light to an ellipsoidal tertiary mirror atop the receiver. The full VLBI signal chain includes a hydrogen maser and coherence monitoring loops to account for the unusual range of environmental temperatures at the site. Mark 6 data modules are shipped after flights resume in the austral spring season, around November 1.

M87-3 Data Processing and Calibration

Footnotes

136 The bandwidth of an EHT observation is typically expressed as a recording rate in gigabit-per-second, or Gbps. The recording rate in Gbps is four times the recorded bandwidth in GHz, a factor of two coming from the need to take samples at a rate of twice the bandwidth (Nyquist rate), and another factor of two because each sample is 2 bits.

137 The SEFD of a radio telescope is the total system noise represented in units of equivalent incident flux density above the atmosphere (see Paper III, Equation (3)).

138 The visibility is the complex two-point correlation of the electric field measured on a VLBI baseline (see Thompson et al. 2017, Chapter 1).

139 https://vlbi.org/vdif/

140 For more information on CASPER, please see https://casper.berkeley.edu/.

141 See https://www.xilinx.com/support/documentation/data_sheets/ds150.pdf.

142 An alternative DBE that is planned to be deployed at some EHT sites is the third-generation Digital BaseBand Converter (DBBC3 ; Tuccari et al. 2014).

143 https://bitbucket.org/vlbi

144 See also the related SMA Memo 163 at https://www.cfa.harvard.edu/sma/memos/163.pdf.

M87-1 : l'ombre du trou noir supermassif

bruno — 2019-04-14T15:27:36Z

L'ombre du trou noir supermassif

Lorsqu'ils sont entourés d'une zone d'émission transparente, les trous noirs devraient révéler une ombre sombre provoquée par la déviation de la lumière gravitationnelle et la capture de photons à l'horizon des événements. Pour visualiser et étudier ce phénomène, nous avons assemblé le Télescope Event Horizon (EHT), un réseau mondial d'interférométrie à très longue base observant à une longueur d'onde de 1,3 mm.
Cela nous permet de reconstruire des images à l'échelle événement-horizon du trou noir supermassif situé au centre de la galaxie elliptique géante M87. Nous avons résolu la source radio compacte centrale en un anneau à émission lumineuse asymétrique d'un diamètre de 42 ± 3 µas, circulaire et englobant une dépression centrale en luminosité avec un rapport de flux $ \gtrsim 10:1 $.

L'anneau d'émission est récupéré en utilisant différents schémas d'étalonnage et d'imagerie, son diamètre et sa largeur restant stables sur quatre observations différentes effectuées à des jours différents. Dans l'ensemble, l'image observée correspond aux attentes concernant l'ombre d'un trou noir de Kerr, telles que prédites par la relativité générale. L'asymétrie de la luminosité dans l'anneau s'explique par la diffusion relativiste de l'émission d'un plasma tournant à une vitesse proche de celle de la lumière autour d'un trou noir.
Nous comparons nos images à une vaste bibliothèque de simulations de trous noirs magnétohydrodynamiques relativistes par lancés de rayons et en déduisons une masse centrale de $ M = (6,5 \pm 0,7) \times 10^9 M_{\odot} $. Nos observations par ondes radio fournissent ainsi une preuve puissante de la présence de trous noirs supermassifs dans les centres des galaxies et en tant que moteurs centraux des noyaux galactiques actifs. Ils présentent également un nouvel outil pour explorer la gravité dans sa limite la plus extrême et à une échelle de masse jusqu'ici inaccessible.

1. Introduction

Les trous noirs sont une prédiction fondamentale de la théorie de la relativité générale (GR ; Einstein 1915). Une caractéristique déterminante des trous noirs est leur horizon d'événements, une limite causale à sens unique dans l'espace-temps à partir de laquelle même la lumière ne peut pas s'échapper (Schwarzschild 1916). La production de trous noirs est générique dans la GR (Penrose 1965) et, plus d'un siècle après Schwarzschild, ils restent au cœur des questions fondamentales concernant l'unification de la RG avec la physique quantique (Hawking 1976 ; Giddings 2017).

Les trous noirs sont courants en astrophysique et se trouvent sur une large gamme de masses. Les preuves concernant les trous noirs de masse stellaire proviennent de rayons X (Webster et Murdin, 1972 ; Remillard et McClintock, 2006) et de mesures d'ondes gravitationnelles (Abbott et al., 2016). On pense que les trous noirs supermassifs, dont les masses atteignent des millions à des dizaines de milliards de masses solaires, existent au centre de presque toutes les galaxies (Lynden-Bell 1969 ; Kormendy & Richstone 1995 ; Miyoshi et al. 1995), y compris au centre galactique. (Eckart & Genzel 1997 ; Ghez et al. 1998 ; Gravity Collaboration et al. 2018a) et dans le noyau de la galaxie elliptique proche M87 (Gebhardt et al. 2011 ; Walsh et al. 2013).

Les noyaux galactiques actifs (AGN) sont des régions centrales lumineuses qui peuvent éclipser la totalité de la population stellaire de leur galaxie hôte. Certains de ces objets, les quasars, sont les sources stables les plus lumineuses de l'univers (Schmidt 1963 ; Sanders et al. 1989) et sont supposés être alimentés par des trous noirs supermassifs accumulant de la matière à des cadences très élevées grâce à un disque d'accrétion optiquement épais et géométriquement mince (Shakura & Sunyaev 1973 ; Sun & Malkan 1989). En revanche, la plupart des réseaux AGN de l'univers local, y compris le centre galactique et M87, sont associés à des trous noirs supermassifs alimentés par des flux d'accrétion ténus et chauds avec des taux d'accrétion beaucoup plus bas (Ichimaru 1977 ; Narayan & Yi 1995 ; Blandford & Begelman 1999 ; Yuan Et Narayan 2014).

Dans de nombreux AGN, des jets de plasma relativistes collimatés (Bridle & Perley 1984 ; Zensus 1997) lancés par le trou noir central contribuent à l'émission observée. Ces jets peuvent être alimentés soit par des champs magnétiques filant l'horizon des événements, en extrayant l'énergie de rotation du trou noir (Blandford & Znajek, 1977), ou par le flux d'accrétion (Blandford & Payne, 1982). L'émission proche de l'horizon des noyaux galactiques actifs de faible luminosité (LLAGNs ; Ho, 1999) est produite par le rayonnement synchrotron qui atteint son maximum dans la radio par l'infrarouge lointain. Cette émission peut être produite dans le flux d'accrétion (Narayan et al. 1995), le jet (Falcke et al. 1993) ou les deux (Yuan et al. 2002).

Vu de l'infini, un trou noir non tournant de Schwarzschild (1916) a un rayon de capture de photons $ R_c= \sqrt{27} r_g $ , où $ r_g \equiv GM/c^2 $ est l'échelle de longueur caractéristique d'un trou noir. Le rayon de capture des photons est supérieur au rayon $ R_S $ de Schwarzschild qui marque l'horizon des événements d'un trou noir non tournant, $ R_S \equiv 2 r_g $. Les photons qui s'approchent du trou noir avec un paramètre d'impact $ b\lt R_c $ sont capturés et plongent dans le trou noir (Hilbert 1917) ; les photons avec $ b \gt R_c $ s'échappent à l'infini ; les photons avec $ b = R_c $ sont capturés sur une orbite circulaire instable et produisent ce que l'on appelle communément lune lentille en forme d'anneau.
Dans la métrique de Kerr (1963), qui décrit les trous noirs avec un moment angulaire de spin, Rc change avec l'orientation du rayon par rapport au vecteur moment angulaire, et la section transversale du trou noir n'est pas nécessairement circulaire (Bardeen, 1973). Ce changement est faible ($ \lesssim\ 4\% $), mais potentiellement détectable (Takahashi 2004 ; Johannsen & Psaltis 2010).

Les simulations de Luminet (1979) ont montré que, pour un trou noir encastré dans un disque d'accrétion optiquement épais et géométriquement fin, le rayon de capture des photons apparaîtrait à un observateur distant comme un mince anneau d'émission dans une image du disque d'accrétion à lentilles. Pour combiner les trous noirs incrustés dans une zone d'émission optiquement mince et géométriquement épaisse, comme dans les LLAGN, la combinaison d'un horizon d'événements et d'une flexion claire conduit à l'apparition d'une ombre sombre ainsi que d'un anneau d'émission brillant qui devrait être détectable avec les expériences sur la très longue ligne de base d'interférométrie(VLBI) (Falcke et al. 2000a). Sa forme peut apparaître comme un croissant en raison de sa rotation rapide et de son rayonnement relativiste (Falcke et al. 2000b ; Bromley et al. 2001 ; Noble et al. 2007 ; Broderick & Loeb 2009 ; Kamruddin & Dexter 2013 ; Lu et al. 2014).

