Observing Black Holes (BHs) The First Discoveries - Discovery (1961-63) Quasi-Stellar Radio Sources as the most energe c and distant members of a class of objects. - Center of a giant Ellip cal Galaxy è Blazar: AGN with Rela vis c jet 3C273 - Cosmological red-shi z = 0.158 cz ≈ dH(t0) from the Hubble-law we get the distance of 2.5 Gyr (750 Mpc)
- Discovery (1972) binary BH system “In the case of Cyg X-1 black hole – is the most conserva ve hypothesis” Edwin Salpeter
Cyg X-1 Orbits, 5.6 days, an unseen op cally (but bright X-ray) object. The companion has a mass of ~ 30 M¤ \]$%.'#$_*8$7$%B'($*75$*B-##*;1%*<=)*>?@*"=*b$D,$%c#*,-Z* V-##*;L(.C1(*;2V3*;1%*"'(-%=*#=#7$B#** 2V]_*>?%-=*.1BD-.7*#7-%R*V.1BD_*!DC.-,*.1BD-('1(*#7-%R*i*W*V.eV]3*
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'*W*HfQJ*k*@QU* BHs as astronomical sources • Primordial BHs They have been formed at the early stages of the universe Not discovered, yet. Only upper limits (mostly from gamma-ray observa ons).
• Stellar mass BHs (mainly this lecture) A typical galaxy like the Milky Way should harbour 107 − 108 stellar black holes There are more than twenty good candidates in close binary systems. Accre on, jets. Observed at all wavelenghts.
Isolated stellar mass BHs are not discovered up to now. But there are interes ng candidates among microlensing events.
• Intermediate mass BHs Their existence is uncertain, but there are good candidates among ULX. Observed in radio, x-rays, and op cs.
• Supermassive BHs (Sgr A* this lecture) There are many good candidates with mass es mates. In the center of our Galaxy with extremely high certainty there is supermassive BH. Accre on, jets, dal discrup ons of normal stars. Observed at all wavelenghts.
• Micro BHs Forms at Planck scales. There are no observa onal evidences. CERN: Micro BH created by HE 14 TeV p-p collisions by the LHC, they would disintegrate rapidly, in around 10-27 7 seconds. Hawking radia on “BHs evaporate by radia ng away their energy” Forma on of Stellar Black Holes
Note: The fact that General Rela vity does predict the existence of BHs and that General Rela vity is a reliable theory of gravita on does not necessarily prove the existence of BHs, because General Rela vity does not describe the astrophysical processes by which a BH may form.
E.g., White Holes, Wormholes, Parallel Universe, Travelling in me exist from GR, but they exist in real ? <1%$?.1,,-D#$*#LD$%(1&-*D%1)$('71%#*
a$Z*B1O$,#*D%$O'.7*75-7*B1#7*1;*#7-%#* w@XV * D%1OL.$* +0#* 2#$$* 75$* %$&'$Z* `*#7-%*BL#7*5-&$*-7*,$-#7*X*CB$#R* ! MB-%x*-%>'&_*@SUfQUGJFS3* "L7*(1*B1%$*75-(*fU*71*SU*CB$#R* 75$* B-##* 1;* 75$* ML(* 2<3* 71* L(O$%)1* <1%$?.1,,-D#$* #LD$%(1&-* $]D,1#'1(Q* r!***0')5*B-##*2;$Z3* r!***n1Z?B-##*2B-P1%'7=3* r!***jn>*A*L,7%-,LB'(1L#*>?%-=*#1L%.$#* •! V1#7*1;*,1Z?B-##*-%$*7%-(#'$(7#Q* •! V'.%1iL-#-%#l*M-B$*B-'(* D%1D$%C$#*,'/$*KL-#-%#*
y$7#* +0*5-&$*a!*0`:N*
yQ*`Q*s5$$,$%* Some records
M33 X-7 15.65+/-1.45 Msolar (Orosz et al. 2007). Paredes arXiv: 0907.3602
BH candidates Among 20 good galac c candidates 17 are X-ray novae. 3 belong to HMXBs (Cyg X-1, LMC X-3, GRS 1915+105).
