arXiv:1901.06226v1 [astro-ph.HE] 18 Jan 20192 1. INTRODUCTION Supermassive black holes (SMBHs) play a crucial role in shaping our Universe: they evolve symbiotically with their host

Draft version January 21 2019Typeset using LATEX twocolumn style in AASTeX62

The Size Shape and Scattering of Sagittarius A at 86 GHz First VLBI with ALMA

S Issaoun1 2 M D Johnson2 L Blackburn2 C D Brinkerink1 M Moscibrodzka1 A Chael2 C Goddi1 3

I Martı-Vidal4 J Wagner5 S S Doeleman2 H Falcke1 T P Krichbaum5 K Akiyama6 7 8 U Bach5

K L Bouman2 G C Bower9 A Broderick10 I Cho11 12 G Crew7 J Dexter13 V Fish7 R Gold14 10

J L Gomez15 K Hada8 A Hernandez-Gomez16 17 M Janszligen1 M Kino8 M Kramer5 L Loinard16 18

R-S Lu19 5 S Markoff20 D P Marrone21 L D Matthews7 J M Moran2 C Muller1 5 F Roelofs1 E Ros5

H Rottmann5 S Sanchez22 R P J Tilanus1 3 P de Vicente23 M Wielgus2 J A Zensus5 and G-Y Zhao11

1Department of AstrophysicsIMAPP Radboud University PO Box 9010 6500 GL Nijmegen The Netherlands2Harvard-Smithsonian Center for Astrophysics 60 Garden Street Cambridge MA 02138 USA

3ALLEGROLeiden Observatory Leiden University PO Box 9513 2300 RA Leiden The Netherlands4Department of Space Earth and Environment Chalmers University of Technology Onsala Space Observatory 439 92 Onsala Sweden

5Max-Planck-Institut fur Radioastronomie Auf dem Hugel 69 D-53121 Bonn Germany6National Radio Astronomy Observatory 520 Edgemont Rd Charlottesville VA 22903 USA

7Massachusetts Institute of Technology Haystack Observatory 99 Millstone Rd Westford MA 01886 USA8National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo 181-8588 Japan

9Institute of Astronomy and Astrophysics Academia Sinica PO Box 23-141 Taipei 10617 Taiwan10Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo Ontario N2L 2Y5 Canada

11Korea Astronomy and Space Science Institute Daedeokdaero 776 Yuseonggu Daejeon 34055 Korea12University of Science and Technology Gajeong-ro 217 Yuseong-gu Daejeon 34113 Korea

13Max-Planck-Institut fur Extraterrestrische Physik Giessenbachstr 1 85748 Garching Germany14Institut fur Theoretische Physik Johann Wolfgang Goethe-Universitat Max-von-Laue-Straszlige 1 60438 Frankfurt Germany

15Instituto de Astrofısica de Andalucıa-CSIC Glorieta de la Astronomıa sn E-18008 Granada Spain16Instituto de Radioastronomıa y Astrofısica Universidad Nacional Autonoma de Mexico Morelia 58089 Mexico

17IRAP Universit de Toulouse CNRS UPS CNES Toulouse France18Instituto de Astronomıa Universidad Nacional Autonoma de Mexico Apartado Postal 70-264 04510 Ciudad de Mexico Mexico

19Shanghai Astronomical Observatory Chinese Academy of Sciences Shanghai 200030 China20Anton Pannekoek Institute for Astronomy University of Amsterdam 1098 XH Amsterdam The Netherlands

21University of Arizona 933 North Cherry Avenue Tucson AZ 85721 USA22Institut de RadioAstronomie Millimetrique (IRAM) Granada Spain

23Observatorio de Yebes (IGN) Apartado 148 19180 Yebes Spain

(Received October 19 2018 Accepted December 7 2018)

ABSTRACT

The Galactic Center supermassive black hole Sagittarius A (Sgr Alowast) is one of the most promis-ing targets to study the dynamics of black hole accretion and outflow via direct imaging with verylong baseline interferometry (VLBI) At 35 mm (86 GHz) the emission from Sgr Alowast is resolvable withthe Global Millimeter VLBI Array (GMVA) We present the first observations of Sgr Alowast with thephased Atacama Large Millimetersubmillimeter Array (ALMA) joining the GMVA Our observationsachieve an angular resolution of sim87microas improving upon previous experiments by a factor of twoWe reconstruct a first image of the unscattered source structure of Sgr Alowastat 35 mm mitigating ef-fects of interstellar scattering The unscattered source has a major axis size of 120 plusmn 34microas (12 plusmn 34Schwarzschild radii) and a symmetrical morphology (axial ratio of 12+03

minus02) which is further supportedby closure phases consistent with zero within 3σ We show that multiple disk-dominated models ofSgr Alowast match our observational constraints while the two jet-dominated models considered are con-strained to small viewing angles Our long-baseline detections to ALMA also provide new constraintson the scattering of Sgr Alowast and we show that refractive scattering effects are likely to be weak forimages of Sgr Alowast at 13 mm with the Event Horizon Telescope Our results provide the most stringentconstraints to date for the intrinsic morphology and refractive scattering of Sgr Alowast demonstrating theexceptional contribution of ALMA to millimeter VLBI

Keywords accretion ndash galaxies individual Sgr A ndash Galaxy center ndash techniques interferometric

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1 INTRODUCTION

Supermassive black holes (SMBHs) play a crucial rolein shaping our Universe they evolve symbiotically withtheir host galaxies and are the cause of extreme en-vironmental changes via accretion outflows jets andmergers (eg Ferrarese amp Merritt 2000 Gebhardt et al2000) They are believed to be the origin of the mostenergetically efficient and powerful processes in the Uni-verse and yet we are far from fully grasping how theseprocesses are launched and maintained (eg Boccardiet al 2017 Padovani et al 2017) Several theories havebeen put forward to explain accretion and jet launchingmechanisms of SMBHs but observational evidence todiscriminate among theoretical models remains scarce(eg Yuan amp Narayan 2014 Fragile 2014)

Sagittarius A (Sgr Alowast) is the radio source associ-ated with the closest known SMBH with a mass M sim41 times 106M located at the center of our Milky Wayat a distance D sim 81 kpc (Ghez et al 2008 Reid 2009Gillessen et al 2009 Gravity Collaboration et al 2018a)The angular size of the Schwarzschild radius for Sgr Alowast

is thus estimated to be RSch = 2GMc2 sim 10microas Dueto its proximity Sgr Alowast subtends the largest angle on thesky among all known SMBHs and is thus the ideal lab-oratory to study accretion and outflow physics (Goddiet al 2017)

Theoretical models of the dominating component ofthe radio emission in Sgr Alowast fall into two broad classesa relativistic compact jet model or a radiatively inef-ficient accretion flow (Narayan et al 1995 Falcke amp

Markoff 2000 Ozel et al 2000 Yuan et al 2003) How-ever the southern declination and strong interstellarscattering of Sgr Alowast (see more details in Section 22)lead to uncertainty in its intrinsic radio structure de-spite decades of centimeter wavelength very long base-line interferometry (VLBI) observations (eg Alberdiet al 1993 Marcaide et al 1999 Bower et al 2004 Shenet al 2005 Lu et al 2011a Bower et al 2014) Conse-quently these observations have so far been unable todecisively constrain the dominating emission model forSgr Alowast to either of those two classes Additional lines ofevidence provide support for both models For instancefrequency-dependent time lags in light-curves of Sgr Alowast

suggest expanding outflows during flares (eg Yusef-Zadeh et al 2006 2008 Brinkerink et al 2015) VLBIobservations at 7 mm have found evidence for significantintrinsic anisotropy in some epochs (Bower et al 2014)although the anisotropy is not universally seen for otherinstruments and epochs (eg Zhao et al 2017) so theanisotropy may be episodic or may be due to limitationsin the scattering mitigation or model fitting procedure

VLBI in the mm-regime can reach the smallest spatialscales in Sgr Alowast enabling detection and imaging of theintrinsic structure At a wavelength of 13 mm obser-

vations with the Event Horizon Telescope (EHT) haveshown that the radio emission occurs on scales compa-rable to the event horizon (Doeleman et al 2008 Fishet al 2011 Johnson et al 2015 Fish et al 2016 Lu et al2018) On these scales general relativistic effects suchas the ldquoshadowrdquo cast by the black hole are expected todetermine the source morphology (Falcke et al 2000)limiting the view of the innermost accretion flow Atlonger wavelengths scatter-broadening by the interstel-lar medium (ISM) strongly hinders any attempt to probeintrinsic structure Observations at 35 mm where ac-cretion flow kinematics may give rise to an outflow orcompact jet and where scatter-broadening becomes sub-dominant to intrinsic structure can distinguish betweenthe two classes of models via detailed comparisons ofobservations and simulations and help understand thefundamental nature of the radio emission from Sgr Alowast

The first 35 mm VLBI detection of Sgr Alowast by Rogerset al (1994) gave an initial estimate of the scatteredsource size using a circular Gaussian fit Krichbaumet al (1998) used three stations to measure the firstclosure phases (consistent with zero) at 35 mm on asmall triangle Closure phases are a robust observablesince the closed sum of phases in a triangle removesany station-based instrumental effect A zero value indi-cates symmetry in the spatial scales probed by the threebaselines involved in the closure measurement a non-zero value implies asymmetry (eg Rauch et al 2016Thompson et al 2017) Subsequent observations withimproved sensitivity and baseline coverage used closureamplitudes for elliptical Gaussian model-fitting but theminor axis of the scattered source along the north-south direction remained difficult to constrain becauseof predominantly east-west array configurations (Doele-man et al 2001 Shen et al 2005 Bower et al 2006 Luet al 2011a)

The addition of the Large Millimeter Telescope Al-fonso Serrano (LMT) and the Robert C Byrd GreenBank Telescope (GBT) enabled more precise esti-mates of the intrinsic size and shape of Sgr Alowast andrevealed non-zero closure phases indicating either in-trinsic source asymmetry or substructure from inter-stellar scattering (Ortiz-Leon et al 2016 Brinkerinket al 2016 hereafter O16 B16) Further analysis byBrinkerink et al (2018 hereafter B18) found a slightexcess of flux density (sim1 of total flux density) east ofthe phase center giving clear deviation from the purelyGaussian geometry that was assumed in model-fittingThus these improved observations support moving be-yond simple Gaussian model-fitting to test more com-plex source models Imaging is a natural next step asit does not assume a particular morphological model

The development of phased-array capability at the At-acama Large Millimetersubmillimeter Array (ALMA)gives unprecedented sensitivity at 35 mm (Doeleman

The Size Shape and Scattering of Sagittarius A 3

2010 Fish et al 2013 Matthews et al 2018) In ad-dition to its sensitivity the geographical location ofALMA provides long north-south baselines to North-ern hemisphere sites probing regions where scatteringis sub-dominant to intrinsic structure In this paperwe present the first VLBI observations of Sgr Alowast withphased ALMA joining twelve stations of the Global Mil-limeter VLBI Array (GMVA) These observations im-prove north-south resolution by more than a factor ofthree compared to previous 35 mm experiments andthey allow us to reconstruct the first unscattered imageof Sgr Alowast at 35 mm

The organization of the paper is as follows In Sec-tion 2 we give an overview of the relevant backgroundfor models of the intrinsic structure and scattering ofSgr Alowast After summarizing the observations and datareduction (Section 3) and the imaging (Section 4) wepresent our GMVA+ALMA image and discuss data- andimage-derived properties of the intrinsic source in thecontext of previous 35 mm experiments in Section 5 InSection 6 we discuss our new constraints on theoreticalmodels for Sgr Alowast and its scattering We summarize ourresults in Section 7