Le diamètre projeté observé de l'anneau d'émission, qui contient le rayonnement principalement de l'anneau photonique à lentille gravitationnelle, est proportionnel à Rc et donc à la masse du trou noir, mais dépend également non trivialement de nombreux facteurs : la résolution d'observation, le vecteur de spin du trou noir et de son inclinaison, ainsi que la taille et de la structure de la région émettrice. Ces facteurs sont généralement de l'ordre de l'unité et peuvent être calibrés à l'aide de modèles théoriques.

Les simulations relativistes générales modernes des flux d'accrétion et du transfert radiatif produisent des images réalistes des ombres et des croissants des trous noirs pour une vaste gamme de modèles d'émission proche de l'horizon (Broderick & Loeb 2006 ; Mościbrodzka et al. 2009 ; Dexter et al. 2012 ; Dibi et al 2012, Chan et al 2015, Mościbrodzka et al 2016, Porth et al 2017, Chael et al 2018a, Ryan et al 2018, Davelaar et al 2019). Ces images peuvent être utilisées pour tester les propriétés de base des trous noirs, telles que prédites dans GR (Johannsen & Psaltis 2010 ; Broderick et al. 2014 ; Psaltis et al. 2015), ou dans d'autres théories de la gravité (Grenzebach et al. 2014 ; Younsi et al. 2016 ; Mizuno et al. 2018). Ils peuvent également être utilisés pour tester des alternatives aux trous noirs (Bambi & Freese 2009 ; Vincent et al. 2016 ; Olivares et al. 2019).

VLBI à une longueur d'onde d'observation de 1,3 mm (230 GHz) avec des lignes de base de l'échelle du diamètre de la Terre est nécessaire pour résoudre les ombres du noyau de M87 (M87 * ci-après) et du centre galactique du Sagittaire A * (Sgr A *, Balick & Brown 1974), les deux trous noirs supermassifs avec les plus grandes tailles angulaires apparentes (Johannsen et al. 2012). À 1,3 mm et aux longueurs d'onde plus courtes, les lignes de base VLBI de diamètre terrestre atteignent une résolution angulaire suffisante pour résoudre l'ombre des deux sources, tandis que les spectres des deux sources deviennent optiquement minces, révélant ainsi la structure de la région d'émission la plus à l'intérieur. Les premières expériences Pathfinder (Padin et al. 1990 ; Krichbaum et al. 1998) ont démontré la faisabilité des techniques VLBI à des longueurs d'onde d'environ 1,3 mm. Au cours de la décennie suivante, un programme visant à améliorer la sensibilité du VLBI de 1,3 mm par le développement de l'instrumentation à large bande a conduit à la détection de structures à l'échelle d'horizon des événements dans Sgr A * et M87 * (Doeleman et al. 2008, 2012). S'appuyant sur ces observations, la collaboration EHT (Event Horizon Telescope) a été établie pour assembler une matrice VLBI globale fonctionnant à une longueur d'onde de 1,3 mm avec la résolution angulaire, la sensibilité et la couverture de base requises pour imager les ombres dans M87 * et Sgr A *.

Dans cet article, nous présentons et discutons les premières images à l'échelle événement-horizon du candidat pour le trou noir supermassif M87 * issu d'une campagne EHT VLBI menée en avril 2017 à une longueur d'onde de 1,3 mm. Les documents d'accompagnement décrivent plus en détail l'instrument (EHT Collaboration et al. 2019a, document II), la réduction des données (EHT Collaoration et al. 2019b, ci-après désigné Paper III), l'imagerie de l'ombre M87 (EHT Collaboration et al. 2019c). , ci-après Paper IV), les modèles théoriques (EHT Collaboration et al. 2019d, ci-après Paper V ) et estimation de la masse des trous noirs (EHT Collaboration et al. 2019e, ci-après Paper VI).

2. Le cœur de la radio dans M87

Dans Curtis (1918), Heber Curtis a détecté un élément linéaire dans M87, appelé plus tard jet de Baade & Minkowski (1954). Le jet est vu comme une source radio brillante, Virgo A ou 3C 274 (Bolton et al. 1949 ; Kassim et al. 1993 ; Owen et al. 2000), qui s'étend jusqu'à 65 kpc avec un âge estimé à environ 40 Myr et une puissance cinétique d'environ $ 10^{35} $ à $ 10^{38} J s^{-1} $ (de Gasperin et al. 2012 ; Broderick et al. 2015). Il est également bien étudié dans l'optique (Biretta et al. 1999 ; Perlman et al. 2011), les rayons X (Marshall et al. 2002) et les bandes de rayons gamma (Abramowski et al. 2012). L'extrémité amont du jet est marquée par une source radio compacte (Cohen et al. 1969). De telles sources radio compactes sont omniprésentes dans les LLAGN (Wrobel & Heeschen 1984 ; Nagar et al. 2005) et sont supposées être des signatures de trous noirs supermassifs.

Les structures radio du jet à grande échelle (Owen et al. 1989 ; de Gasperin et al. 2012) et du noyau de M87 (Reid et al. 1989 ; Junor et al. 1999 ; Hada et al. 2016 ; Mertens et al 2016 ; Kim et al 2018b ; Walker et al 2018) ont été résolues de manière très détaillée et à plusieurs longueurs d'onde. En outre, le nivellement de l'effet de décalage de noyau (Blandford & Königl, 1979), où la position apparente du noyau radio se déplace dans la direction du jet en amont avec une longueur d'onde décroissante, passant d'une transparence accrue à l'auto-absorption du synchrotron, indique que à 1,3 mm, M87 * coïncide avec le trou noir supermassif (Hada et al. 2011). L'enveloppe de la branche du jet conserve une forme quasi parabolique sur une large plage de distances allant de $ \sim 10^5\ r_g $ à $ \sim 20\ r_g $ (Asada et Nakamura 2012 ; Hada et al. 2013 ; Nakamura et Asada 2013 ; Nakamura et al. 2018 ; Walker et al 2018).

Les observations VLBI à 1,3 mm ont révélé un diamètre de la région d'émission d'environ 40 µas, ce qui est comparable à la structure attendue à l'échelle de l'horizon (Doeleman et al. 2012 ; Akiyama et al. 2015). Cependant, ces observations n'ont pas pu imager l'ombre du trou noir en raison de la couverture de base limitée.

Sur la base de trois mesures récentes de la population stellaire, nous adoptons ici une distance par rapport à M87 de $ 16,8 \pm 0,8 Mpc $ (Blakeslee et al. 2009 ; Bird et al. 2010 ; Cantiello et al. 2018, voir l'article VI).

En utilisant cette distance et la modélisation de la brillance de surface et de la dispersion de la vitesse stellaire aux longueurs d'onde optiques (Gebhardt & Thomas 2009 ; Gebhardt et al. 2011), nous déduisons que la masse de M87 * est égale à $ M = {6.2}_{- 0.6} ^ {+ 1,1} \times {10} ^ {9} M_\odot $(voir le tableau 9 dans le document VI).
D'autre part, les mesures de masse modélisant la structure cinématique du disque de gaz (Harms et al. 1994 ; Macchetto et al. 1997) ont donné
$ M={3.5}_{-0.3}^{+0.9}\times {10}^{9} M_\odot $ (Walsh et al. 2013, Paper VI). Ces deux estimations de masse, issues de la dynamique des étoiles et des gaz, prédisent un diamètre d'ombre théorique pour un trou noir de Schwarzschild de
$ {37.6}_{-3.5}^{+6.2}\,\mu \mathrm{as} $ and $ {21.3}_{-1.7}^{+5}\,\mu \mathrm{as} $ respectivement.

3. Le télescope Horizon des événements

EHT (Paper II) est une expérience VLBI qui mesure directement les visibilités, ou composantes de Fourier, de la distribution de la luminosité radio du ciel. Lors de la rotation de la Terre, chaque paire de télescopes du réseau échantillonne de nombreuses fréquences spatiales. La matrice a une résolution angulaire nominale de $ \lambda / L $, où $ \lambda $ est la longueur d'onde d'observation et L, la longueur de ligne de base projetée maximale entre les télescopes de la matrice (Thompson et al. 2017). De cette manière, VLBI crée un télescope virtuel qui couvre presque tout le diamètre de la Terre.

Pour mesurer la visibilité interférométrique, les télescopes largement séparés échantillonnent et enregistrent simultanément le champ de rayonnement de la source. La synchronisation à l'aide du système de positionnement global GPS permet généralement un alignement temporel de ces enregistrements en quelques dizaines de nanosecondes. Chaque station est équipée d'un étalon de fréquence maser à l'hydrogène. Avec les conditions atmosphériques observées lors de nos observations, le temps d'intégration cohérent était généralement de 10 s (voir la figure 2 du document II). L'utilisation d'étalons de fréquence maser à l'hydrogène sur tous les sites EHT assure la cohérence sur l'ensemble de la matrice sur cette période. Après les observations, les enregistrements sont organisés dans un emplacement central, aligné dans le temps, et les signaux de chaque paire de télescopes sont corrélés de manière croisée.