New candidates s ll appear. For on of the latest see 1008.0597
(J. Orosz, from astro-ph/0606352) Candidates proper es
(astro-ph/0606352) Also there are about 20 “candidates to candidates”. Detector MAXI recently added several new BH candidates BH Spectrum !"#$%&'()$#(*+!"#$%&'()$#(*+
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:);*#&+3/*&23);(73)+&$)&:);*#&+3/*&23);(73)+&$)& $22#*73)&;(+<&2$)&43#/ $22#*73)&;(+<&2$)&43#/ =(+23+(-% =(+23+(-% !!!!!!!!"#$%&!'()**)+,!- !!!!!!!!"#$%&!'()**)+,!-
>1*&!"#$%&,5*2-#?/&(+&=*#%&23/5.*@A& >1*&!"#$%&,5*2-#?/&(+&=*#%&23/5.*@A& • &>1*#/$.&*/(++(3)&4#3/&-1*&$22#*73)&;(+<&B/?.7"'.$2<'3;%C& •• &>1*#/$.&*/(++(3)&4#3/&-1*&$22#*73)&;(+<&B/?.7"'.$2<'3;%C&&D*5#32*++()8&'%&*)*#8*72&*.*2-#3)+&B0$#/&8$+E&F*-+EC& &G?21&/3#*HHH&B*/(++(3)&I&$'+3#573)&4*$-?#*+J&#*K*273)J&*-2HHHC •• &D*5#32*++()8&'%&*)*#8*72&*.*2-#3)+&B0$#/&8$+E&F*-+EC& • &G?21&/3#*HHH&B*/(++(3)&I&$'+3#573)&4*$-?#*+J&#*K*273)J&*-2HHHC X-ray binaries Black Hole X-ray spectra
historically observed/classified in X-rays !"#$%&'()$#(*+ './ !+,-
(%)&%'()*
!"#$%&''
'./ !+,- JETs X-ray binaries
Corona T~107 K M-1/4 – last stable orbit temperature at Eddington luminosity
Op cs/UV – QSO X-ray - μQSO
X-ray Binary Jets exist on all scales
X-ray binaries Low-Luminosity AGN
Mirabel & Rodriguez (1994) VLBI: Falcke, Nagar, Wilson et al. (2000) Jets
O en the radio emission is more symmetric on the large scale and asymmetric on the small scale
The core is defined based on the spectral index: flat (α ~ 0)
[to find which component is the radio core is not always easy: core free-free absorp on can complicate the story!] A prototypical radio galaxy
Lobes
Core Hot-spots Jets
§ Any size: from pc to Mpc § First order similar radio morphology (but differences depending on radio power, op cal luminosity & orienta on) § Typical radio power 1023 to 1028 W/Hz Jet Forma on
• All rela vis c cosmic jet sources may be connected by a common basic mechanism
– A promising model for that is magnetohydrodynamic accelera on by rota ng, twisted magne c fields • “Spin Paradigm” can explain qualita vely a number of sta s cal proper es of AGN – Geometrically thick accre on flows are more efficient at launching jets • In Microquasars this principle may explain the correla on between the produc on of a jet and the presence of a hot, geometrically thick accre on flow • This also may be testable in some Seyfert AGN as well – Slow accelera on and collima on of these jets is probably the norm • There is some evidence for this in AGN jets – Highly rela vis c jet flows may be produced by strong, straight magne c fields
• All galac c cosmic jet sources, including supernovae and gamma-ray bursts, may be connected by a common origin as well: different outcomes of the last stage of evolu on in a massive star Basic Principles of Magnetohydrodynamic Jet Produc on • Basic MHD mechanism: – Blandford (1976); Lovelace (1976) – Accelera on by rota ng black holes (Blandford & Znajek [1977]) – Accelera on by rota ng [thin] accre on disks (Blandford & Payne [1982])
• First numerical simula ons: Uchida & Shibata (1985) • Key ingredients in their “Sweeping Pinch” mechanism – Thick accre on disk or torus – Keplerian differen al rota on (Ω ∝ R-3/2) – Ini al strong ver cal magne c field (strong enough to slow disk rota on) – J × B force splits up into magne c pressure and tension: -∇ (B2 / 8π) + (B • ∇B) / 4π
• Typical results (e.g., Kudoh et al [1998]; Uchida et al. [1999]) – Differen al rota on twists up field into toroidal component, slowing rota on
– Disk accretes inward, further enhancing differen al rota on and Bϕ – Greatest field enhancement is at torus inner edge
2 – Magne c pressure gradient (dBϕ / dZ) accelerates plasma out of system 2 – Magne c tension [hoop stress] (–Bϕ /R) pinches and collimates the ou low into a jet – Ou low jet speed is of order the escape velocity from the inner edge of the torus (Vjet ~ VAlfven ~ Vesc) – Jet direc on is along the rota on axis
Kudoh, Matsumoto, & Shibata (2002) Simulated jet evolution in the ISM !"#$%&'()$#(*+
radio IR opt X-ray
Disc BH hard state Jet
high energy companion tail! star (inner regions) !"#$%&'()$#(*+
radio IR opt X-ray
Disc BH soft state Jet ?