2 BACKGROUND

21 Theoretical models for Sgr A emission

Sgr Alowast is a bright radio source with a spectrum thatrises with frequency until it peaks near 1 mm (eg Fal-cke et al 1998 Bower et al 2015) The long-standingdebate on whether the radiomm emission from Sgr Alowast

is produced by a radiatively inefficient accretion diskor by a relativistic compact jet present near the blackhole (eg Narayan et al 1995 Markoff et al 2007Moscibrodzka et al 2014 Ressler et al 2015 Connorset al 2017 Davelaar et al 2018 Chael et al 2018a andreferences therein) has not been resolved

Radiative models of Sgr Alowast based on three-dimensionalgeneral relativistic magnetohydrodynamic (GRMHD)simulations of Kerr black hole accretion naturally com-bine the disk and jet scenarios Electrons and ions arenot in thermal equilibrium in the hot diffuse Sgr Alowast

accretion flow therefore simulations with the same gasdynamics (determined by the ions) can have quite dif-ferent appearances at 35 mm depending on electronthermodynamics assumptions In particular both thedisk and jet emission dominated models can be realizedwithin a single simulation by adopting a specific distri-bution for electron heatingacceleration in magnetizedplasma in post-processing (eg Moscibrodzka amp Fal-cke 2013) Alternatively electron-ion thermodynamicswith a specified prescription for the particle heatingfrom dissipation can be incorporated self-consistentlywith the other variables in a single simulation In thisframework Ressler et al (2017) and Chael et al (2018a)have shown that both jet- and disk-dominated imagescan be produced at 35 mm depending on the underly-

ing physical model for electron heating evolved in thesimulation

These models are mainly used to predict 13 mm EHTobservations (eg Chan et al 2015) At 13 mm we ex-pect the emission to originate near the event horizonwhere effects such as gravitational lensing and relativis-tic Doppler boosting distort any emission into a ringcrescent or a spot-like shape making any distinction be-tween dominating emission models difficult At 35 mmwe can potentially constrain the geometry and electronmicro-physics of the GRMHD simulations by modelingemission maps in which the physics of accretion ratherthan relativistic effects shapes the source geometry

22 Interstellar Scattering of Sgr Alowast

The index of refraction of a plasma depends on den-sity so density inhomogeneities in the ionized ISM leadto multi-path propagation of radio waves The scatter-ing is chromatic with scattering angles proportional tothe squared wavelength of a propagating wave Becausethe scattering arises from density irregularities scatter-ing properties are stochastic by nature their statisticalproperties depend on the power spectrum Q(q) of den-sity variations where q denotes a wavevector Alongmany lines of sight the scattering is well characterizedusing a simplified description in which the scatteringmaterial is confined within a single thin screen alongthe line of sight For background and reviews on inter-stellar scattering see Rickett (1990) Narayan (1992) orThompson et al (2017)

The line of sight to Sgr Alowast is particularly heavily scat-tered as is evidenced by an image with a Gaussianshape and a size that is proportional to wavelengthsquared for wavelengths λ gtsim 1 cm (Davies et al 1976van Langevelde et al 1992 Bower et al 2004 Shenet al 2005 Bower et al 2006 Johnson et al 2018) Inaddition the scattering of Sgr Alowast is anisotropic withstronger angular broadening along the east-west axisthan along the north-south axis (Frail et al 1994) Theangular broadening has a full width at half maximum(FWHM) of (1380 plusmn 0013)λ2

cm mas along the majoraxis and (0703 plusmn 0013)λ2

cm mas along the minor axiswith the major axis at a position angle 819 plusmn 02

east of north (Johnson et al 2018 hereafter J18) Forcomparison the intrinsic source has an angular size ofsim04λcm mas (J18) so the ratio of intrinsic size to scat-ter broadening is sim03λcm along the major axis andsim06λcm along the minor axis Consequently obser-vations at 35 mm are the longest wavelengths with ac-tive VLBI for which the intrinsic structure is not sub-dominant to scattering (VLBI observations of Sgr Alowast atwavelengths between 35 mm and 7 mm are very difficultbecause of atmospheric oxygen absorption)

As discussed by Psaltis et al (2018) and J18 the λ2

and Gaussian scattering behavior of Sgr Alowast are univer-sally expected if 1) the intrinsic source size θsrc is sub-dominant to the scatter broadening angle θscatt and 2)

4

the diffractive scale of the scattering rdiff sim λθscatt

is smaller than the dissipation scale of turbulence inthe scattering material Thus even though the angularbroadening size and shape are measured very preciselyfor Sgr Alowast at centimeter wavelengths the constraints onthe overall scattering properties are quite weak The ex-pected dissipation scale in the ISM is 102minus103 km (egSpangler amp Gwinn 1990) so the expected transition tonon-λ2 and non-Gaussian scattering (ie when the dis-sipation scale is comparable to the diffractive scale) forSgr Alowast occurs at wavelengths of a few millimeters Con-sequently the scattering properties of Sgr Alowast measuredat centimeter wavelengths cannot be confidently extrap-olated to millimeter wavelengths The uncertainties canbe parameterized using physical models for the scat-tering material which typically invoke an anisotropicpower-law for the power spectrum of phase fluctuationswith the power-law extending between a maximum scale(the outer scale rout) and a minimum scale (the innerscale rin) In such a generalization the scattering prop-erties depend on a spectral index α and on the innerscale of the turbulence rin In this paper we use thescattering model presented in Psaltis et al (2018) withparameters for Sgr Alowast determined by J18

The discovery by Gwinn et al (2014) of scattering-induced substructure in images of Sgr Alowast at 13 cm givesan additional constraint on the scattering propertiesof Sgr Alowast This substructure is caused by modes inthe scattering material on scales comparable to the im-age extent (much larger than rdiff) so scattering mod-els with identical scatter-broadening may still exhibitstrong differences in their scattering substructure Thesubstructure manifests in the visibility domain as ldquore-fractive noiserdquo which is an additive complex noise com-ponent with broad correlation structure across baselinesand time (Johnson amp Narayan 2016) Using observa-tions of Sgr Alowast from 13 mm to 30 cm J18 have shownthat the combined image broadening and substructurestrongly constrains the power spectrum of density fluc-tuations However a degeneracy between α and rin per-sists and extrapolating the strength of refractive effectsto millimeter wavelengths is still quite uncertain

Two scattering models effectively bracket the rangeof possibilities for Sgr Alowast One model (hereafter J18)has a power-law spectral index α = 138 (near the ex-pected value for 3D Kolmogorov turbulence α = 53)and rin = 800 km (near the expected ion gyroradius inthe ionized ISM) The second is motivated by Goldre-ich amp Sridhar (2006 herafter GS06) who proposed thatthe scattering of Sgr Alowast could be caused by thin currentsheets in the ISM it has α = 0 and rin sim 2 times 106 kmThe inner scale in this latter model is several ordersof magnitude larger than originally proposed by GS06but this larger value is required to produce the refrac-tive noise observed at 13 and 35 cm Both the J18 andGS06 models are consistent with all existing measure-ments of the angular broadening of Sgr Alowast and with the

refractive noise at centimeter wavelengths but the GS06model would produce more refractive noise than the J18model on long baselines at 35 mm with even more pro-nounced enhancement for EHT observations (by roughlyan order of magnitude see Zhu et al 2018) While long-baseline measurements at 35 mm can discriminate be-tween these possibilities observations to-date have beeninadequate for an unambiguous detection of refractivesubstructure at this wavelength (O16 B16 B18) Newobservations with ALMA joining 35 mm VLBI with un-precedented resolution and sensitivity give the oppor-tunity for long-baseline detections of refractive noise atmillimeter wavelengths that can enable discriminationbetween the two scattering models

3 OBSERVATIONS AND DATA REDUCTION

Observations of Sgr Alowast (αJ2000 = 17h45m40s0361δJ2000 = minus2900prime28primeprime168) were made with the GMVAcomposed of the eight Very Long Baseline Array(VLBA) antennas equipped with 86 GHz receivers theGreen Bank Telescope (GB) the Yebes 40-m telescope(YS) the IRAM 30-m telescope (PV) the Effelsberg100-m telescope (EB) and the ALMA phased array(AA) consisting of 37 phased antennas The observa-tions were conducted on 3 April 2017 as part of thefirst offered VLBI session with ALMA (project codeMB007) We recorded a total bandwidth of 256 MHzper polarization divided in 4 intermediate frequencies(IFs) of 116 channels each The 12 h track (4 h withthe European sub-array and 8 h with ALMA) includedthree calibrator sources 1749+096 NRAO 530 andJ1924minus2914 The total integration time on Sgr Alowast withALMA was 576 h

The data were processed with the VLBI correlatorat the Max Planck Institute for Radio Astronomy us-ing DiFX (Deller et al 2011) After correlation reduc-tion was carried out using the Haystack ObservatoryPostprocessing System1 (HOPS) supported by a suiteof auxiliary calibration scripts presented in Blackburnet al (2018) with additional validation and cross-checksfrom the NRAO Astronomical Image Processing Sys-tem (AIPS Greisen 2003) The HOPS software pack-age in its current form arose out of the developmentof the Mark IV VLBI Correlator see Whitney et al(2004) During the HOPS reduction ALMA baselineswere used to estimate stable instrumental phase band-pass and delay between right and left circular polariza-tion relative to the other stations ALMA or GBT base-lines (depending on signal-to-noise) were used to removestochastic differential atmospheric phase within a scanBecause atmospheric phase corrections are required onshort (simsecond) timescales leading to a large numberof free parameters to fit a round-robin calibration wasused to avoid self-tuning baseline visibility phases on

1 httpswwwhaystackmitedutechvlbihopshtml


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strong detectionweak detectionnon-detection

ALMA-GBTALMA-VLBAGBT-VLBAintra-Europeintra-VLBA

(100 as) 1

00 05 10 15 20 25Baseline (G )

100

101

102

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al-to

-noi

se ra

tio

Previous Max Baseline ALMA-GBTALMA-VLBAGBT-VLBAintra-Europeintra-VLBA

Figure 1 Top The (uv)-coverage of Sgr Alowast Each sym-

bol denotes a scan-averaged measurement filled colored cir-

cles are strong detections hollow colored circles are weak

detections (constrained fringe delay and rate but signal-to-

noise ratio (SNR) lt 6) and hollow gray circles are non-

detections (unconstrained fringe delay and rate) after pro-

cessing through HOPS Bottom The SNR for scan-averaged

visibilities on Sgr Alowast as a function of projected baseline

length showing only detections All detections beyond

sim1 Gλ are on baselines to ALMA

each 58 MHz IF were estimated using only the remain-ing 3 IFs which have independent thermal noise Theintegration time for rapid phase corrections was auto-matically chosen by balancing errors from random ther-mal variation to those due to atmospheric phase driftand thus varied with the available signal-to-noise Themedian effective integration time was 45 seconds Dur-ing a final stage of reduction with the HOPS fringe fitterfourfit fringe solutions for each scan were fixed to asingle set of station-based delays and rates These were

derived from a least-squares solution to baseline detec-tions where unconstrained stations were removed fromthe dataset No interpolation of these fringe solutionswas performed across scans as the solutions were notstable within their necessary tolerance to maintain co-herence After these phase corrections our data haveenough phase coherence to allow longer averaging times

We performed a-priori amplitude calibration usingprovided telescope gain information and measured sys-tem temperatures during the observations The hetero-geneity of the stations in the GMVA required us to adopta careful approach to the amplitude calibration Thecalibration for ALMA was fully provided by the ALMAquality assurance (QA2) team (Goddi et al 2018) andsystem equivalent flux densities (SEFDs) were generatedwith a high time cadence by PolConvert (Martı-Vidalet al 2016) Both YS and PV measure effective sys-tem temperatures via the chopper wheel method andthus do not require an additional opacity correction totheir SEFDs However the rest of the array (VLBAGB EB) measures system temperatures via the noisediode method requiring an additional opacity correctionto account for atmospheric attenuation of the visibilityamplitudes Unfortunately several VLBA stations ob-served in difficult weather conditions (ice wind rain)leading to limited detections on baselines to Owens Val-ley (OV) North Liberty (NL) and Pie Town (PT) sta-tions Additionally observations at PV suffered fromphase coherence losses in the signal chain during the ob-servations leading to poor quality data and lower vis-ibility amplitudes on those baselines which cannot berescaled with a-priori calibration information Figure 1shows the detections and non-detections for Sgr Alowast (toppanel) and corresponding signal-to-noise ratio of scan-averaged visibilities for Sgr Alowast detections All detectionsbeyond sim1 Gλ are on baselines to ALMA After a-prioricalibration we can proceed with imaging routines to de-termine the morphology of the calibrators and the targetsource