Bien que le VLBI soit bien établi aux longueurs d'onde centimétriques et millimétriques (Boccardi et al. 2017 ; Thompson et al. 2017) et qu'il puisse être utilisé pour étudier l'environnement immédiat des trous noirs (Krichbaum et al. 1993 ; Doeleman et al. 2001), l'extension du VLBI à une longueur d'onde de 1,3 mm a nécessité des développements techniques à long terme. Les défis aux longueurs d'onde plus courtes incluent l'augmentation du bruit dans les récepteurs radio, l'opacité atmosphérique accrue, les fluctuations de phase accrues dues à la turbulence atmosphérique et la diminution de l'efficacité et de la taille des radiotélescopes dans les bandes d'observation millimétrique et submillimétrique. Lancé en 2009 (Doeleman et al. 2009a), l'équipe EHT a lancé un programme visant à relever ces défis en augmentant la sensibilité des matrices. Le développement et le déploiement de systèmes VLBI à large bande (Whitney et al. 2013 ; Vertatschitsch et al. 2015) ont conduit à des vitesses d'enregistrement des données qui dépassent maintenant de plus d'un ordre de grandeur celles des baies cm-VLBI typiques. Des efforts parallèles pour soutenir la mise à niveau des infrastructures sur d'autres sites VLBI, notamment le télescope Atacama Large Millimeter / submillimeter Array (ALMA ; Matthews et al. 2018 ; Goddi et al. 2019) et Atacama Pathfinder Experiment (APEX) au Chili (Wagner et al. 2015), le grand télescope millimétrique Alfonso Serrano (LMT) au Mexique (Ortiz-León et al. 2016), le télescope IRAM de 30 m sur le pico Veleta (PV) en Espagne (Greve et al. 1995), l'observatoire submillimétrique du télescope en Arizona (SMT ; Baars et al. 1999), le télescope James Clerk Maxwell (JCMT) et le réseau submillimètre (SMA) à Hawaii (Doeleman et al. 2008 ; Primiani et al. 2016 ; Young et al. 2016), et le télescope du pôle Sud (SPT) en Antarctique (Kim et al. 2018a) ont étendu la gamme des lignes de base et de la couverture EHT, ainsi que la zone de collecte globale du réseau. Ces développements ont multiplié par 30 la sensibilité de l'EHT par rapport aux premières expériences confirmant des structures à l'horizon dans M87 * et Sgr A * (Doeleman et al. 2008, 2012 ; Akiyama et al. 2015 ; Johnson et al. 2015

Pour les observations à une longueur d'onde de 1,3 mm présentées ici, la collaboration EHT a mis en place un réseau mondial VLBI de huit stations réparties sur six emplacements géographiques. La longueur de la ligne de base variait de 160 m à 10 700 km vers M87 *, ce qui donnait un réseau avec une résolution théorique de la limite de diffraction d'environ 25 μas (voir Figures 1 et 2 et document II).

Figure 1
Huit stations de la campagne EHT 2017 sur six sites géographiques vus du plan équatorial. Les lignes de base pleines représentent la visibilité mutuelle sur M87 * (déclinaison de + 12 °). Les lignes de base en pointillés ont été utilisées pour la source d'étalonnage 3C279 (voir les papiers III et IV).

Figure 2
Figure 2. Dessus : couverture (u, v) pour M87 *, agrégée sur les quatre jours d'observation. (u, v) les coordonnées de chaque paire d'antennes sont la longueur de la ligne de base projetée par la source, exprimée en unités de la longueur d'onde d'observation λ, et sont données pour les paires conjuguées. Les lignes de base vers ALMA / APEX et JCMT / SMA sont redondantes. Les lignes circulaires en pointillés indiquent les longueurs de la ligne de base correspondant à des espacements de franges de 50 et 25 µa. En bas : les amplitudes de visibilité finales calibrées de M87 * en fonction de la longueur de ligne de base projetée le 11 avril. Les lignes de base redondantes pour APEX et JCMT sont tracées en losange. Les barres d'erreur correspondent aux incertitudes thermiques (statistiques). La transformée de Fourier d'un modèle en anneau mince de symétrie azimutale de diamètre 46 µa est également représentée avec une ligne pointillée pour comparaison.

4. Observations, corrélation et étalonnage

Nous avons observé M87 * les 5, 6, 10 et 11 avril 2017 avec l'EHT. Les conditions météorologiques étaient uniformément bonnes à excellentes, avec des opacités atmosphériques du zénith médian la nuit à 230 GHz allant de 0,03 à 0,28 sur les différents emplacements. Les observations ont été programmées en une série de balayages de trois à sept minutes, avec des balayages M87 * entrelacés avec ceux du quasar 3C 279. Le nombre de balayages obtenus sur M87 * par nuit variait de 7 (10 avril) à 25 ( 6 avril) en raison de différents horaires d'observation. Une description des observations M87 *, de leur corrélation, de leur étalonnage et des produits de données finaux validés est présentée dans le document III et brièvement résumée ici.

À chaque station, le signal astronomique dans les deux polarisations et deux bandes de fréquences adjacentes larges de 2 GHz, centrées à 227,1 et 229,1 GHz, a été converti en bande de base à l'aide de techniques hétérodynes standard, puis numérisé et enregistré à un débit total de 32 Gbps. La corrélation des données a été réalisée à l'aide d'un corrélateur logiciel (Deller et al. 2007) à l'observatoire MIT Haystack et à l'Institut Max-Planck de Radioastronomie, chacun gérant l'une des deux bandes de fréquences. Les différences entre les deux corrélateurs indépendants se sont révélées négligeables par l'échange de quelques balayages identiques à des fins de comparaison croisée. À la corrélation, les signaux ont été alignés sur une référence de temps commune en utilisant une géométrie de la Terre a priori et un modèle d'horloge.

Une étape ultérieure d'ajustement des franges a identifié des détections de la puissance du signal corrélée lors du calibrage en phase des données pour les retards résiduels et les effets atmosphériques. L'utilisation d'ALMA en tant que station de référence très sensible a permis de corriger de manière critique les distorsions ionosphériques et troposphériques des autres sites. L'ajustement des franges a été effectué avec trois pipelines automatisés indépendants, chacun adapté aux caractéristiques spécifiques des observations EHT, telles que la large bande passante, la susceptibilité à la turbulence atmosphérique et l'hétérogénéité des réseaux (Blackburn et al. 2019 ; Janssen et al. 2019, Papier III ). Les pipelines utilisaient un logiciel standard pour le traitement des données radio-interférométriques (Greisen 2003 ; Whitney et al. 2004 ; McMullin et al. 2007, I.M. van Bemmel et al. 2019, en préparation).

Les données des pipelines à ajustement marginal ont été mises à l'échelle des coefficients de corrélation à une échelle de densité de flux physique uniforme (en Jansky) en utilisant une estimation a priori indépendante de la sensibilité de chaque télescope. La précision des sensibilités des stations dérivées a été estimée à une amplitude comprise entre 5% et 10%, bien que certaines pertes non caractérisées (dues par exemple à un pointage ou à une focalisation médiocres) puissent dépasser le budget d'erreur. En supposant des valeurs de densité de flux totales dérivées des données interférométriques ALMA (Goddi et al. 2019) et en utilisant la redondance des matrices via l'étalonnage du réseau (document III), nous avons affiné l'étalonnage en amplitude absolue des télescopes colocalisés et dotés de lignes de base redondantes, c'est-à-dire ALMA / APEX et JCMT / SMA.

Le rapport signal / bruit moyen sur balayage moyen pour M87 * était > 10 sur les lignes de base non ALMA et > 100 sur les lignes de base pour ALMA, conduisant à de petites erreurs statistiques sur l'amplitude et la phase de visibilité. Les comparaisons entre les trois pipelines indépendants, les deux polarisations et les deux bandes de fréquences ont permis d'estimer des erreurs de base systématiques d'environ 1 ° dans la phase de visibilité et de 2% pour les amplitudes de visibilité. Ces petites erreurs limitantes subsistent après la sensibilité des stations d'ajustement et les phases de stations inconnues via un étalonnage automatique (Pearson & Readhead, 1984) et affectent les quantités de fermeture interférométriques (Rogers et al., 1974 ; Readhead et al., 1980). Suite à la validation des données et aux comparaisons entre pipelines, une seule sortie de pipeline a été désignée comme jeu de données principal de la première publication de données scientifiques EHT et utilisée pour les résultats ultérieurs, tandis que les sorties des deux autres pipelines offrent des jeux de données de validation complémentaires.