high energy companion tail! star (inner regions) ComplexComplex Physics vs.Physics simple vs. exercises simple exercises a word on radiative efficiency Complex Physics vs. simple exercises
a word on radiative efficiency
0.6 X ! L LR XBs AGN
radiatively inefficient Spin of a Black Hole 45$*;L,,*1"#$%&$O*.1(C(LLB*#D$.7%LB*
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•! +%1-O*2Z'O75*1;*-*;$Z*/$u3* -(O*#1B$CB$#*%$O#5'{$O*6$* b?#5$,,*,'($*D%1|,$#*;%1B*-* &-%'$7=*1;*-..%$C()*.1,,-D#$O* 1"P$.7#Q**
+%1-O$($O*$B'##'1(*:%1(*,'($*OL$*71*[N* 81DD,$%R*,')57*"$(O'()R*-(O*,$(#'()* $Ä$.7#*v* * d%1"'()*#7%1()*)%-&'7-C1(-,*|$,O#** Z'75*>?%-=*6$?,'($#*;%1B*-..%$C1(*O'#/#* Discs around black holes: a look from aside
Disc temperature
Discs observed from infinity. Le : non-rota ng BH, Right: rota ng.
h p://web.pd.astro.it/calvani/ 37 Fe-lines from relativistic accretion disks 6-,-()-*GUUS* 6$?,'($*D%1|,$*;%1B*%$,-C&'#C.*-..%$C1(*O'#/#* Line profile integrated over entire flow encodes:
-!Strong field relativistic effect: Doppler shifts and boosting, gravitational redshift, strong field lensing, black hole spin
-!Observed in both Active Galactic Nuclei and X-ray binaries
V[<*J?FU?@S*******>VV?a$Z71(*O-7-*
\]-BD,$_* 45$*;-.7*75-7*75$*,'($*$]7$(O#*71*75$*%$O*#'O$* "$,1Z*f*/$u*'#**'(7$%D%$7$O*-#*75$*#')(*1;*%-D'O* %17-C1(*275$*O'#.*$]7$(O#*'(#'O$*FN)3R*b$%%*+0Q* \]-BD,$#_* <=)(L#*>?@* a-%%1Z*,'($#_*%$}$.C1(*'(*1L7$%* O'#/* * +%1-O*,'($* <1(#'#7$(7*Z'75* äTfUã*=$%*W*H=3*
>4\*y@JSU?SUU* u$%=*"%1-O*#/$Z$O*,'($*
=$%*W*@QGf*=3* (*W*UQIIX* Measuring spins of stellar-mass BHs
Suzaku spin measurements program
A very complicated model. a > 0.93 (90% confidence)
43 ff* SMBH in our Galaxy
The region around Sgr A*
The result of sumam on of 11 exposi ons by Chandra (590 ksec).
Red 1.5-4.5 keV, Green 4.5-6 keV, Blue 6-8 keV.
The field is 17 to 17 arcminutes (approximatelly 40 to 40 pc).