4 IMAGING

We employ the eht-imaging library2 a regularizedmaximum likelihood imaging software package to im-age our sources (Chael et al 2016 2018b) Due to theelevated noise level for the VLBA in our observationsand the scattering properties of Sagittarius A standardimaging software packages like AIPS (Greisen 2003) orDifmap (Shepherd et al 1995) do not offer the flexibil-ity and necessary tools to obtain an unscattered imageof the source The eht-imaging library is a Python-based software package that is easily scriptable flexibleand modular It is able to make images with variousdata products (closure phase and amplitude bispectravisibilities) and it contains a suite of image ldquoregulariz-

2 httpsgithubcomachaeleht-imaging

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ALMA-GBTALMA-SpainALMA-VLBAGBT-SpainGBT-VLBAVLBA-Spainintra-Europeintra-VLBA

(100 as) 1

4002000200400Relative RA ( as)

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200

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Rel

ativ

e D

ec (

as)

025

050

075

100

125

150

175

Bri

ghtn

ess

(mJy

as

2 )

Figure 2 Left the (uv)-coverage of NRAO 530 (symbols are as defined in Figure 1) Right closure-only image of NRAO 530

using the eht-imaging library (Chael et al 2018b) the contour levels start from 12 of the peak and increase in factors of

two The observations have a uniform-weighted beam = (111 times 83) microas PA = 32

3210123u [G ]

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Rel

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as)

005

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015

020

025

030

Bri

ghtn

ess

(mJy

as

2 )Figure 3 Left the (uv)-coverage of J1924minus2914 (symbols are as defined in Figure 1) Right closure-only image of

J1924minus2914 using the eht-imaging library (Chael et al 2018b) the contour levels start from 12 of the peak and increase in

factors of two The observations have a uniform-weighted beam = (122 times 88) microas PA = 36 The European stations did not

observe this source

ersrdquo such as maximum entropy and sparsity regulariza-tion The library also possesses a routine for ldquostochasticopticsrdquo a regularized implementation of scattering miti-gation presented in Johnson (2016) making it a naturalchoice for our analysis In this section we present ourimaging methods for both calibrators (Section 41) andfor Sgr Alowast (Section 42)

41 Calibrators NRAO 530 and J1924minus2914

Both NRAO 530 and J1924minus2914 appear point-like toALMA when acting as a connected-element interferome-

ter (sim70 kλ sim3 arcseconds resolution) with NRAO 530having a flux density of 28 plusmn 03 Jy and J1924minus2914having a flux density of 50 plusmn 05 Jy (as measuredby interferometric-ALMA) Even on the angular scalesprobed by VLBI both sources are very compact andstable making them ideal for imaging The operationaldifficulties and poor weather conditions at the VLBAwere largely offset by the high sensitivity of ALMA Theextent of all detections is shown in the left panel of Fig-ure 2 for NRAO 530 and Figure 3 for J1924minus2914 Athird calibrator was also observed 1749+096 but only


for a few minutes with the full array and is thus omittedfrom further analysis

The large number of detections on both NRAO 530and J1924minus2914 led to a correspondingly large num-ber of closure phases and closure amplitudes We thusimaged both sources using only closure quantities fol-lowing the method from Chael et al (2018b) constrain-ing the total flux of the image to match measurementsfrom interferometric-ALMA We present images of thetwo calibrators in Figure 2 and Figure 3 (right panels)The morphology of NRAO 530 is consistent with previ-ous observations of the source (Bower et al 1997 Boweramp Backer 1998 Feng et al 2006 Chen et al 2010 Luet al 2011b) The elongation of the J1924minus2914 jet inthe north-west direction at 86 GHz is consistent withmm-jet studies from previous observations at 43 GHzby Shen et al (2002) and 230 GHz by Lu et al (2012)These two sources are common calibrators for Sgr AlowastThey are therefore particularly useful to study at mul-tiple frequencies to adequately calibrate observations at13 mm from the EHT

Table 1 Station median multiplicative gains to the visibil-

ity amplitudes

Station SgrAlowast NRAO 530 J1924minus2914

BR 22+15minus08 17+05

minus05 20+14minus18

FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178


NOTEmdash Median (and 95th percentile) multiplicative gains

to the visibility amplitudes for common stations from the two

calibration methods 1) self-calibration of Sgr Alowast amplitudes

below 075Gλ to the Gaussian source estimated from O16

B18 and 2) self-calibration of NRAO 530 and J1924minus2914

observations to the images produced with closure phases and

closure amplitudes The European stations and ALMA are

not shown as they are not self-calibrated for all three sources

We flagged NL and PT due to their high median gain and

erratic gain solutions

42 Sagittarius A

421 Self-calibration

We obtained far fewer detections on Sgr Alowast than onthe calibrators and our detections also had lower signal-to-noise ratio (SNR) Consequently we did not haveenough information to synthesize images of Sgr Alowast using

only closure quantities Moreover due to the subopti-mal performance of the VLBA (bad weather signal losslikely from pointing issues) additional amplitude cali-bration was necessary to mitigate severe signal losses atvarious stations

We utilized two methods for amplitude calibration

1 we self-calibrated to closure-only images of NRAO530 and J1924minus2914 to obtain smoothed stationgain trends

2 we self-calibrated all Sgr Alowast visibility amplitudeswithin 075Gλ (predominantly intra-VLBA mea-surements) using an anisotropic Gaussian visibil-ity function determined by previous 35 mm exper-iments (O16 B18) with the total flux set by theinterferometric-ALMA measurement

For the second method we used a visibility func-tion corresponding to a Gaussian source size of 215 by140microas with a position angle of 80 (east of north) anda total flux density of 20plusmn02 Jy The choice of theGaussian size is motivated by similar results obtainedfor O16 and B18 taken one month apart showing stablesource dimensions Both these experiments had the highsensitivity of the LMT adding north-south coverage torecover the minor axis size with greater accuracy thanolder experiments In our interferometric-ALMA mea-surements Sgr Alowast has flux density variations at the 10level on a timescale of about 4 hours not significantlyaffecting our static imaging Note that gains were de-rived by self-calibration using only short baselines butbecause they are station-based they were then appliedto correct visibility amplitudes on longer baselines aswell

The two methods gave comparable gain solutionshence validating the Gaussian assumption for short-baseline measurements (Table 1 shows median multi-plicative station gains to the visibility amplitudes) Weflagged the VLBA stations NL and PT which showedextreme signal loss in both methods The GBT per-formed well for all three sources so we chose to keepthe original a-priori calibration Because GBT is onlylinked to NL in the inner 075 Gλ baseline cut for Sgr Alowastthe derived gains for GBT introduce large variations tothe ALMA-GBT amplitudes that come from difficultylocking NL gains due to its bad weather Ignoring theself-calibration solutions gave more stable amplitudes onthe ALMA-GBT baseline

Figure 4 shows the scan-averaged visibilities for Sgr Alowast

after self-calibration of the inner 075 Gλ baselines to theGaussian source size (method 2) All detections above1 Gλ are new measurements to ALMA The ALMA-GBT baseline has significantly higher flux density thanexpected from the minor axis of the previously fittedGaussian source size from O16 and B18 VLBA de-tections to ALMA show clear deviations from Gaussianbehavior

8

Previous Max Baseline

Major Axis Minor Axis

ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)

Figure 4 Noise-debiased correlated flux density of Sgr Alowast as a function of projected baseline length for data after self-calibrating

to the Gaussian source from O16 and B18 using only baselines shorter than 075 Gλ Because the a-priori calibration for the

GBT was excellent (see Table 1) we did not apply the derived GBT gains Dashed dark blue curves show expected visibilities

along the major and minor axes for an anisotropic Gaussian source with FWHM of 215 microas by 140 microas (the source size from

O16 and B18) All detections beyond sim1Gλ are baselines to ALMA and all show marked deviations from the Gaussian curves


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )

Figure 5 Left the scattered image of Sgr Alowast reconstructed with the second moment regularizer and stochastic optics

(θmaj = 228 plusmn 46 microas θmin = 143 plusmn 20 microas from LSQ) Right the reconstructed image from stochastic optics (Johnson 2016)

of the intrinsic source (θmaj = 120 plusmn 34 microas θmin = 100 plusmn 18 microas from LSQ) In each panel the ellipses at the bottom indicate

half the size of the scatter-broadening kernel (θmaj = 1599 microas θmin = 795 microas PA = 819) and of the observing beam

422 Imaging with regularized maximum likelihood

The performance of the VLBA impaired our ability tomodel-fit to the dataset and obtain an accurate sourcesize estimate using only short baselines (ie baselinesthat do not heavily resolve the source) In additionlarge measurement uncertainties for the visibility am-plitudes on intra-VLBA baselines made image conver-

gence difficult and unstable We thus implemented anew imaging regularization we constrained the secondcentral moment of the image to match more robust mea-surements of the scattered source size from Gaussianmodel fitting to previous observations (O16 B18) Ifwe think of the centroid (first moment) of the image asthe mean position of the emission its variance (or sec-


model

th+

dis

k (6

0)

model J18 scatt reconst observed

beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)

beam2kernel2 beam2kernel2

th je

t (90

)


20015010050050100150200

th+

jet (

90)


Figure 6 Model and reconstructed images from four example 3D GRMHD models plotted here in linear scale The contour

levels represent 25 50 and 75 of the peak flux The first column shows the original model images as given from simulations

ldquoth+κ diskrdquo is a thermal disk model with 1 accelerated particles in a power-law (κ) distribution ldquoth jetrdquo is a thermal jet

model ldquoth+κ jetrdquo is a thermal jet model with 10 accelerated particles in a κ distribution (Moscibrodzka et al 2009 2014

2016 Davelaar et al 2018) The inclinations of the models are given in the parentheses The second column shows the model

images scattered with the J18 scattering model these are the images sampled to make the simulated observations The third

column shows the observed (scattered) image reconstructed with the second moment regularizer and stochastic optics and the

fourth column shows the reconstructed image from stochastic optics of the corresponding intrinsic source In the third and

fourth columns the ellipses at the bottom indicate half the size of the scatter-broadening kernel and of the observing beam

10

ond moment) is the spread of emission from the meanequivalent to the extent of the source along its prin-cipal axes (Hu 1962) The regularization is equivalentto constraining the curvature of the visibility functionat zero baseline This method helps to calibrate short-baseline visibilities during the imaging process whileallowing long-baseline detections to ALMA to still re-cover smaller scale structure in our images This methodis now included and implemented in the eht-imaginglibrary via gradient descent minimization (the effectsand fidelity of the regularizer will be presented in Is-saoun et al (2018)) We also made use of the ldquostochasticopticsrdquo scattering mitigation code from Johnson (2016)to disentangle the effects of scattering and produce theintrinsic image of Sgr Alowast