Les visibilités complexes calibrées finales V (u, v) correspondent aux composantes de Fourier de la distribution de la luminosité dans le ciel à la fréquence spatiale (u, v) déterminée par la ligne de base projetée exprimée en unités de la longueur d'onde d'observation (van Cittert 1934 ; Thompson et al 2017). La figure 2 montre la couverture (u, v) et les amplitudes de visibilité calibrées de M87 * pour le 11 avril. Les amplitudes de visibilité ressemblent à celles d'un anneau fin (c'est-à-dire une fonction de Bessel J0 ; voir la figure 10.12 dans Thompson et al. 2017). Un tel modèle d'anneau de diamètre 46 μas a un premier zéro à 3,4 Gλ, correspondant au minimum en densité de flux observé et est consistant à une densité de flux réduite sur la plus longue ligne de base Hawaii / Espagne (JCMT / SMA-PV) proche de 8 Gλ . Ce modèle particulier d'anneau, représenté par une ligne pointillée dans le panneau inférieur de la figure 2, est uniquement illustratif et ne correspond pas à toutes les caractéristiques des données. Tout d'abord, les amplitudes de visibilité sur les lignes de base VLBI les plus courtes suggèrent qu'environ la moitié de la densité de flux compact observée sur la ligne de base ALMA – APEX d'environ 2 km est résolue par le faisceau interféromètre (document IV). Deuxièmement, les différences de la profondeur du premier minimum comme fonction de l'orientation, aussi bien que les phases de fermeture mesurées largement non nulles, indiquent un certain degré d'asymétrie dans la source (fascicules III, VI). Enfin, les amplitudes de visibilité ne représentent que la moitié des informations dont nous disposons. Nous explorerons ensuite des images et des modèles géométriques plus complexes pouvant correspondre aux amplitudes et phases de visibilité mesurées.
fin de la vérif

5. Images et caractéristiques

Nous avons reconstruit des images à partir des visibilités EHT calibrées, qui fournissent des résultats indépendants des modèles (papier IV). Cependant, la reconstruction d'images à partir de données EHT présente deux défis majeurs. Premièrement, les lignes de base EHT échantillonnent une gamme limitée de fréquences spatiales, correspondant à des échelles angulaires comprises entre 25 et 160 µas. Comme le plan (u, v) n'est que faiblement échantillonné (figure 2), le problème inverse est sous-contraint. Deuxièmement, les visibilités mesurées manquent d'étalonnage de phase absolue et peuvent avoir de grandes incertitudes d'étalonnage d'amplitude.

Pour relever ces défis, les algorithmes d'imagerie incorporent des hypothèses et des contraintes supplémentaires conçues pour produire des images physiquement plausibles (par exemple positives et compactes) ou conservatrices (par exemple, lisses), tout en restant cohérentes avec les données. Nous avons exploré deux classes d'algorithmes pour reconstruire des images à partir de données EHT. La première classe d'algorithmes est l'approche CLEAN traditionnelle utilisée en interférométrie radio (par exemple, Högbom 1974 ; Clark 1980). CLEAN est une approche de modélisation inverse qui déconvolution de la fonction d'étalement de point d'interféromètre à partir des visibilités transformées de Fourier. Lors de l'application de CLEAN, il est nécessaire d'auto-calibrer de manière itérative les données entre les séries d'imagerie pour résoudre les erreurs d'amplitude et de phase variables dans le temps dans les données. La seconde classe d'algorithmes est ce que l'on appelle le maximum de vraisemblance régularisé (RML ; par exemple, Narayan & Nityananda 1986 ; Wiaux et al. 2009 ; Thiébaut 2013). RML est une approche de modélisation directe qui recherche une image non seulement cohérente avec les données observées, mais qui favorise également les propriétés d'image spécifiées (par exemple, le lissage ou la compacité). Comme avec CLEAN, les méthodes RML permettent généralement d'interférer entre l'imagerie et l'auto-étalonnage, bien qu'elles puissent également être utilisées pour l'imagerie directe sur des quantités de fermeture robustes, à l'abri des erreurs d'étalonnage liées aux stations. Des méthodes RML ont été largement développées pour l'EHT (par exemple, Honma et al. 2014 ; Bouman et al. 2016 ; Akiyama et al. 2017 ; Chael et al. 2018b ; voir aussi le document IV).

Chaque algorithme d'imagerie possède une variété de paramètres libres pouvant affecter de manière significative l'image finale. Nous avons adopté une approche d'imagerie en deux étapes pour contrôler et évaluer les biais dans les reconstructions à partir de nos choix de ces paramètres. Lors de la première étape, quatre équipes ont travaillé indépendamment pour reconstruire les premières images EHT de M87 * en utilisant une première version de données d'ingénierie. Les équipes ont travaillé sans interaction pour minimiser les biais partagés, mais chacune a généré une image avec une caractéristique similaire : un anneau de diamètre 38–44 µas avec une luminosité accrue au sud (voir la figure 4 du papier IV).

Au cours de la deuxième étape de l'imagerie, nous avons développé trois pipelines d'imagerie, chacun utilisant un logiciel et une méthodologie associés différents. Chaque pipeline a étudié une gamme de paramètres d'imagerie, produisant entre $ \sim 10^3\ et\ 10^4 $ images à partir de différentes combinaisons de paramètres. Nous avons déterminé un ensemble supérieur de combinaisons de paramètres produisant des images de M87 * compatibles avec les données observées et reconstruisant des images précises à partir de jeux de données synthétiques correspondant à quatre modèles géométriques connus (anneau, croissant, disque plein et double source asymétrique). ). Pour tous les pipelines, les images Top-Set montraient un anneau asymétrique d'un diamètre d'environ 40 µa, avec des différences apparaissant principalement dans les résolutions angulaires effectives obtenues par différentes méthodes.

Pour chaque pipeline, nous avons déterminé la combinaison unique de paramètres d'imagerie de référence du Top-Set qui a donné les meilleurs résultats pour tous les ensembles de données synthétiques et pour chaque méthodologie d'imagerie associée (voir la figure 11 dans le papier IV). Étant donné que les résolutions angulaires des images reconstruites varient selon les pipelines, nous avons rendu floues chaque image avec une résolution circulaire gaussienne jusqu'à une résolution angulaire conservatrice commune de 20 µas. La partie supérieure de la figure 3 montre une image de M87 * du 11 avril obtenue en faisant la moyenne des images fiduciales floues des trois pipelines. L'image est dominée par un anneau avec un profil asymétrique azimutal orienté selon un angle de position de 170 ° à l'est du nord. Bien que l'angle de position mesuré augmente d'environ 20 ° entre les deux premiers jours et les deux derniers jours, les caractéristiques de l'image sont globalement cohérentes pour les différentes méthodes d'imagerie et pour les quatre jours d'observation. Ceci est montré dans la partie inférieure de la figure 3, qui rapporte les images sur différents jours (voir aussi la figure 15 dans le papier IV). Ces résultats sont également cohérents avec ceux obtenus par ajustement dans le domaine de visibilité des modèles de magnétohydrodynamique géométrique et relativiste (GRMHD) (papier VI).

fig3
En haut : image EHT de M87 * tirée des observations du 11 avril 2017, à titre d'exemple représentatif des images recueillies lors de la campagne de 2017. L'image est la moyenne de trois méthodes d'imagerie différentes après convolution avec un noyau gaussien circulaire pour donner des résolutions adaptées. Le plus gros des trois noyaux (FWHM 20 μas) est indiqué en bas à droite. L'image est affichée en unités de température de luminosité, $ T_b = S \ lambda^ {2} / 2 {k} _ {{\ rm {B}}} {\ rm {\ Omega}} $, où S est la densité de flux, λ est la longueur d'onde d'observation, kB est la constante de Boltzmann et Ω est l'angle solide de l'élément de résolution. En bas : images similaires prises au cours de différents jours montrant la stabilité de la structure de base de l'image et l'équivalence entre différents jours. Le Nord est en haut et l'Est est à gauche.

6. Modélisation théorique

L'apparence de M87 * a été modélisée avec succès à l'aide de simulations GRMHD, qui décrivent un disque magnétique turbulent, chaud, en orbite autour d'un trou noir de Kerr. Ils produisent naturellement un jet puissant et peuvent expliquer la distribution spectrale de l'énergie à large bande observée dans les LLAGN. À une longueur d'onde de 1,3 mm, et comme observé ici, les simulations prédisent également une ombre et un anneau d'émission asymétrique. Ce dernier ne coïncide pas nécessairement avec l'orbite circulaire la plus interne, ISCO, mais est plutôt lié à l'anneau de photons lentillé. Pour explorer ce scénario en détail, nous avons créé une bibliothèque d'images synthétiques (bibliothèque d'images) décrivant les flux d'accrétion magnétisés sur les trous noirs du GR145 (papier V). Les images elles-mêmes sont produites à partir d'une bibliothèque de simulations (Simulation Library) rassemblant les résultats de quatre codes résolvant les équations de GRMHD (Gammie et al. 2003 ; Sa̧dowski et al. 2014 ; Porth et al. 2017 ; Liska et al. 2018). . Les éléments de la bibliothèque de simulation ont été couplés à trois codes de traçage de rayons et de transfert de radiations relativistes généraux (GRRT, Bronzwaer et al. 2018 ; Mościbrodzka et Gammie 2018 ; Z. Younsi et al. 2019, en préparation). Nous nous limitons à fournir ici une brève description des configurations initiales et des scénarios physiques explorés dans les simulations ; voir l'article V pour des détails sur les codes GRMHD et GRRT, qui ont fait l'objet d'une validation croisée pour en vérifier l'exactitude et la cohérence (Gold et al. 2019 ; Porth et al. 2019).

Une simulation typique de GRMHD dans la bibliothèque est caractérisée par deux paramètres : le spin sans dimension $ a _ {*} \ equiv {J_c} / {{GM}} ^ {2} $, où J et M sont respectivement le moment angulaire de rotation et masse du trou noir et flux magnétique sans dimension sur l'horizon des événements $ \ phi \ equiv {\ rm {\ Phi}} / {(\ dot {M} {R} _ {{\ rm {g}}} ^ {2})} ^ {1/2} $, où Φ et $ \ dot {M} $sont respectivement le flux magnétique et le flux de masse (ou taux d'accrétion) à travers l'horizon. Etant donné que les simulations GRMHD s'adaptent à la masse du trou noir, M n'est défini que lors de la production des images de synthèse avec les codes GRRT. Le flux magnétique est généralement non nul car le champ magnétique est piégé dans le trou noir par le flux d'accrétion et maintenu par les courants dans le plasma environnant.

Ces deux paramètres permettent de décrire des disques d'accrétion progressifs ($ a_* \geq 0 $) ou rétrogrades ($ a_* \lt 0 $) par rapport à l'axe de rotation du trou noir, et dont les écoulements d'accrétion sont soit SANE (de Standard and Normal Evolution, Narayan et al. 2012) avec phgr 1, ou MAD (de Magnetically Arrested Diskk, Narayan et al. 2003) avec $ \Phi \sim 15 $.146 En substance, les flux d'accrétion SANE sont caractérisés par un flux magnétique sans dimension modérée et résultent de champs magnétiques initiaux plus petits que ceux des flux MAD. De plus, les angles d'ouverture de l'entonnoir magnétique dans les flux SANE sont généralement inférieurs à ceux des flux MAD. En variant $ a_*\ et\ \Phi $, nous avons effectué 43 simulations haute résolution, tridimensionnelles et à long terme, couvrant bien les propriétés physiques des écoulements d'accrétion magnétisés sur les trous noirs de Kerr.

Toutes les simulations GRMHD ont été initialisées avec un tore faiblement aimanté gravitant autour du trou noir et entraînées dans un état de turbulence dû à des instabilités, notamment l'instabilité magnétorotationnelle (Balbus & Hawley, 1991), atteignant rapidement un état quasi stationnaire. Une fois la simulation terminée, les propriétés d'écoulement pertinentes à différents moments sont collectées pour être utilisées pour le post-traitement ultérieur des codes GRRT. La génération d'images de synthèse requiert, outre les propriétés du fluide (champ magnétique, champ de vitesse et densité de la masse au repos), les coefficients d'émission et d'absorption, l'inclinaison i (angle entre le vecteur moment cinétique accrétion-écoulement et la ligne de visée), l'angle de position PA (angle est-nord, c'est-à-dire, dans le sens inverse des aiguilles d'une montre, de la projection sur le ciel du moment angulaire d'accrétion-écoulement), la masse du trou noir M et la distance D à l'observateur.

Comme on pense que les photons à 1,3 mm de longueur d'onde observés par l'EHT sont produits par l'émission synchrotron, dont les coefficients d'absorption et d'émission dépendent de la fonction de distribution électronique, nous considérons que le plasma est composé d'électrons et d'ions qui ont la même température dans la régions du flux dominées magnétiquement (entonnoir), mais dont la température est sensiblement différente dans les régions dominées par le gaz (plan médian du disque). En particulier, nous considérons que le plasma est composé d'ions non relativistes de température Ti et d'électrons relativistes de température Te. Une simple prescription pour le rapport des températures des deux espèces peut alors être imposée sous la forme d'un paramètre unique (Mościbrodzka et al. 2016), de telle sorte que le gros de l'émission provient soit de faibles magnétisations (petite Rhigh, Te sime Ti / Rhigh) ou fortement magnétisées (grandes régions de Rhigh, Te sime Ti). Dans les modèles SANE, le disque (jet) est faiblement (fortement) aimanté, de sorte que les modèles Rhigh (élevés) produisent la plus grande partie de l'émission dans le disque (jet). Dans les modèles MAD, il existe partout des régions fortement magnétisées et les émissions proviennent principalement du plan médian du disque. Bien que cette prescription ne soit pas la seule possible, elle présente l'avantage d'être simple, suffisamment générique et robuste (voir l'annexe V pour une discussion sur les particules non thermales et le refroidissement radiatif).

Étant donné que chaque simulation GRMHD peut être utilisée pour décrire plusieurs scénarios physiques différents en modifiant la fonction de distribution d'électrons prescrite, nous avons utilisé la bibliothèque de simulation pour générer plus de 420 scénarios physiques différents. Chaque scénario est ensuite utilisé pour générer des centaines d'instantanés à différents moments de la simulation, ce qui permet de créer plus de 62 000 objets dans la bibliothèque d'images. À partir des images, nous avons créé des visibilités de modèle qui correspondent au programme d'observation EHT et les avons comparées aux visibilités VLBI mesurées, comme détaillé dans le document VI.

À titre d'exemple, la rangée supérieure de la figure 4 montre trois instantanés de modèle GRMHD de la bibliothèque d'images avec des spins et un type de flux différents, optimisés pour les phases de fermeture et les amplitudes des données du 11 avril. Pour ces modèles, nous avons produit des visibilités simulées pour l'horaire et les paramètres météorologiques du 11 avril et les avons étalonnées avec un pipeline synthétique de génération et d'étalonnage de données (Blecher et al. 2017 ; Janssen et al. 2019 ; Roelofs et al. 2019a). Les données simulées ont ensuite été imagées avec le même pipeline que celui utilisé pour les images observées. Les similitudes entre les images simulées (rangée du bas de la figure 4) et les images observées (figure 3) sont remarquables.

fig4
En haut : trois exemples de modèles d'instantanés parmi les mieux adaptés extraits de la bibliothèque d'images des simulations GRMHD du 11 avril correspondant à différents paramètres de spin et flux d'accrétion. En bas : mêmes modèles théoriques, traités par un pipeline de simulation VLBI avec le même calendrier, les mêmes caractéristiques de télescope et les mêmes paramètres météorologiques que lors de la simulation du 11 avril, et reproduits de la même manière que dans la Figure 3. Notez que même si l'ajustement aux observations est identique. bon dans les trois cas, ils font référence à des scénarios physiques radicalement différents ; Cela met en évidence le fait qu'un seul bon ajustement n'implique pas qu'un modèle est préféré aux autres (voir Papier V).

Globalement, lors de la combinaison de toutes les informations contenues dans les bibliothèques de simulation et d'image, l'origine physique des caractéristiques d'émission de l'image observée dans M87 * peut être résumée comme suit.

Premièrement, l'image observée est compatible avec l'hypothèse qu'elle est produite par un flux d'accrétion magnétisé en orbite autour de l'horizon des événements d'un trou noir de Kerr. L'anneau asymétrique est produit par une combinaison d'une forte lentille gravitationnelle et d'un faisceau relativiste, tandis que la dépression du flux central est la signature observationnelle de l'ombre du trou noir. Fait intéressant, tous les modèles d'accrétion sont cohérents avec l'image EHT, à l'exception des modèles a * = −0,94 MAD, qui ne produisent pas d'images suffisamment stables (c'est-à-dire que la variance entre les instantanés est trop grande pour être cohérente avec la image observée).