To reach our final result we first imaged the scat-tered source using closure quantities and visibility am-plitudes (with equal weights) The regularizers used inthe scattered image with a weighting of 10 of thedata weights were Gull-Skilling maximum entropy to-tal squared variation and second moment regularizationwith the second moment matrix given by that of theGaussian used for self-calibration Each of these regu-larizers favors particular image features while enforc-ing image positivity and a total flux density constraintGull-Skilling entropy favors pixel-by-pixel similarity tothe prior image (we used the previously fitted Gaussiansource as the prior) Total-squared variation regular-ization favors small image gradients producing smoothedges (see Chael et al (2018b) for a detailed discussionof these regularizers) Second moment regularizationconstrains the second derivative of the visibility functionat the zero baseline (which is proportional to the secondcentral image moment) to match a specified value wethereby constrained our short baselines to match thoseof the Gaussian source measured in previous experi-ments (O16 B18) without imposing assumptions on thevisibilities measured by longer baselines which reflectimage substructure In the scattering mitigation codethe second moment regularization is only applied to theobserved image such that the intrinsic image derived bythe scattering deconvolution is not directly constrainedby the regularizer but still remains within physical sizeranges After imaging with closure quantities and cor-rected visibility amplitudes we then self-calibrated thevisibility phases and amplitudes to the obtained scat-tered image before imaging with stochastic optics (usingthe same regularization parameters)

The stochastic optics framework is implementedwithin the eht-imaging library via regularized max-imum likelihood The code solves for the unscatteredimage by identifying separating and mitigating the twomain components of the scattering screen introducedin Section 2 small-scale diffractive modes that blur theimage causing the ensemble-average scattered image tobe a convolution of the true image and the scatteringkernel (predominantly east-west scatter-broadening)

and large-scale refractive modes that introduce stochas-tic image substructure (ripples distorting the image)The code simultaneously solves for the unscattered im-age and the large-scale phase screen causing refractivescattering while assuming a given model for the diffrac-tive blurring kernel and the refractive power spectrumQ(q) (governing the time-averaged scattering proper-ties) In our case we used the scattering kernel (witha size of (1599 times 795)microas PA of 819) and powerspectrum (with α = 138 and rin = 800 km) from theJ18 scattering model See Johnson (2016) for a moredetailed description of the method Two iterations ofstochastic imaging and self-calibration are done for con-vergence We present in Figure 5 our resulting intrinsicand scattered images of Sgr Alowast

423 Uncertainties of image-derived parameters

To determine the uncertainties in the imaging methodand size measurements for Sgr Alowast we performed imag-ing tests on simulated observations where the intrin-sic model image was known We tested our imagingmethod on four snapshots from 3D GRMHD simulationsof Sgr Alowastat 86 GHz (Moscibrodzka et al 2009 20142016 Davelaar et al 2018) using the same samplingcoverage and noise as our observations The model im-ages were scattered with the J18 scattering model andsampled with our GMVA+ALMA coverage before be-ing imaged via the same imaging routine applied to theSgr Alowast data described above

While the imaging procedure is identical these recon-structions do have some advantages relative to our re-construction of the actual observations For example weused the ensemble-average properties of the J18 scatter-ing model as inputs to the scattering mitigation iewe assume perfect knowledge of the diffractive scatter-ing kernel and the time-averaged power spectrum Wealso measure the second moment of the scattered simu-lated images and use it as an exact input to the secondmoment regularization Because the scattering is sub-dominant to intrinsic structure and because the secondmoment is estimated to excellent accuracy in previousexperiments we do not expect either of these effects tosignificantly advantage the reconstructions of simulateddata

In Figure 6 we present the original 3D GRMHD modelimages the model images scattered with the J18 scatter-ing model (as observed in the simulated observations)and the reconstructed observed (scattered) and intrinsicimages from the imaging method In Table 2 we com-pare the true intrinsic source sizes from the models tothe intrinsic source sizes derived from the imaging rou-tine We determined the source size parameters usingtwo methods first by measuring the second central mo-ment of the image (2nd mom) and deriving Gaussianparameters and second by doing a 2D Gaussian fit witha least-squares minimization (LSQ) onto the image


Table 2 Comparison of the true size and the derived size from imaging from synthetic datasets for four simulated images

Model Method θmaj (microas) θmin (microas) Axial ratio PA (deg)

Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876

Difference 630 (04θbeam) 345 (01θbeam) 016 (01θbeam) 178 (06θbeam)

LSQ

True 797 770 104 1099

Image 1019 596 17 08

Difference 222 (01θbeam) 174 (01θbeam) 066 (01θbeam) 693 (amp 04θbeam)

Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742

Difference 362 (03θbeam) 258 (01θbeam) 005 (002θbeam) 604 (amp θbeam)

LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792

Difference 251 (01θbeam) 130 (plusmn01θbeam) 018 (002θbeam) 05 (01θbeam)

NotemdashIn each case we compute the sizes using two methods directly from the image second central moment (ldquo2nd momrdquo)

and from a 2D Gaussian fit to the image with least-squares minimization (ldquoLSQrdquo) We give the absolute difference between the

true and estimated values and also express the difference as a fraction of the projected beam FWHM θbeam along the measured

axis or as the fraction of the propagated error from the beam-widths on both axes for the axial ratio The uncertainty on

the position angle (PA) is expressed as the fraction of one-dimensional beam blurring of the image for which the standard

deviation in PA with blurring along different directions matches the difference between the true and measured PA (see text

for additional details)

Next we evaluate the difference between true and re-constructed image parameters We sought to define anapproach that quantifies these differences in a way thatis related to the reconstructed image properties and theobserving beam When expressed in this way we canuse parameter errors on these reconstructed simulatedimages to predict uncertainties on parameters derivedfrom our reconstructed image with data

To this end Table 2 expresses the difference betweenthe true and measured source major and minor axes asa fraction of the projected beam FWHM θbeam alongthe corresponding axis For the axial ratio we expressthe difference between the true and measured ratios as

a fraction of the cumulative error from both axes (theprojected beam-widths along the measured major andminor axes added quadratically)

However while it is straightforward and well-motivatedto express uncertainties on axis lengths and their ratioin terms of the observing beam uncertainty on the po-sition angle (PA) is more subtle We opted to createan ensemble of beam-convolved reconstructed imagesand to use the scatter in the PA of the ensemble as anestimate of the PA uncertainty The ensemble of imagesis constructed by convolving the single reconstructedimage with an ensemble of narrow beams sampling allposition angles Each of these beams has a major axis

12

Table 3 Observed and intrinsic sizes for Sgr Alowast at 86 GHz

Referenceθmajobs θminobs PAobs Axial ratio θmajint θminint PAint Axial ratio

(microas) (microas) (deg) robs (microas) (microas) (deg) rint

Rogers et al (1994) 150 plusmn 50 - - - lt 130 - - -

Krichbaum et al (1998) 190 plusmn 30 - - - - - - -

Doeleman et al (2001) 180 plusmn 20 - - - lt 130 - - -

Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -

Lu et al (2011a) 210 plusmn 10 130 plusmn 10 83 plusmn 2 16 plusmn 01 139 plusmn 17 102 plusmn 21 - 14 plusmn 03

O16 BD183C 213 plusmn 2 138 plusmn 4 81 plusmn 2 154 plusmn 004 142 plusmn 9 114 plusmn 15 - 12 plusmn 02

O16 BD183D 222 plusmn 4 146 plusmn 4 75 plusmn 3 152 plusmn 005 155 plusmn 9 122 plusmn 14 - 13 plusmn 02

B18 (closamp) 2151 plusmn 04 145 plusmn 2 779 plusmn 04 148 plusmn 001 - - - -

B18 (selfcal) 217 plusmn 22 165 plusmn 17 77 plusmn 15 13 plusmn 02 - - - -

J18 BD183C 215 plusmn 4 139 plusmn 4 81 plusmn 3 155 plusmn 005 143+11minus12 114+7

minus8 - 125+020minus016

This work (2nd mom)lowast 239 plusmn 57 172 plusmn 103 84 plusmn 2 14+11minus04 176 plusmn 57 152 plusmn 103 852 plusmn 44lowastlowast 12+11

minus02

This work (LSQ)lowast 228 plusmn 46 143 plusmn 20 86 plusmn 2 16 plusmn 03 120 plusmn 34 100 plusmn 18 960 plusmn 32lowastlowast 12+03minus02

NotemdashlowastImage-domain size estimates The stated uncertainties are derived using the largest parameter errors for reconstructions

of simulated imageslowastlowastPosition angle estimates are not meaningfully constrained because of the near symmetry of the majorminor axes

size given by the projected observing beam size alongthe same position angle and a minor axis size of zeroWe thereby stretch the image along each direction upto the extent of the observing beam and examine theoverall dependence of the reconstructed image on thisstretching With this approach images that are nearlyisotropic will have large PA uncertainty while highlyelongated images (relative to the beam size) will havesmall PA uncertainty

In general we find that the LSQ method fares betterthan 2nd moment for determining the source parameterslikely due to weak extended flux in the images skewingthe second moment parameters to larger values As ex-pected both methods perform poorly when determin-ing the position angle of a fairly symmetrical source forwhich it remains largely unconstrained However formore elongated source geometry both methods are ableto accurately recover the intrinsic position angle Weadopt the LSQ method to quantify the size of Sgr Alowast viaimage-domain fitting Although the Gaussian approxi-mation does not describe fully our source morphologyit is suitable for comparisons to visibility-domain modelfits from previous observations of Sgr Alowast presented inSection 5

5 RESULTS

51 Intrinsic source constraints from imaging

Figure 5 shows the unscattered and scattered imagesof Sgr Alowast as imaged following the method describedin Section 4 The (uniform-weighted) beam size of theSgr Alowast observations is (235times87) microas with a position an-

gle (east of north) of 536 While the shorter baselinesof the array (intra-VLBA VLBA-GBT intra-European)see primarily a Gaussian source elongated in the east-west direction longer baselines are expected to pickup on non-Gaussian source structure or refractive noisefrom interstellar scattering In this particular observa-tion our longest baselines are mainly north-south toALMA (see Figure 1) where scattering has less of aneffect on the source As seen in Figure 5 left panelthe reconstructed scattered image looks very smoothand Gaussian-like showing no obvious refractive noisein the image We also see a similar outcome in ourimaging tests presented in Section 423 Although thescattered images (second column in Figure 6) have visi-ble ripples of scattering substructure the reconstructedscattered images (third column) appear very smoothThis is likely because our GMVA+ALMA observationssample low levels of refractive noise mainly along thenorth-south direction whereas our east-west sensitiv-ity and resolution do not provide adequate detectionsof scattering substructure to be able to reconstruct thefine structure in the scattered images Thus the low levelof refractive noise detected on our ALMA baselines doesnot produce visible distortions in the reconstructed scat-tered image

We present the measured source sizes using our twomethods (2nd mom and LSQ) in Table 3 along with his-torical measurements and estimates The uncertaintiesare conservative estimates taken from the largest rela-tive uncertainties on the parameters of simulated imagesfor each method (see Table 2) We assume a Gaussian


source geometry for size estimates and comparisons butthis may not be the correct source model As seen in theexample images (Figure 6) the true and reconstructedintrinsic images are not Gaussian therefore this choiceof parametrization is only to simplify comparisons withprevious measurements and simulations We find thatour source size measurements are consistent with previ-ous observations and indicate the source dimensions andsmall asymmetry are persistent across multiple years

Lastly we note that uncertainties in the intrinsic sizecaused by remaining uncertainties in the scattering ker-nel are quite small (ltsim 10microas) even allowing for the fullrange of uncertainty on α and rin (J18) The reasonthey are small is because the scattering parameters forangular broadening are estimated to an accuracy of afew percent and because the intrinsic structure is notsubdominant to scatter broadening

50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD

SGRANRAO530J1924-2914


8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

Figure 7 Scan-averaged closure phases for Sgr Alowast

NRAO 530 and J1924minus2914 on three triangles (LA-KP-

FD GBT-KP-FD ALMA-GBT-FD) formed after processing

through HOPS The larger uncertainties on the ALMA-GBT-

FD triangle are primarily because of low correlated flux den-

sity on the ALMA-FD baseline (see Figure 4) Non-zero clo-

sure phase indicates source asymmetry Although NRAO 530

and J1924minus2914 show significant deviations from zero all

Sgr Alowast closure phases are consistent with zero within 3σ

52 Intrinsic source constraints from closure phases

Closure phases provide an alternative and complemen-tary assessment of source asymmetry directly from ob-servations They are weakly affected by refractive scat-tering and are unaffected by station-based calibrationissues Thus they offer robust information on the in-trinsic properties of Sgr Alowast