Deuxièmement, l'asymétrie nord-sud dans l'anneau d'émission est contrôlée par la rotation du trou noir et permet de déduire son orientation. Dans les modèles de disque corotatifs (où le moment angulaire de la matière et du trou noir sont alignés), la paroi de l'entonnoir, ou la gaine du jet, tourne avec le disque et le trou noir ; dans les modèles à disque contre-rotatif, la paroi de l'entonnoir lumineux tourne avec le trou noir mais contre le disque. L'asymétrie nord-sud est compatible avec les modèles dans lesquels la rotation du trou noir est dirigée à l'opposé de la Terre et est incompatible avec les modèles dans lesquels la rotation est dirigée vers la Terre.

Troisièmement, en adoptant une inclinaison de 17 ° entre le jet qui approche et la ligne de mire (Walker et al. 2018), l'orientation ouest du jet et un modèle de disque corotatif, la matière dans la partie inférieure de l'image se déplace vers la observateur (rotation dans le sens horaire vu de la Terre). Ceci est cohérent avec la rotation du gaz ionisé sur des échelles de 20 pc, soit 7 000 rg (Ford et al. 1994 ; Walsh et al. 2013) et avec le sens inféré de rotation des observations VLBI à 7 mm (Walker et al. 2018).

Enfin, les modèles avec * = 0 sont désavantagés par l'exigence d'observation très conservatrice voulant que la puissance du jet soit $ P_{jet} \gt 10^{42} erg s^{-1} $. En outre, dans les modèles qui produisent un jet suffisamment puissant, celui-ci est alimenté par extraction de l'énergie de rotation des trous noirs par le biais de mécanismes analogues au processus de Blandford – Znajek.

7. Comparaison de modèles et estimation de paramètres

Dans Paper VI, la masse du trou noir provient de l'ajustement aux données de visibilité des modèles géométriques et GRMHD, ainsi que des mesures du diamètre de l'anneau dans le domaine de l'image. Nos mesures restent cohérentes dans les méthodologies, les algorithmes, les représentations de données et les ensembles de données observées.

Motivés par les structures en anneau d'émission asymétriques observées dans les images reconstruites (section 5) et par les structures d'émission similaires observées dans les images de simulations GRMHD (section 6), nous avons développé une famille de modèles de croissant géométrique (voir par exemple Kamruddin & Dexter 2013). ) pour comparer directement aux données de visibilité. Nous avons utilisé deux algorithmes d'inférence bayésiens distincts et démontré que de tels modèles de croissant sont statistiquement préférés par rapport à d'autres modèles géométriques de complexité comparable que nous avons explorés. Nous trouvons que les modèles de croissant fournissent des ajustements aux données qui sont statistiquement comparables à ceux des images reconstruites présentées dans la section 5, ce qui nous permet de déterminer les paramètres de base des croissants. Les modèles les mieux adaptés pour la bague à émission asymétrique ont des diamètres de 43 ± 0,9 µa et des largeurs fractionnaires par rapport à un diamètre inférieur à 0,5. L'émission chute brusquement à l'intérieur de l'anneau d'émission asymétrique, la dépression centrale ayant une luminosité u003c10% de la luminosité moyenne de l'anneau.

Les diamètres des modèles de croissant géométriques mesurent les tailles caractéristiques des régions émettrices qui entourent les ombres et non les tailles des ombres elles-mêmes (voir, par exemple, Psaltis et al. 2015 ; Johannsen et al. 2016 ; Kuramochi et al. 2018, pour les biais potentiels).

Nous modélisons le diamètre angulaire croissant d en termes de rayon gravitationnel et de distance, $ \theta_g \equiv GM/c^2D $, as $ d = \alpha \Theta_g $, where $ \alpha $ est une fonction du spin, de l'inclinaison et de $ R_{high} $ ($ \alpha \simeq 9,6-10,4 $ correspond à l'émission de l'anneau de photons lentillé seulement). Nous calibrons $ \alpha $en ajustant les modèles géométriques du croissant à un grand nombre de données de visibilité générées à partir de la bibliothèque d'images. Nous pouvons également adapter les visibilités des modèles générés à partir de la bibliothèque d'images aux données M87 *, ce qui nous permet de mesurer directement $ \Theta_g $ directement.Cependant, une telle procédure est compliquée par la nature stochastique de l'émission dans le flux d'accrétion (voir, par exemple, Kim et al. 2016). Pour rendre compte de cette structure turbulente, nous avons développé un formalisme et de multiples algorithmes permettant d'estimer les statistiques des composants stochastiques à l'aide d'ensembles d'images issus de simulations GRMHD individuelles. Nous constatons que les données de visibilité ne sont pas incompatibles avec la réalisation de nombreuses simulations GRMHD. Nous concluons que les paramètres de modèle récupérés sont cohérents d'un algorithme à l'autre. : mauvaise substitution

Enfin, nous extrayons le diamètre, la largeur et la forme de la bague directement à partir d'images reconstituées (voir la section 5). Les résultats sont cohérents avec les estimations de paramètres des modèles de croissant géométriques. En suivant la même procédure d'étalonnage GRMHD, nous déduisons les valeurs de θg et α pour les images reconstruites avec maximum de vraisemblance régularisée et CLEAN.

En combinant les résultats de toutes les méthodes, nous mesurons des diamètres de zone d'émission de 42 ± 3 µa, des tailles angulaires du rayon gravitationnel θg = 3,8 ± 0,4 µa et des facteurs d'échelle compris entre α = 10.7 et 11.5, avec des erreurs associées d'environ 10%. Pour la distance de 16,8 ± 0,8 Mpc adoptée ici, la masse du trou noir est M = (6,5 ± 0,7) × 109 M⊙ ; l'erreur systématique fait référence au niveau de confiance de 68% et est beaucoup plus grande que l'erreur statistique de 0,2 × 109 M⊙. De plus, en traçant le pic de l'émission dans l'anneau, nous pouvons déterminer la forme de l'image et obtenir un rapport entre les axes majeur et mineur de l'anneau inférieur à 4 : 3 ; cela correspond à un écart inférieur à 10% par rapport à la circularité en termes de distance racine-carré par rapport à un rayon moyen.

Le tableau 1 récapitule les paramètres mesurés des caractéristiques de l'image et les propriétés des trous noirs déduites, en fonction des données de toutes les bandes et de tous les jours combinés. La masse de trous noirs inférée favorise fortement la mesure basée sur la dynamique stellaire (Gebhardt et al. 2011). La taille, l'asymétrie, le contraste de luminosité et la circularité des images reconstruites et des modèles géométriques, ainsi que le succès des simulations GRMHD dans la description des données interférométriques, concordent avec les images EHT de M87 * associées à une émission fortement focalisée de la
proximité d'un trou noir Kerr.

Tableau 1
Dérivé du domaine de l'image. bDérivé de l'ajustement du modèle en croissant. cLes erreurs de masse et les erreurs systématiques sont les moyennes des trois méthodes (modèles géométriques, modèles GRMHD et extraction d'anneaux dans le domaine de l'image). dLa valeur exacte dépend de la méthode utilisée pour extraire d, qui se reflète dans la plage donnée. eRederived from vraisemblance distributions (Paper VI).

8. Discussion

Un certain nombre d'éléments renforcent la robustesse de notre image et la conclusion que celle-ci est compatible avec l'ombre d'un trou noir telle que prédite par GR. Premièrement, notre analyse a utilisé plusieurs techniques indépendantes d'étalonnage et d'imagerie, ainsi que quatre ensembles de données indépendantes prises quatre jours différents dans deux bandes de fréquences distinctes. = ε dans Johannsen & Psaltis 2010). Deuxièmement, la structure de l'image correspond bien aux prévisions précédentes (Dexter et al. 2012 ; Mościbrodzka et al. 2016) et est bien reproduite par notre vaste effort de modélisation présenté à la section 6. Troisièmement, parce que notre mesure de la masse du trou noir dans M87 * est non incompatible avec toutes les mesures de masse antérieures, cela nous permet de conclure que l'hypothèse nulle de la métrique de Kerr (Psaltis et al. 2015 ; Johannsen et al. 2016), à savoir l'hypothèse selon laquelle le trou noir est décrit par Kerr métrique, n'a pas été violé. Quatrièmement, l'anneau d'émission observé reconstruit dans nos images est proche de circulaire avec un rapport axial lesssim4 : 3 ; de même, les images de la moyenne temporelle de nos simulations GRMHD montrent également une forme circulaire. Après avoir associé à la forme de l'ombre un écart par rapport à la circularité inférieur à 10%, nous pouvons définir une limite initiale d'ordre quatre sur les écarts relatifs de le moment quadripolaire de la valeur de Kerr (Johannsen & Psaltis 2010). Autrement dit, si Q est le moment quadripolaire d'un trou noir de Kerr et que ΔQ l'écart déduit de la circularité, notre mesure - et le fait que l'angle d'inclinaison est supposé petit - implique que ΔQ / Q lesssim 4 (ΔQ / Q

Enfin, en comparant les amplitudes de visibilité de M87 * avec les données de 2009 et 2012 (Doeleman et al. 2012 ; Akiyama et al. 2015), la taille globale du cœur de la radio à une longueur d'onde de 1,3 mm n'a pas changé de manière appréciable, malgré la variabilité du flux total. densité. Cette stabilité est cohérente avec l'hypothèse selon laquelle la taille de l'ombre est une caractéristique liée à la masse du trou noir et non aux propriétés d'un flux plasmatique variable.

Il est également simple de rejeter certaines interprétations astrophysiques alternatives. Par exemple, il est peu probable que l'image soit produite par un jet caractéristique, car les observations VLBI multi-époques du jet de plasma dans M87 (Walker et al. 2018) à des échelles situées en dehors de l'horizon ne montrent pas d'anneaux circulaires. La même chose est généralement vraie pour les jets AGN dans les grandes enquêtes VLBI (Lister et al. 2018). De même, si l'anneau apparent apparaissait comme un alignement aléatoire de taches d'émissions, elles auraient également dû s'éloigner à des vitesses relativistes, c'est-à-dire environ 5 μas par jour (Kim et al. 2018b), ce qui a entraîné des changements structurels et des tailles mesurables. Les modèles GRMHD de cônes à jet creux pourraient montrer dans des conditions extrêmes des caractéristiques d'anneau stables (Pu et al. 2017), mais cet effet est inclus dans une certaine mesure dans notre bibliothèque de simulation pour les modèles avec Rhighu003e 10. Enfin, un anneau d'Einstein formé par gravitation La lentille d'une région claire dans le contre-jet nécessiterait un alignement précis et une taille supérieure à celle mesurée en 2012 et 2009.

Dans le même temps, il est plus difficile d'éliminer les alternatives aux trous noirs dans les GR, car une ombre peut être produite par tout objet compact dont l'espace-temps est caractérisé par des orbites à photons circulaires instables (Mizuno et al. 2018). En effet, si la métrique de Kerr reste une solution dans certaines théories alternatives de la gravité (Barausse et Sotiriou 2008 ; Psaltis et al. 2008), les solutions de trou noir autres que celles de Kerr existent dans une variété de théories modifiées de ce type (Berti et al. 2015). . De plus, les alternatives exotiques aux trous noirs, telles que les singularités nues (Shaikh et al. 2019), les étoiles du boson (Kaup, 1968 ; Liebling & Palenzuela, 2012) et les gravastars (Mazur et Mottola, 2004 ; Chirenti et Rezzolla, 2007), sont des solutions admissibles GR et fournissent des modèles concrets, bien que artificiels. Certains de ces objets compacts exotiques peuvent déjà se révéler incompatibles avec nos observations étant donné notre masse maximale antérieure. Par exemple, les ombres de singularités nues associées aux espaces-temps de Kerr avec $ | a _ * | \ gt 1 $ sont nettement plus petits et très asymétriques par rapport aux trous noirs de Kerr (Bambi & Freese 2009). De plus, certains types de trous de ver couramment utilisés (Bambi 2013) prédisent des ombres beaucoup plus petites que celles que nous avons mesurées.

Cependant, les autres candidats objets compacts doivent être analysés avec plus de soin. Les étoiles en boson sont un exemple d'objets compacts ayant des orbites de photons circulaires, mais sans surface ni horizon d'événements. Dans un tel espace-temps, les géodésiques nuls sont redirigées vers des observateurs distants (Cunha et al. 2016), de sorte que l'ombre puisse en principe être remplie par l'émission d'images obtenues par lentilles de sources radioélectriques distantes, générant ainsi une image miroir complexe du ciel. Plus important encore, l'accrétion afflue sur les bosons se comporte différemment, car ils ne produisent pas de jets, mais des torres d'accrétion bloqués qui les distinguent des trous noirs (Olivares et al. 2019). Les Gravastars fournissent des exemples d'objets compacts ayant des orbites de photons instables et une surface dure, mais pas un horizon d'événements. Dans ce cas, alors qu'une seule image du flux d'accrétion pourrait en principe être très similaire à celle d'un trou noir, les différences de dynamique d'écoulement à la surface stellaire (H. Olivares et al. 2019, en préparation) champs (Lobanov 2017), ou un rayonnement excessif dans l'infrarouge (Broderick & Narayan 2006) permettrait de distinguer un gravastar d'un trou noir.

Globalement, les résultats obtenus ici offrent un nouveau moyen d'étudier les espaces-temps des objets compacts et complètent la détection des ondes gravitationnelles provenant de trous noirs de masse stellaire en coalescence avec LIGO / Virgo (Abbott et al. 2016). Nos contraintes sur les déviations par rapport à la géométrie de Kerr reposent uniquement sur la validité du principe d'équivalence et ne tiennent pas compte de la théorie de la gravité sous-jacente, mais peuvent être utilisées pour mesurer, avec une précision toujours meilleure, les paramètres de la métrique d'arrière-plan. D'autre part, les observations actuelles des fusions sur les ondes gravitationnelles explorent la dynamique de la théorie sous-jacente, mais ne peuvent pas s'appuyer sur la possibilité de mesures multiples et répétées de la même source.

Pour souligner la complémentarité des observations électromagnétiques des trous noirs par ondes gravitationnelles et électromagnétiques, nous notons que l'une des caractéristiques fondamentales des trous noirs dans les ressources génétiques est que leur taille est proportionnelle à la masse., Pour souligner la complémentarité des observations gravitationnelle des ondes électromagnétiques et des trous noirs, nous notons qu'une caractéristique de base des trous noirs dans GR est que leur taille varie linéairement avec la masse.

Enfin, le cœur de la radio dans M87 est assez typique des jets radio puissants en général. Il se situe sur le plan fondamental de l'activité des trous noirs pour les cœurs radio (Falcke et al. 2004), reliant via de simples lois d'échelle les propriétés radio et rayons X des candidats trous noirs de faible luminosité à travers des échelles de masse et de taux d'accrétion très différentes. Cela suggère qu'ils sont alimentés par un objet commun invariant en échelle. Par conséquent, établir la nature des trous noirs pour M87 * confirme également le paradigme général selon lequel les trous noirs sont la source de puissance des galaxies actives.

9. Conclusion et perspectives

Nous avons assemblé EHT, un réseau mondial VLBI fonctionnant à une longueur d'onde de 1,3 mm et imaginé des structures à l'échelle de l'horizon autour du candidat trou noir supermassif de M87. En utilisant plusieurs méthodes indépendantes de calibration, d'imagerie et d'analyse, nous trouvons que l'image est dominée par une structure en anneau de 42 ± 3 µa de diamètre, plus lumineuse dans le sud. Cette structure présente une dépression de luminosité centrale avec un contraste supérieur à 10 : 1, que nous identifions à l'ombre du trou noir. La comparaison des données avec une bibliothèque étendue d'images synthétiques obtenues à partir de simulations GRMHD couvrant différents scénarios physiques et conditions de plasma révèle que les caractéristiques de base de notre image sont relativement indépendantes du modèle astrophysique détaillé. Cela nous permet d'obtenir une estimation de la masse du trou noir de M = (6,5 ± 0,7) × 109 M⊙. Sur la base de notre modélisation et des informations sur l'angle d'inclinaison, nous déduisons le sens de rotation du trou noir dans le sens des aiguilles d'une montre, c'est-à-dire que la rotation du trou noir est à l'opposé de nous. L'excès de luminosité dans la partie sud de la bague d'émission s'explique par le faisceau relativiste de matériau tournant dans le sens des aiguilles d'une montre, comme le voit l'observateur, c'est-à-dire que la partie inférieure de la région d'émission se déplace vers l'observateur.

Des observations futures et des analyses plus poussées permettront de tester plus précisément la stabilité, la forme et la profondeur de l'ombre. L'une de ses caractéristiques clés est qu'il devrait rester en grande partie constant dans le temps car la masse de M87 * ne devrait pas changer de manière mesurable sur les échelles de temps humaines. L'analyse polarimétrique des images, que nous rapporterons à l'avenir, fournira des informations sur le taux d'accrétion via la rotation de Faraday (Bower et al. 2003 ; Marrone et al. 2007 ; Kuo et al. 2014 ; Mościbrodzka et al. 2017) et sur le flux magnétique. Des images de plus haute résolution peuvent être obtenues en utilisant une longueur d'onde plus courte, soit 0,8 mm (345 GHz), en ajoutant plus de télescopes et, dans un avenir plus lointain, avec une interférométrie spatiale (Kardashev et al. 2014 ; Fish et al. 2019 ; Palumbo et al. 2019 ; F. Roelofs et al. 2019b, en préparation).