We computed closure phases for all sources from scan-averaged visibilities The GMVA+ALMA array con-tains 13 stations yielding many triangles with a widerange of sizes As seen in Figures 2 and 3 there are

multiple long-baseline detections to ALMA on calibra-tors that do not appear for Sgr Alowast (Figure 1) We thusselected three example triangles of different sizes andorientations that are present for the two main calibratorsources (NRAO 530 and J1924minus2914) and with multipledetections for Sgr Alowast

We present in Figure 7 the closure phases on three rep-resentative triangles a small intra-VLBA (LA-KP-FD)triangle an east-west medium-sized triangle to GBT(GB-KP-FD) and a long north-south triangle to ALMA(AA-GB-FD) Although all three triangles provide ro-bust detections for all three sources with non-zero clo-sure phases for the calibrators Sgr Alowast closure phases re-main very close to zero the weighted mean closure phaseon AA-GB-FD is minus11plusmn24 the weighted mean closurephase on GB-KP-FD is minus17 plusmn 11 and the weightedmean closure phase on LA-KP-FD is minus18 plusmn 11 Thelargest closure phases on all three triangles deviate fromzero by less than 3σ

O16 and B16 detected small non-zero closure phases(ltsim10) on triangles including the highly sensitive LMTandor GBT These non-zero closure phases were ob-served on triangles not present in our GMVA+ALMAobservations and they probed different scales and direc-tions from our new predominantly north-south triangleswith ALMA Deviations of a few degrees as observed byO16 and B16 fall within our confidence bounds due tolow signal-to-noise on VLBA baselines and thus wouldnot be detectable with our current observations More-over the geometrical models to describe the asymme-try in B16 produce closure phases on our triangles thatwould be indistinguishable from zero with our currentmeasurements Thus our results are consistent withprevious observations of Sgr Alowast

6 DISCUSSION

61 Constraints on the Refractive Scattering of Sgr Alowast

Our longest baselines heavily resolve the scattered im-age of Sgr Alowast while also providing exceptional sensitivity(especially baselines to ALMA) Therefore they are sen-sitive to a non-Gaussian scattering kernel (from a finiteinner scale) and to ldquorefractive noiserdquo which correspondsto image substructure introduced by interstellar scatter-ing In this section we use our long-baseline measure-ments to constrain scattering models for Sgr Alowast

Figure 8 shows our detected correlated flux density asa function of baseline length The ALMA-GBT baselineprobing scales along the minor axis of the source mea-sures significantly higher correlated flux density thanpredicted from the Gaussian curves from model fit-ting to shorter baseline data shown as the dark bluedashed curves in Figure 8 (O16 B18) This enhance-ment could either indicate non-Gaussian intrinsic struc-ture (eg a compact core with a diffuse halo) or anon-Gaussian scattering kernel (requiring an inner scalerin 15 times 109λ asymp 5000 km) For example the ALMA-GBT measurements are comparable to the values pre-

14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)

Figure 8 Noise-debiased correlated flux density for Sgr Alowast as a function of projected baseline length for data after self-

calibrating to the Gaussian source from O16 B18 using only baselines shorter than 075 Gλ Because the a-priori calibration

for the GBT was excellent (see Table 1) we did not apply the derived GBT gains Baseline labels are ordered by median

baseline length Intra-European baselines are entirely constrained by the self-calibration and are omitted here for clarity

Dark blue dashed curves show expected visibilities along the major and minor axes for an anisotropic Gaussian source with

FWHM of (215microas 140microas) light blue dotted curves show the visibility expected for an anisotropic intrinsic Gaussian source

(140microas 100microas) scattered with the non-Gaussian kernel from the J18 scattering model which has an image size (via 2nd mom)

of (216microas 132microas) red curves show the expected renormalized refractive noise along the major and minor axes for the J18 and

GS06 scattering models Detections on baselines longer than 1Gλ are only obtained for baselines oriented close to the minor axis

of the scattering kernel (all are ALMA-VLBAGBT) Labeled black triangles show upper limits (4σ) on four sensitive baselines

at other orientations all of which have corresponding detections for our calibrators Colored lines show the anisotropic Gaussian

model curves for the corresponding data

dicted for an anisotropic Gaussian intrinsic source com-bined with the J18 scattering model which has rin =800 km shown as the light blue dotted curves in Fig-ure 8

We also detect correlated flux density on baselinesthat are expected to entirely resolve the scatteredsource Here the enhanced flux density indicates thepresence of image substructure that can either be intrin-sic or scattering-induced For scattering substructurethe signal is expected to be significantly stronger forbaselines that are aligned with the major axis of thescattering (see Figure 8) The two candidate scatteringmodels presented in Section 22 (with different spec-tral index α and inner scale rin governing the refractivenoise power spectrum) predict different levels of refrac-tive noise along both the major and minor axes of thescattering the GS06 model predicts on average nearlyone order of magnitude more correlated flux density onlong baselines than the J18 model However our mostsensitive detections (ALMA-VLBAGBT) are along theminor axis of the scattering

The mean visibility amplitude (after debiasing to ac-count for thermal noise) on baselines longer than 18 Gλis 6 mJy Because this amplitude may contain contri-butions from both scattering substructure and intrin-sic substructure it only determines an upper limit onthe level of refractive noise from scattering substruc-ture Moreover even if there were no intrinsic substruc-ture contribution on these baselines the 6 mJy signalwould still not directly determine the level of refractivenoise because refractive noise is stochastic the inner95 of visibility amplitudes sampled on a single baselineover different scattering realizations will fall in the range[016 19]timesσ where σ is the RMS ldquorenormalizedrdquo refrac-tive noise (ie refractive noise after removing the contri-butions of flux modulation and image wander which ourobservations would absorb into the overall calibrationsee J18)

We can tighten the constraints on refractive noise bycombining samples from many baselines although thesewill be correlated (see Johnson amp Narayan 2016) Fol-lowing the Monte Carlo approach of J18 we find that


combining baselines longer than 18 Gλ gives a 95 con-fidence range for the mean amplitude of refractive noiseon a baseline with (u v) = (1167minus1638) times 109λ of 3-18 mJy if the 6 mJy of correlated flux density is entirelyfrom refractive noise For comparison the J18 modelpredicts a mean refractive noise amplitude of approx-imately 7 mJy on this baseline while the GS06 modelpredicts a mean refractive noise of 60 mJy on this base-line Thus the GS06 model is incompatible with ourmeasurements The GS06 model also significantly over-predicts the signal on our baselines oriented closer tothe major axis for which our measurements only pro-vide upper limits (labeled black triangles in Figure 8)

If the minor axis detections are from scattering sub-structure then they would represent the first detectionsof substructure along this axis The presence of sub-structure along the minor axis requires that magneticfield variations transverse to the line of sight are not re-stricted to a narrow angular range (the field wander ismore likely to sample all angles but with a preferencefor angles that are aligned with the minor axis of thescattering) Minor axis substructure would eliminatefor example the ldquoboxcarrdquo model for refractive fluctua-tions in Psaltis et al (2018) which describes magneticfield wander as a uniform distribution over a limitedrange of angles

62 Constraints on accretion flow and jet models

The intrinsic image of Sgr Alowast at 3 mm shown in Fig-ure 5 allows us to discriminate between the two mainclasses of models that now must fit the tight source sizeand morphology constraints derived from both model-fitting (from previous experiments) and our image-domain measurements We can explore a small subset ofGRMHD simulations to assess possible constraints fromour observables Due to our unconstrained estimate ofthe PA we opted to compare the major axis size andthe asymmetry (axial ratio) which are independent ofthe PA of the source on the sky

Figure 9 compares the sizes and morphology of7313 mm images from a sample of 3D-GRMHD sim-ulations of either disk or jet dominated emission atvarying viewing angle with respect to the black holespin axis with observational constraints from current(Table 3) and previous observations of Sgr Alowast (see Table4 in J18) Model images are generated by combining thedynamical model with ray-tracing and radiative transferusing only synchrotron opacities To estimate the sizeof the radiating region in model images we calculate theeigenvalues of the matrix formed by taking the secondcentral moment of the image on the sky (ie the lengthof the ldquoprincipal axesrdquo Hu 1962)

Producing a ray-traced image from single-fluidGRMHD simulations requires providing the electrondistribution function (hereafter eDF) which is uncon-strained in traditional single-fluid GRMHD simulationsThermal disk models (ldquoTh diskrdquo in Figure 9) assume a

thermal Maxwell-Juttner eDF and a proton-to-electrontemperature ratio3 TpTe = 3 everywhere (motivatedby results of Moscibrodzka et al 2009) Models de-noted as ldquoTh jetrdquo have TpTe = 20 in the accretion diskand TpTe = 1 along the magnetized jet which allowsthe jet to outshine the disk at mm-wavelengths (thisjet model has been introduced by Moscibrodzka et al(2014 2016)) There is a family of models in-betweenthese two extreme cases In the models denoted asldquoTh+κ diskrdquo the eDF is hybrid 1 percent of all elec-trons are non-thermal described by a κ eDF Addingnon-thermal electrons to the emission model results inmore extended disk images as the non-thermal elec-trons produce a diffuse ldquohalordquo around the synchrotronphotosphere The ldquohalordquo contributes to the disk sizeestimates (Mao et al 2017) Finally the ldquoTh+κ jetrdquomodel is a 3D version of the κminusjet model introduced byDavelaar et al (2018) with 10 percent of jet electronsin a κ eDF In both hybrid models the κ parameter isset to 4 (see Davelaar et al 2018 for details)

We find that only disks with a hybrid eDF at mod-erate viewing angles and both jet-models with viewingangles ltsim 20 are consistent with 13 and 3 mm sizes andasymmetry constraints This limit is consistent withthe recent low-inclination constraints derived from or-bital motions in near-infrared Sgr Alowast flares by GravityCollaboration et al (2018b) observed with the GRAV-ITY instrument In the tested models the dependencyof the source sizes as a function of observing wavelengthis shallower than the θ sim λ dependency estimated frommulti-wavelength observations of Sgr Alowast (Figure 13 inJ18) Hence none of the models that satisfy 133 mmsource sizes can account for the 7 mm source size

Although GRMHD simulations of black hole accretionare inherently time-variable causing the size and asym-metry to fluctuate in time these changes are smallerthan 10 percent We conclude that current modelsunder-predict the observed 7 mm emission size evenwhen accounting for size and asymmetry fluctuationsin time In simulations the 7 mm photons are emit-ted from larger radii where the accretion flow structureis less certain due to lower grid resolution the initialconditions (finite size torus with pressure maximum atr = 24 GMc2) and boundary conditions of the simula-tion that only allow for plasma outflows These issuesas well as the electron acceleration should be addressedby future radiative GRMHD simulations of Sgr Alowast

3 Standard GRMHD simulations provide only the fluid pres-sure which is dominated by the protons In a perfect fluid thepressure in a grid zone gives a proton temperature For stronglysub-Eddington accretion flows with LBolLEdd asymp 10minus8 protonsand electrons are not necessarily well coupled by Coulomb colli-sions In these GRMHD simulations the electron temperatures arenot self-consistently computed but they are essential in calculatingsynchrotron emission The electron temperature is parameterizedby a coupling ratio TpTe between the proton and electron tem-perature

16

0 30 60 90 120 150 180Inclination [degrees]