Une autre source primaire d'ISE, Sgr A *, a une masse mesurée avec précision de trois ordres de grandeur inférieure à celle de M87 *, avec des échelles de temps dynamiques de minutes au lieu de jours. Pour observer l'ombre de Sgr A *, il faudra prendre en compte cette variabilité et atténuer les effets de diffusion causés par le milieu interstellaire (Johnson 2016 ; Lu et al. 2016 ; Bouman et al. 2018). L'analyse non-image dépendante du temps peut être utilisée pour suivre potentiellement le mouvement de la matière émettrice près du trou noir, comme cela a récemment été rapporté par des observations interférométriques dans le proche infrarouge (Gravity Collaboration et al. 2018b). Ces observations fournissent des tests et des sondes séparés de ressources génétiques à une autre échelle de masse (Broderick et Loeb, 2005 ; Doeleman et al., 2009b ; Roelofs et al., 2017 ; Medeiros et al., 2017).

En conclusion, nous avons montré qu'il était désormais possible d'étudier directement l'ombre des candidats candidats aux trous noirs supermassifs au moyen d'ondes électromagnétiques, transformant ainsi cette frontière insaisissable d'un concept mathématique en une entité physique pouvant être étudiée et testée par le biais d'observations astronomiques répétées.

M87-2 Array et Instrumentation

M87-0-intro

bruno — 2019-04-14T12:46:02Z

Focus sur les premiers résultats du télescope Horizon

Nous rapportons la première image d'un trou noir.
Ce numéro de Focus montre des images d'ultra-haute résolution angulaire des émissions radio du trou noir supermassif censé se trouver au cœur de la galaxie M87 (Figure 1). Une caractéristique de ces images est un anneau brillant irrégulier mais clair, dont la taille et la forme concordent étroitement avec l'orbite photonique à lentilles attendue d'un trou noir de 6,5 milliards de masse solaire. Peu de temps après l'introduction de la relativité générale par Einstein, les théoriciens ont établi la forme analytique complète de l'orbite des photons et simulé pour la première fois son apparence cristallisée dans les années 1970. Dans les années 2000, il était possible d'esquisser "l'ombre" formée dans l'image lorsque l'émission synchrotron d'un flux d'accrétion optiquement mince se cristallisait dans la gravité du trou noir. Pendant ce temps, des preuves d'observation ont commencé à se construire pour l'existence de trous noirs au centre des galaxies actives et dans notre propre Voie Lactée. En particulier, une progression régulière de la radioastronomie a permis des observations d'interférométrie de très longue base (VLBI) à des longueurs d'onde toujours plus courtes, ciblant des trous noirs supermassifs présentant les plus vastes horizons d'événements apparents : M87 et Sgr A * au centre galactique. Les tailles compactes de ces deux sources ont été confirmées par des études à 1,3 mm, exploitant d'abord des lignes de base allant d'Hawaï au continent américain, puis avec une résolution accrue des lignes de base vers l'Espagne et le Chili.

Au cours de la dernière décennie, l'EHT a étendu ces premières mesures de taille pour lancer la campagne plus ambitieuse d'imagerie de l'ombre elle-même. Du 5 au 11 avril 2017, le télescope Event Horizon (EHT) a observé M87 et ses calibreurs quatre jours différents à l'aide d'un réseau comprenant huit radiotélescopes répartis sur six emplacements géographiques : Arizona (États-Unis), Chili, Hawaii (États-Unis) et Mexique. , le pôle Sud et l'Espagne (Figure 2). Des années de préparation (et une étonnante avalanche de beau temps sur toute la planète) ont porté leurs fruits avec un rendement extraordinaire en données de plusieurs pétaoctets ( $ 2^{50} \approx 10^{15} $ ).
Les résultats présentés ici, des observations à l'interprétation en passant par les images, proviennent d'une équipe d'instruments, d'algorithmes, de logiciels, de modélisation et d'experts en théorie, à la suite d'un effort énorme de la part d'un groupe de scientifiques qui couvrent toutes les étapes de la carrière, des étudiants de premier cycle aux membres chevronnés du domaine.
Plus de 200 membres de 59 instituts de 20 pays et régions ont consacré des années à cet effort, tous unis par une vision scientifique commune.

La série de lettres de ce numéro présente l'ensemble du projet et les conclusions tirées à ce jour. Le document II s'ouvre avec une description de la matrice EHT, des développements techniques qui ont permis la détection de précurseurs et de la gamme complète d'observations rapportées ici. Grâce au déploiement d'instruments novateurs dans les installations existantes, la collaboration a permis de créer un nouveau télescope doté de fonctionnalités uniques pour l'imagerie des trous noirs. Le document III détaille les observations, le traitement des données, les algorithmes d'étalonnage et des protocoles de validation rigoureux pour les produits de données finaux utilisés pour l'analyse. Le document IV présente l'ensemble du processus et de la méthode de reconstruction de l'image. Les images finales sont apparues après une évaluation rigoureuse des algorithmes d'imagerie traditionnels et de nouvelles techniques adaptées à l'instrument EHT, ainsi que de nombreux mois de test des algorithmes d'imagerie par l'analyse de jeux de données synthétiques.
Le document V utilise des bibliothèques nouvellement assemblées de simulations magnétohydrodynamiques relativistes générales (GRMHD) et de lancés de rayons perfectionné pour analyser les images et les données dans le contexte de l'accrétion de trous noirs et du lancement par jet. Le document VI utilise des ajustements de modèle, la comparaison de simulations avec des données et l'extraction de caractéristiques à partir d'images pour obtenir des estimations formelles de la taille et de la forme de la bague d'émission de lentilles, de la masse du trou noir et des contraintes relatives à la nature du trou noir et à l'espace-temps qui l'entoure . Le document I est un résumé concis.

Notre image de l'ombre limite la masse de M87 à l'intérieur de son orbite à photons, ce qui constitue le cas le plus solide pour l'existence de trous noirs supermassifs. Ces observations concordent avec l'éclaircissement Doppler d'un plasma en mouvement relativiste près du trou noir focalisé autour de l'orbite des photons. Ils renforcent le lien fondamental entre les noyaux galactiques actifs et les moteurs centraux alimentés par l'accrétion de trous noirs grâce à une approche entièrement nouvelle. Dans les années à venir, la collaboration EHT étendra ses efforts pour inclure la polarimétrie complète, la cartographie des champs magnétiques à des échelles d'horizon, des enquêtes sur la variabilité temporelle et une résolution accrue grâce à des observations plus courtes en longueur d'onde.
En bref, ces travaux marquent le développement d'un nouveau domaine de recherche en astronomie et en physique, car nous nous concentrons sur les images de précision des trous noirs à l'échelle de l'horizon. Les chances de mieux cibler nos efforts sont excellentes.

M87-1 : l'ombre du trou noir supermassif

https://iopscience.iop.org/journal/2041-8205/page/Focus_on_EHT

trous noirs : M87

bruno — 2019-04-13T03:41:00Z

Les articles qui parlent du trou noir M87 et de sa photo :
https://www.cnrs.fr/fr/des-astronomes-reussissent-obtenir-la-premiere-image-dun-trou-noir

plus d'infos

First M87 Event Horizon Telescope Results. fr en en

I. The Shadow of the Supermassive Black Hole fr en en

II. Array and Instrumentation fr en en

III. Data Processing and Calibration fr en en

IV. Imaging the Central Supermassive Black Hole fr en en

V. Physical Origin of the Asymmetric Ring fr en en

VI. The Shadow and Mass of the Central Black Hole fr en en

Pour plus d'informations :

https://eventhorizontelescope.org
https://www.iram-institute.org/
https://blackholecam.org/

Ressources :

L'image du trou noir de la galaxie M87, en haute définition : https://cloud.iram.fr/index.php/s/Jis7m2ay1r4Sn9m

Photos du télescope de 30 mètres de l'Iram :
https://cloud.iram.fr/index.php/apps/gallery/s/9qXwgiyw2zzOMdX
https://cloud.iram.fr/index.php/apps/gallery/s/DHOL3Puy4brfaDW (de nuit)

Photos de l'observatoire NOEMA :
https://cloud.iram.fr/index.php/s/kf6nLbXQtwBSGEK

Illustration du réseau mondial EHT : https://cloud.iram.fr/index.php/s/HAGIEvS7eHgfTAY

Ressources vidéo : https://cloud.iram.fr/index.php/s/7sFoL08QhT5m6YM

Chaîne Youtube de l'Iram : https://www.youtube.com/channel/UCanGP9bu9y0dQokV-4305KQ?view_as=subscriber

Visite virtuelle du télescope de 30 mètres de l'Iram : https://www.iram-institute.org/EN/content-page-385-6-385-0-0-0.html