102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work

Th diskTh jetTh+ diskTh+ jet

1 mm3 mm7 mm

1 mm3 mm7 mm

Figure 9 Intrinsic size and asymmetry (axial ratio) estimates from observations of Sgr Alowast at 1 3 and 7 mm vs theoretical

predictions based on 3D GRMHD simulations of black hole accretion flows Line color encodes the wavelength of observation

and the bands are size and asymmetry bounds from model-fitting (J18) The upper and lower size and asymmetry image-domain

bounds from this work are shown as solid magenta lines Data constraints at 1 mm extend to a lower asymmetry bound of

10 Various line types correspond to models with varying prescriptions for electron acceleration and diskjet dominated flows

generated at each wavelength ldquothrdquo for a purely thermal disk or jet dominated emission model ldquoth+κrdquo for a thermal model

with accelerated particles (1 for disk and 10 for jet) in a power-law (κ) distribution (Moscibrodzka et al 2009 2014 2016

Davelaar et al 2018) Left Intrinsic source sizes as a function of the viewing angle Right Intrinsic asymmetry (axial ratio) as

a function of the viewing angle


102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm




bounds from this work are shown as solid magenta lines Data constraints at 1 mm extend to a lower asymmetry bound of 10

Various line types correspond to models with varying prescription for electron heating and black hole spin generated at each

wavelength ldquoHrdquo for the Howes turbulent cascade prescription ldquoRrdquo for the Rowan magnetic reconnection prescription ldquoLordquo

for a non-spinning black hole and ldquoHirdquo for a black hole with a dimensionless spin of 09375 (Howes 2010 Rowan et al 2017

Chael et al 2018a) Left Intrinsic source sizes as a function of the viewing angle Right Intrinsic asymmetry (axial ratio) as a

function of viewing angle


We also explored another set of 3D simulationsfrom Chael et al (2018a) performed with the two-temperature radiative GRMHD code KORAL (Sadowskiet al 2013 2014 2017 see Figure 10) Unlike thesimulations presented in Figure 9 where the electrontemperature (and potential non-thermal component)is assigned to the simulation in post-processing KORALevolves the electron temperature throughout the simula-tion self-consistently with contributions from radiativecooling Coulomb coupling and dissipative heatingWhile the physics of radiation and Coulomb coupling iswell understood the dissipative heating of electrons andions is governed by unconstrained plasma microphysicsthat occurs at scales far smaller than the grid scale ofthe simulation

Chael et al (2018a) investigated two different phys-ical prescriptions for the electron dissipative heatingThe first prescription is the Landau-damped turbulentcascade model of Howes (2010) Since this prescriptionprimarily heats electrons in regions where the plasmais highly magnetized it produces prominent emissionfrom the jet and outflow of the GRMHD simulationsat 35 mm(see also Ressler et al 2017) The other pre-scription for electron heating investigated in Chael et al(2018a) is based on particle-in-cell simulations of par-ticle heating from magnetic reconnection presented inRowan et al (2017) This prescription heats electronsand ions equally and only in highly magnetized regionsresulting in cooler jet regions with less emission than thedisk In total Chael et al (2018a) presented four simula-tions spanning the two heating prescriptions considered(ldquoHowesrdquo or ldquoHrdquo for the turbulent cascade prescriptionof Howes 2010 and ldquoRowanrdquo or ldquoRrdquo for the reconnec-tion prescription of Rowan et al 2017) and two valuesof the dimensionless black hole spin (a = 0 for ldquoLordquoand a = 09375 for ldquoHirdquo)

Figure 10 shows that all four models presented inChael et al (2018a) fit the 13 mm constraints andmostly fit the 3 mm image-domain constraints How-ever only the H-Hi and R-Lo models fit the model-fitting 3 mm range at moderate viewing angles and allmodels fail to match 7 mm constraints However thesesimulations were only run over a relatively short timeand inflow equilibrium in the disk was only establishedup to sim20 RSch while the 7 mm emission extends tosim35 RSch To accurately compare the predictions fromthese two heating models with predictions at 7 mm andlonger wavelengths the simulations will have to be runlonger using initial conditions adapted to producing anaccretion disk in equilibrium past 20 RSch

Figure 11 demonstrates the plausible range of intrin-sic source sizes vs asymmetries at 3 mm for all of themodels we have explored Here it is evident which mod-els fall into the permitted region Given that our mod-eling does not involve any detailed parameter fittingthe agreement between models and observables is en-couraging Disk and jet models with different heating

10 15 20 25 30 35 40 45 503mm intrinsic asymmetry ( maj min)

102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]

Th diskTh+ disk Th jetTh+ jetH-HiR-HiH-LoR-Lo3 mm model-fitting3 mm imaging

Figure 11 3 mm models compared to the plausible range

from 3 mm data via model-fitting (J18) and image-domain

constraints (this work) Various line types correspond

to models with varying prescriptions for electron accelera-

tionheating (Moscibrodzka et al 2009 2014 2016 Davelaar

et al 2018 Chael et al 2018a)

prescriptions are also likely to have distinct polarimet-ric characteristics that can be compared to observables(eg Gold et al 2017 Moscibrodzka et al 2017)

Furthermore we can directly compare closure phasesfrom the different models with those presented in Sec-tion 5 Closure phases observed are an additional ro-bust criterion to discriminate between models they areindependent of imaging assumptions the beam of theobservations and scattering effects In Figure 12 wecompare the scan-averaged closure phases from Sgr Alowast

for the three representative triangles to four examplemodels the thermal+κ disk model at an inclinationof 60 and the thermal jet model at an inclination of5 which fit the major axis and asymmetry boundsgiven by the 35 mm observations and the thermal+κjet model and thermal-only jet model both at an incli-nation of 90 which do not fit the 35 mm bounds Wesimulated observations of the four different models withthe same stations and coverage as our GMVA+ALMAdataset and compare the closure phases for the originalmodel images (Figure 12 top panel) for the model scat-tered with the J18 refractive scattering (center panel)and for the ldquoensemble averagerdquo models scattered onlywith the scattering kernel (no refractive noise bottompanel) We find that for the small and medium trian-gles it is very difficult to distinguish between modelsas they all have closure phases near zero similar to ourmeasurements (Fraga-Encinas et al 2016) However forthe large triangle (ALMA-GBT-FD) two models show

18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscatteredunscattered

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD

SGRAth+ disk i=60th jet i=5th jet i=90th+ jet i=90

GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble averageensemble average

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scatteringJ18 scattering

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

Figure 12 Scan-averaged closure phases for Sgr Alowast on three

triangles (LA-KP-FD GBT-KP-FD ALMA-GBT-FD) with

predictions for a thermal+κ-distribution disk model (th+κ

disk i = 60) thermal+κ-distribution jet model (th+κ jet

i = 90) and thermal jet model (th jet i = 5 and i = 90)

where i is the inclination Each model is shown without scat-

tering (top) with ensemble-average scattering (center) and

with a single realization of scattering (bottom) Note that

ensemble-average scattering does not affect closure phase

and even a single realization of the scattering has little effect

on the closure phases for these triangles

strong non-zero closure phases the thermal+κ and thethermal-only jet models at 90 inclination Interestinglythese are also the example models that do not fit the in-trinsic asymmetry and size bounds from 35 mm Wealso find that interstellar scattering as modeled by J18does not strongly affect intrinsic closure phase for boththe ensemble average and fully scattered cases the twojet models at 90 inclination clearly deviate from what ismeasured on the largest triangle The Howes and Rowanmodels are omitted from the comparisons in Figure 12for clarity as they are all very symmetrical and compacttheir closure phase behavior is similar to the thermal+κdisk and the thermal jet models nearly or fully pointedalong the line of sight

While our comparisons to simulations are limited toa handful of GRMHD models they demonstrate thestrong constraints provided by multi-wavelength mea-surements of size shape and point-symmetry of Sgr Alowast

7 SUMMARY

We have presented observations of Sgr Alowast usingALMA in concert with the GMVA at 86 GHz These arethe first observations to use ALMA as part of a VLBIarray improving the angular resolution for observationsof Sgr Alowast at this frequency by more than a factor of twoThe improved resolution and sensitivity have allowed usto reconstruct an intrinsic image of Sgr Alowast for the firsttime at this frequency which is also the first image ofSgr Alowast for which the scattering is subdominant to intrin-sic structure We find that the intrinsic image of Sgr Alowast

has an asymmetry (axial ratio) of 12+03minus02 and a major

axis of 120 plusmn 34 microas although we cannot constrain theposition angle because of the highly symmetric intrinsicsource

We have demonstrated that the geometrical proper-ties of the intrinsic image and observed closure phasestightly constrain accretion flow models onto Sgr AlowastOur measurements require models to have symmetricalmorphology 86 GHz radio emission spanning 12 plusmn 34Schwarzschild radii and closure phases close to zero onthe triangles sampled in our observation For the eighttheoretical simulations we have considered at 35 mmour data are compatible with disk models at all inclina-tions and jet models fully or nearly pointed along theline of sight None of the simulations we consider isable to simultaneously match size and asymmetry limitsfrom 1 3 and 7 mm observations due to the relativelysmall domain simulated by state of the art 3D GRMHDmodels

While GRMHD models are promising to describeemission near the horizon semi-analytical models for theaccretion flow and jet can be more readily extended tolarger domains (eg Broderick et al 2016 Gold et al2017 Pu amp Broderick 2018) In addition it is morestraightforward to explore parameter dependencies forsemi-analytic models The model of Broderick et al(2016) is compatible with our 35 mm size and asymme-


try estimates Exploring whether these models can becompatible with the full set of multi-wavelength size andasymmetry constraints for Sgr Alowast is a promising avenuefor continued study

In addition to the overall image morphology we havediscovered non-Gaussian structure along the minor axisof Sgr Alowast hinting at either a non-Gaussian intrinsicsource or a non-Gaussian scattering kernel Compar-isons of the observed visibility amplitudes against twoscattering models showed that the scattering model pre-sented by Goldreich amp Sridhar (2006) over-predicts thecorrelated flux density on long baselines to ALMA (18-24 Gλ) This model also overpredicts the flux densityon east-west baselines longer than 1 Gλ Thus thismodel for the scattering of Sgr Alowast is conclusively ruledout by our observations The exclusion of the GS06model shows that refractive scattering is likely to weaklyaffect 13 mm images with the EHT

The scattering model presented by Johnson et al(2018) on the other hand predicts comparable levelsof refractive noise to the excess flux density we have ob-served on baselines above 18 Gλ However using oursingle observation with ALMA we cannot conclusivelydetermine whether those detections are entirely due torefractive noise or if they are a combination of intrinsicsource structure and scattering substructure Continuedobservations of Sgr Alowast will elucidate these questions in-cluding deeper VLBI observations at 22 and 43 GHz tobetter estimate the inner scale from the shape of thescatter-broadening kernel (eg Zhao et al 2018) andadditional GMVA+ALMA observations that will sam-ple different realizations of the scattering screen

This work is supported by the ERC Synergy GrantldquoBlackHoleCam Imaging the Event Horizon of BlackHolesrdquo Grant 610058 We thank the National Sci-ence Foundation (AST-1126433 AST-1614868 AST-1716536) and the Gordon and Betty Moore Founda-tion (GBMF-5278) for financial support of this workThis work was supported in part by the Black HoleInitiative at Harvard University which is supported by

a grant from the John Templeton Foundation K Ais a Jansky Fellow of the National Radio AstronomyObservatory M K acknowledges the financial sup-port of JSPS KAKENHI grants No JP18K03656 andJP18H03721 R-S L is supported by the NationalYouth Thousand Talents Program of China and by theMax-Planck Partner Group L L acknowledges the fi-nancial support of DGAPA UNAM (project IN112417)and CONACyT Mexico I C acknowledges the finan-cial support of the National Research Foundation of Ko-rea (NRF) via a Global PhD Fellowship Grant (NRF-2015H1A2A1033752) This paper makes use of the fol-lowing ALMA data ADSJAOALMA2016100413VALMA is a partnership of ESO (representing its mem-ber states) NSF (USA) and NINS (Japan) togetherwith NRC (Canada) MOST and ASIAA (Taiwan) andKASI (Republic of Korea) in cooperation with the Re-public of Chile The Joint ALMA Observatory is oper-ated by ESO AUINRAO and NAOJ This research hasmade use of data obtained with the Global MillimeterVLBI Array (GMVA) which consists of telescopes oper-ated by the (Max-Planck-Institut fur Radioastronomie)(MPIfR) IRAM Onsala Metsahovi Yebes the KoreanVLBI Network the Green Bank Observatory and theLong Baseline Observatory (LBO) The VLBA is an in-strument of the LBO which is a facility of the NationalScience Foundation operated by Associated UniversitiesInc The data were correlated at the DiFX correlator ofthe MPIfR in Bonn Germany This work is partly basedon observations with the 100-m telescope of the MPIfRat Effelsberg This work made use of the Swinburne Uni-versity of Technology software correlator (Deller et al2011) developed as part of the Australian Major Na-tional Research Facilities Programme and operated un-der licence

Software AIPS (Greisen 2003) DiFX (Deller et al2011) HOPS (Whitney et al 2004 Blackburn et al 2018)KORAL (Sadowski et al 2013 2014 2017) PolConvert(Martı-Vidal et al 2016) eht-imaging library (Chael et al2016) Stochastic Optics (Johnson 2016)

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Alberdi A Lara L Marcaide J M et al 1993 AampA

277 L1

Blackburn L Chan C-K Crew G B et al 2018 in

prep

Boccardi B Krichbaum T P Ros E amp Zensus J A

2017 AampA Rev 25 4

Bower G C amp Backer D C 1998 ApJL 507 L117

Bower G C Backer D C Wright M et al 1997 ApJ

484 118

Bower G C Falcke H Herrnstein R M et al 2004

Science 304 704

Bower G C Goss W M Falcke H Backer D C amp

Lithwick Y 2006 ApJL 648 L127

Bower G C Markoff S Brunthaler A et al 2014 ApJ

790 1

Bower G C Markoff S Dexter J et al 2015 ApJ 802

69

Brinkerink C D Falcke H Law C J et al 2015 AampA

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Brinkerink C D Muller C Falcke H et al 2016

MNRAS 462 1382 (B16)

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Brinkerink C D Muller C Falcke H D et al 2018

ArXiv e-prints arXiv181108394 (B18)

Broderick A E Fish V L Johnson M D et al 2016

ApJ 820 137

Chael A Rowan M Narayan R Johnson M amp Sironi

L 2018a MNRAS 478 5209

Chael A A Johnson M D Bouman K L et al 2018b

ApJ 857 23

Chael A A Johnson M D Narayan R et al 2016

ApJ 829 11

Chan C-K Psaltis D Ozel F Narayan R amp

Sadowski A 2015 ApJ 799 1

Chen Y J Shen Z-Q amp Feng S-W 2010 MNRAS

408 841

Connors R M T Markoff S Nowak M A et al 2017

MNRAS 466 4121

Davelaar J Moscibrodzka M Bronzwaer T amp Falcke

H 2018 AampA 612 A34

Davies R D Walsh D amp Booth R S 1976 MNRAS

177 319

Deller A T Brisken W F Phillips C J et al 2011

PASP 123 275

Doeleman S 2010 in 10th European VLBI Network

Symposium and EVN Users Meeting VLBI and the New

Generation of Radio Arrays 53

Doeleman S S Shen Z-Q Rogers A E E et al 2001

AJ 121 2610

Doeleman S S Weintroub J Rogers A E E et al

2008 Nature 455 78

Falcke H Goss W M Matsuo H et al 1998 ApJ 499

731

Falcke H amp Markoff S 2000 AampA 362 113

Falcke H Melia F amp Agol E 2000 ApJL 528 L13

Feng S-W Shen Z-Q Cai H-B et al 2006 AampA 456

97

Ferrarese L amp Merritt D 2000 ApJL 539 L9

Fish V Alef W Anderson J et al 2013 ArXiv

e-prints arXiv13093519

Fish V L Doeleman S S Beaudoin C et al 2011

ApJL 727 L36

Fish V L Johnson M D Doeleman S S et al 2016

ApJ 820 90

Fraga-Encinas R Moscibrodzka M Brinkerink C amp

Falcke H 2016 AampA 588 A57

Fragile P C 2014 SSRv 183 87

Frail D A Diamond P J Cordes J M amp van

Langevelde H J 1994 ApJ 427 L43

Gebhardt K Bender R Bower G et al 2000 ApJL

539 L13

Ghez A M Salim S Weinberg N N et al 2008 ApJ

689 1044

Gillessen S Eisenhauer F Fritz T K et al 2009

ApJL 707 L114

Goddi C Falcke H Kramer M et al 2017

International Journal of Modern Physics D 26 1730001

Goddi C et al 2018 in prep

Gold R McKinney J C Johnson M D amp Doeleman

S S 2017 ApJ 837 180

Goldreich P amp Sridhar S 2006 ApJL 640 L159 (GS06)

Gravity Collaboration Abuter R Amorim A et al

2018a AampA 615 L15

mdash 2018b AampA 618 L10

Greisen E W 2003 in Astrophysics and Space Science

Library Vol 285 Information Handling in Astronomy -

Historical Vistas ed A Heck 109

Gwinn C R Kovalev Y Y Johnson M D amp

Soglasnov V A 2014 ApJL 794 L14

Howes G G 2010 MNRAS 409 L104

Hu M-K 1962 8 179

Issaoun S et al 2018 in prep

Johnson M D 2016 ApJ 833 74

Johnson M D amp Narayan R 2016 ApJ 826 170

Johnson M D Fish V L Doeleman S S et al 2015

Science 350 1242

Johnson M D Narayan R Psaltis D et al 2018 ApJ

865 104 (J18)

Krichbaum T P Graham D A Witzel A et al 1998

AampA 335 L106

Lu R-S Krichbaum T P Eckart A et al 2011a AampA

525 A76

Lu R-S Krichbaum T P amp Zensus J A 2011b

MNRAS 418 2260

Lu R-S Fish V L Weintroub J et al 2012 ApJL

757 L14

Lu R-S Krichbaum T P Roy A L et al 2018 ApJ

859 60

Mao S A Dexter J amp Quataert E 2017 MNRAS 466

4307

Marcaide J M Alberdi A Lara L Perez-Torres M A

amp Diamond P J 1999 AampA 343 801

Markoff S Bower G C amp Falcke H 2007 MNRAS 379

1519

Martı-Vidal I Vlemmings W H T amp Muller S 2016

AampA 593 A61

Matthews L D Crew G B Doeleman S S et al 2018

PASP 130 015002

Moscibrodzka M Dexter J Davelaar J amp Falcke H

2017 MNRAS 468 2214

Moscibrodzka M amp Falcke H 2013 AampA 559 L3


Moscibrodzka M Falcke H amp Noble S 2016 AampA 596

A13

Moscibrodzka M Falcke H Shiokawa H amp Gammie

C F 2014 AampA 570 A7

Moscibrodzka M Gammie C F Dolence J C

Shiokawa H amp Leung P K 2009 ApJ 706 497

Narayan R 1992 Royal Society of London Philosophical

Transactions Series A 341 151

Narayan R Yi I amp Mahadevan R 1995 Nature 374

623

Ortiz-Leon G N Johnson M D Doeleman S S et al

2016 ApJ 824 40 (O16)

Ozel F Psaltis D amp Narayan R 2000 ApJ 541 234

Padovani P Alexander D M Assef R J et al 2017

AampA Rev 25 2

Psaltis D Johnson M Narayan R et al 2018 ArXiv


Pu H-Y amp Broderick A E 2018 ApJ 863 148

Rauch C Ros E Krichbaum T P et al 2016 AampA

587 A37

Reid M J 2009 International Journal of Modern Physics

D 18 889

Ressler S M Tchekhovskoy A Quataert E Chandra

M amp Gammie C F 2015 MNRAS 454 1848

Ressler S M Tchekhovskoy A Quataert E amp Gammie

C F 2017 MNRAS 467 3604

Rickett B J 1990 ARAampA 28 561

Rogers A E E Doeleman S Wright M C H et al

1994 ApJL 434 L59

Rowan M E Sironi L amp Narayan R 2017 ApJ 850 29

Sadowski A Narayan R McKinney J C amp

Tchekhovskoy A 2014 MNRAS 439 503

Sadowski A Narayan R Tchekhovskoy A amp Zhu Y

2013 MNRAS 429 3533

Sadowski A Wielgus M Narayan R et al 2017

MNRAS 466 705

Shen Z-Q Lo K Y Liang M-C Ho P T P amp Zhao

J-H 2005 Nature 438 62

Shen Z-Q Moran J M amp Kellermann K I 2002 in 8th

Asian-Pacific Regional Meeting Volume II ed

S Ikeuchi J Hearnshaw amp T Hanawa 401ndash402

Shepherd M C Pearson T J amp Taylor G B 1995

Bull Am Meteorol Soc 27 903

Spangler S R amp Gwinn C R 1990 ApJL 353 L29

Thompson A R Moran J M amp Swenson Jr G W

2017 Interferometry and Synthesis in Radio Astronomy

3rd Edition doi101007978-3-319-44431-4

van Langevelde H J Frail D A Cordes J M amp

Diamond P J 1992 ApJ 396 686

Whitney A R Cappallo R Aldrich W et al 2004

Radio Science 39 doi1010292002RS002820

Yuan F amp Narayan R 2014 ARAampA 52 529

Yuan F Quataert E amp Narayan R 2003 ApJ 598 301

Yusef-Zadeh F Roberts D Wardle M Heinke C O amp

Bower G C 2006 ApJ 650 189

Yusef-Zadeh F Wardle M Heinke C et al 2008 ApJ

682 361

Zhao G-Y Kino M Cho I-J et al 2017 in IAU

Symposium Vol 322 The Multi-Messenger Astrophysics

of the Galactic Centre ed R M Crocker S N

Longmore amp G V Bicknell 56ndash63

Zhao G-Y et al 2018 in prep

Zhu Z Johnson M D amp Narayan R 2018 arXiv


2

1 INTRODUCTION

Supermassive black holes (SMBHs) play a crucial rolein shaping our Universe they evolve symbiotically withtheir host galaxies and are the cause of extreme en-vironmental changes via accretion outflows jets andmergers (eg Ferrarese amp Merritt 2000 Gebhardt et al2000) They are believed to be the origin of the mostenergetically efficient and powerful processes in the Uni-verse and yet we are far from fully grasping how theseprocesses are launched and maintained (eg Boccardiet al 2017 Padovani et al 2017) Several theories havebeen put forward to explain accretion and jet launchingmechanisms of SMBHs but observational evidence todiscriminate among theoretical models remains scarce(eg Yuan amp Narayan 2014 Fragile 2014)

Sagittarius A (Sgr Alowast) is the radio source associ-ated with the closest known SMBH with a mass M sim41 times 106M located at the center of our Milky Wayat a distance D sim 81 kpc (Ghez et al 2008 Reid 2009Gillessen et al 2009 Gravity Collaboration et al 2018a)The angular size of the Schwarzschild radius for Sgr Alowast

is thus estimated to be RSch = 2GMc2 sim 10microas Dueto its proximity Sgr Alowast subtends the largest angle on thesky among all known SMBHs and is thus the ideal lab-oratory to study accretion and outflow physics (Goddiet al 2017)

Theoretical models of the dominating component ofthe radio emission in Sgr Alowast fall into two broad classesa relativistic compact jet model or a radiatively inef-ficient accretion flow (Narayan et al 1995 Falcke amp

Markoff 2000 Ozel et al 2000 Yuan et al 2003) How-ever the southern declination and strong interstellarscattering of Sgr Alowast (see more details in Section 22)lead to uncertainty in its intrinsic radio structure de-spite decades of centimeter wavelength very long base-line interferometry (VLBI) observations (eg Alberdiet al 1993 Marcaide et al 1999 Bower et al 2004 Shenet al 2005 Lu et al 2011a Bower et al 2014) Conse-quently these observations have so far been unable todecisively constrain the dominating emission model forSgr Alowast to either of those two classes Additional lines ofevidence provide support for both models For instancefrequency-dependent time lags in light-curves of Sgr Alowast

suggest expanding outflows during flares (eg Yusef-Zadeh et al 2006 2008 Brinkerink et al 2015) VLBIobservations at 7 mm have found evidence for significantintrinsic anisotropy in some epochs (Bower et al 2014)although the anisotropy is not universally seen for otherinstruments and epochs (eg Zhao et al 2017) so theanisotropy may be episodic or may be due to limitationsin the scattering mitigation or model fitting procedure

VLBI in the mm-regime can reach the smallest spatialscales in Sgr Alowast enabling detection and imaging of theintrinsic structure At a wavelength of 13 mm obser-

vations with the Event Horizon Telescope (EHT) haveshown that the radio emission occurs on scales compa-rable to the event horizon (Doeleman et al 2008 Fishet al 2011 Johnson et al 2015 Fish et al 2016 Lu et al2018) On these scales general relativistic effects suchas the ldquoshadowrdquo cast by the black hole are expected todetermine the source morphology (Falcke et al 2000)limiting the view of the innermost accretion flow Atlonger wavelengths scatter-broadening by the interstel-lar medium (ISM) strongly hinders any attempt to probeintrinsic structure Observations at 35 mm where ac-cretion flow kinematics may give rise to an outflow orcompact jet and where scatter-broadening becomes sub-dominant to intrinsic structure can distinguish betweenthe two classes of models via detailed comparisons ofobservations and simulations and help understand thefundamental nature of the radio emission from Sgr Alowast

The first 35 mm VLBI detection of Sgr Alowast by Rogerset al (1994) gave an initial estimate of the scatteredsource size using a circular Gaussian fit Krichbaumet al (1998) used three stations to measure the firstclosure phases (consistent with zero) at 35 mm on asmall triangle Closure phases are a robust observablesince the closed sum of phases in a triangle removesany station-based instrumental effect A zero value indi-cates symmetry in the spatial scales probed by the threebaselines involved in the closure measurement a non-zero value implies asymmetry (eg Rauch et al 2016Thompson et al 2017) Subsequent observations withimproved sensitivity and baseline coverage used closureamplitudes for elliptical Gaussian model-fitting but theminor axis of the scattered source along the north-south direction remained difficult to constrain becauseof predominantly east-west array configurations (Doele-man et al 2001 Shen et al 2005 Bower et al 2006 Luet al 2011a)

The addition of the Large Millimeter Telescope Al-fonso Serrano (LMT) and the Robert C Byrd GreenBank Telescope (GBT) enabled more precise esti-mates of the intrinsic size and shape of Sgr Alowast andrevealed non-zero closure phases indicating either in-trinsic source asymmetry or substructure from inter-stellar scattering (Ortiz-Leon et al 2016 Brinkerinket al 2016 hereafter O16 B16) Further analysis byBrinkerink et al (2018 hereafter B18) found a slightexcess of flux density (sim1 of total flux density) east ofthe phase center giving clear deviation from the purelyGaussian geometry that was assumed in model-fittingThus these improved observations support moving be-yond simple Gaussian model-fitting to test more com-plex source models Imaging is a natural next step asit does not assume a particular morphological model

The development of phased-array capability at the At-acama Large Millimetersubmillimeter Array (ALMA)gives unprecedented sensitivity at 35 mm (Doeleman




2 BACKGROUND
















4











3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1

00 05 10 15 20 25Baseline (G )

100

101

102

Sign

al-to

-noi

se ra

tio















4 IMAGING



6

3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1


400

200

0

200

400

Rel

ativ

e D

ec (

as)

025

050

075

100

125

150

175

Bri

ghtn

ess

(mJy

as

2 )




3210123u [G ]

3

2

1

0

1

2

3

v [G

]




400

200

0

200

400

Rel

ativ

e D

ec (

as)

005

010

015

020

025

030

Bri

ghtn

ess

(mJy

as




observe this source









ity amplitudes


BR 22+15minus08 17+05


FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178












42 Sagittarius A











8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361











2 BACKGROUND
















4











3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1

00 05 10 15 20 25Baseline (G )

100

101

102

Sign

al-to

-noi

se ra

tio















4 IMAGING



6

3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1


400

200

0

200

400

Rel

ativ

e D

ec (

as)

025

050

075

100

125

150

175

Bri

ghtn

ess

(mJy

as

2 )




3210123u [G ]

3

2

1

0

1

2

3

v [G

]




400

200

0

200

400

Rel

ativ

e D

ec (

as)

005

010

015

020

025

030

Bri

ghtn

ess

(mJy

as




observe this source









ity amplitudes


BR 22+15minus08 17+05


FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178












42 Sagittarius A











8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








4











3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1

00 05 10 15 20 25Baseline (G )

100

101

102

Sign

al-to

-noi

se ra

tio















4 IMAGING



6

3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1


400

200

0

200

400

Rel

ativ

e D

ec (

as)

025

050

075

100

125

150

175

Bri

ghtn

ess

(mJy

as

2 )




3210123u [G ]

3

2

1

0

1

2

3

v [G

]




400

200

0

200

400

Rel

ativ

e D

ec (

as)

005

010

015

020

025

030

Bri

ghtn

ess

(mJy

as




observe this source









ity amplitudes


BR 22+15minus08 17+05


FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178












42 Sagittarius A











8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361









3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1

00 05 10 15 20 25Baseline (G )

100

101

102

Sign

al-to

-noi

se ra

tio















4 IMAGING



6

3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1


400

200

0

200

400

Rel

ativ

e D

ec (

as)

025

050

075

100

125

150

175

Bri

ghtn

ess

(mJy

as

2 )




3210123u [G ]

3

2

1

0

1

2

3

v [G

]




400

200

0

200

400

Rel

ativ

e D

ec (

as)

005

010

015

020

025

030

Bri

ghtn

ess

(mJy

as




observe this source









ity amplitudes


BR 22+15minus08 17+05


FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178












42 Sagittarius A











8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








6

3210123u [G ]

3

2

1

0

1

2

3v

[G]



(100 as) 1


400

200

0

200

400

Rel

ativ

e D

ec (

as)

025

050

075

100

125

150

175

Bri

ghtn

ess

(mJy

as

2 )




3210123u [G ]

3

2

1

0

1

2

3

v [G

]




400

200

0

200

400

Rel

ativ

e D

ec (

as)

005

010

015

020

025

030

Bri

ghtn

ess

(mJy

as




observe this source









ity amplitudes


BR 22+15minus08 17+05


FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178












42 Sagittarius A











8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361












ity amplitudes


BR 22+15minus08 17+05


FD 22+12minus06 19+12


GB 12+17minus04 11+05


KP 24+22minus06 22+12


LA 22+28minus10 19+17


NL 46+133minus21 47+97


OV 19+31minus10 19+09


PT 114+22minus53 193+178












42 Sagittarius A











8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








8



ALMA-GBT

ALMA-VLBA

GBT-VLBA

intra-Europe

intra-VLBA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)







200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

5075

005

010

015

020

025

Bri

ghtn

ess

(mJy

as

2 )


200

150

100

50

0

50

100

150

200

Rel

ativ

e D

ec (

as)

beam2kernel2

25

50

75

01

02

03

04

05

06

Bri

ghtn

ess

(mJy

as

2 )









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361









model

th+

dis

k (6

0)


beam2kernel2

reconst intrinsic

beam2kernel2

th je

t (5

)


th je

t (90

)


20015010050050100150200

th+

jet (

90)











10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








10












Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361











Th+κ disk (60)

2nd mom

True 1210 973 124 1054

Image 1840 1318 14 876


LSQ

True 797 770 104 1099

Image 1019 596 17 08


Th jet (5)

2nd mom

True 1125 990 114 138

Image 1487 1248 119 742


LSQ

True 880 812 108 1797

Image 655 519 126 1584


Th jet (90)

2nd mom

True 1740 658 264 1798

Image 1781 1353 132 1764


LSQ

True 1608 632 254 1788

Image 1303 424 307 1771


Th+κ jet (90)

2nd mom

True 1824 657 278 1797

Image 1775 1276 14 1776


LSQ

True 1666 629 265 1787

Image 1415 499 283 1792













12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








12







Shen et al (2005) 210+20minus10 130+50

minus13 79+12minus33 16+04

minus05 - - - -









minus02






5 RESULTS








50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361











50

0

50

LA-KP-FDLA-KP-FD

50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD
















6 DISCUSSION




14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








14



GBT-PV

GBT-MK

ALMA-PV

ALMA-MK

J18

GS06

σmaj

σmin

LA-FD

OV-BR

LA-KP

OV-KP

KP-FD

KP-BR

NL-GB

OV-LA

LA-BR

OV-FD

FD-BR

GB-FD

LA-GB

KP-GB

GB-BR

OV-GB

GB-AA

NL-AA

FD-AA

LA-AA

KP-AA

OV-AA

BR-AA

00 05 10 15 20 25

10-2

10-1

100

Baseline (Gλ)

Co

rre

late

dF

lux

De

nsity(J

y)




























16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361



















16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








16


102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


1

2

3

4

5

6

Intri

nsic

asym

met

ry (

maj

m

in)

This work


1 mm3 mm7 mm

1 mm3 mm7 mm











102

6 times 101

2 times 102

3 times 102

4 times 102

Intri

nsic

maj

or a

xis F

WHM

[as

]

This work


100

125

150

175

200

225

250

275

300

Intri

nsic

asym

met

ry (

maj

m

in)

This work

H-HiR-HiH-LoR-Lo

1 mm3 mm7 mm

1 mm3 mm7 mm
















102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361














102

2 times 102

3 times 102

3 m

m in

trins

ic m

ajor

axi

s [as

]











18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








18

50

0

50

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD

unscattered

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD

ensemble average

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD

50

0

50

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD

J18 scattering

LA-KP-FD


50

0

50

Clo

sure

pha

ses

(deg

rees

)

GB-KP-FD


GB-KP-FD


GB-KP-FD


GB-KP-FD



8 9 10 11 12 13 14 15Time (UT hours)

50

0

50

AA-GB-FD














7 SUMMARY













REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361















REFERENCES


277 L1


prep


2017 AampA Rev 25 4



484 118


Science 304 704




790 1


69


576 A41


MNRAS 462 1382 (B16)

20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








20




ApJ 820 137


L 2018a MNRAS 478 5209


ApJ 857 23


ApJ 829 11




408 841


MNRAS 466 4121


H 2018 AampA 612 A34


177 319


PASP 123 275





AJ 121 2610


2008 Nature 455 78


731




97





ApJL 727 L36


ApJ 820 90







539 L13


689 1044


ApJL 707 L114





S S 2017 ApJ 837 180



2018a AampA 615 L15








Hu M-K 1962 8 179





Science 350 1242


865 104 (J18)


AampA 335 L106


525 A76


MNRAS 418 2260


757 L14


859 60


4307




1519


AampA 593 A61


PASP 130 015002


2017 MNRAS 468 2214




A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361










A13


C F 2014 AampA 570 A7






623


2016 ApJ 824 40 (O16)



AampA Rev 25 2





587 A37


D 18 889




C F 2017 MNRAS 467 3604



1994 ApJL 434 L59





2013 MNRAS 429 3533


MNRAS 466 705


J-H 2005 Nature 438 62









3rd Edition doi101007978-3-319-44431-4








Bower G C 2006 ApJ 650 189


682 361








Documents

arXiv:1901.06226v1 [astro-ph.HE] 18 Jan 20192 1. INTRODUCTION Supermassive black holes (SMBHs) play a crucial role in shaping our Universe: they evolve symbiotically with their host