(Park et al.; Chandra data) astro-ph/0311460 A review: arxiv:1311.1841 Towards the event horizon – the supermassive black hole in the Galac c Center 48
M7$,,-%*O=(-B'.#*-%1L(O*M)%*`p*
45$*.-#$*1;*M)%*`p*'#*L('iL$Q* 45-(/#*71*O'%$.7*B$-#L%$B$(7#*1;* #$&$%-,*#7$,,-%*1%"'7#*'7*'#*D1##'",$* 71*)$7*-*&$%=*D%$.'#$*&-,L$*;1%* 75$*B-##*1;*75$*.$(7%-,*1"P$.7Q* * `,#1R*75$%$*-%$*&$%=*#7%'.7*,'B'7#* 1(*75$*#'^$*1;*75$*.$(7%-,*1"P$.7Q* 45'#*'#*&$%=*'BD1%7-(7*7-/'()*'(71* -..1L(7*-,7$%(-C&$#*71*-*+0Q* * 45$*#7-%*M!?G*5-#*75$*1%"'7-,* D$%'1O*@SQG*=%#*-(O*75$*#$B'B-P1%* -]'#*-"1L7*UQUUS*D.Q* *
`*%$&'$Z_*-%>'&_*@SU@QUG@H@**.2#!=1:1;>;!?#&*#(!-:1;
J \(.,1#$O*V-##*(*f*@U *V!* !* * Lx – LR Correla on including SgrA*
General correla on a er proper object mass scaling
(Gallo et al. 03, Falcke et al. 04) A closer look: X-ray bursts from Sgr A*
Chandra. 2-10 keV
2.4 pc 20 pc
1007.4174 53 !"#$#%&''()*(#+,(-#*./)0(12234(( Bursts can happen about once in a day. The flux is increased by a factor of a few (some mes even stronger).
A bright burst was observed on Oct. 3, 2002 (D. Porquet et al. astro-ph/0307110). Dura on: 2.7 ksec. The fluxed increased by a factor ~160. Luminosity: 3.6 1035 erg/s.
In one of the bursts, on Aug. 31,2004, QPOs have been discovered. The characteris c me: 22.2 minutes (astro-ph/0604337). In the framework of a simple model this means that a=0.22.
55 Disk Rossby wave instability The same equa on as for modeling the Iron line profile (see slide Nr. ), but now the ma er mo on around the disk is me depended with a different underlingDie ARTphysics ist (disk erforderlich, Rossby wave instability um die) im Unendlichen beobachtete Lichtkurve zu beschreiben.
56 (Tagger & Melia 2006)
Modelling the Lightcurve during an ourburst
Neigungswinkel ≈ 77°
(Falanga et al. 2007, 2008, 2012) 58 Observa ons at higher energies, above 20 keV
INTEGRAL observa on At present “our” black hole is not ac ve. However, it was not so in the past.
It is suspected that about 350 years ago Sgr A* was in a “high state”. Now the hard emission generated by Sgr A* at this me reached Sgr B2. Sgr B2 is visible due to fluorescence of iron.
(Revnivtsev et al.) About high energy observa ons of the The galac c center region galac c center see the review astro-ph/0511221 is regularly monitored and . by Integral.
59
BRIEF INTRODUCTION TO RAY TRACING DEF!.DE?BG=!.H?@GB?IJH_*;1,,1Z'()*75$*D5171(*7%-P$.71%=*;%1B*75$*$B'##'1(*D1'(7*71* 75$*1"#$%&$%*,1.-C1(*'(*.L%&$O*)$1B$7%'.-,*"-./)%1L(O*
DEKBE.BLH!.DEGMNHD!OH.@PK_*'7*)'&$#*%'#$*71*.1BD,'.-7$*'(7$)%-,#*71*#1,&$Q*aLB$%'.-,* #'BL,-C1(#*-%$*($.$##-%=*-#*-*&-,'O*#LDD1%7*71*"$(.5B-%/*75$*75$1%$C.-,*%$#L,7#*Z'75* 75$*1"#$%&-C1(-,*O-7-Q* The Geometry: Steady Line profiles in Schwarzschild space- me
• Ma er Orbits in a disk (Keplerian) (Timelike geodesics)
• Light bending (Spacelike geodesics)
• Doppler boos ng: (1 + z)
• Solidangle: dΩ(R,dϕ,i,db) (Gravita onal lensing effect)
• (Travel me delay)
(Schwarzschild-Metrik) • Observed flux at inf.: F = ∫∫∫ IνdνdΩ d5171(*)$1O$#'.#*'(*M.5Z-%^#.5',O*#D-.$CB$* 'BD-.7*D-%-B$7$%*
* * * * * J* J* * FeG* * * * ".%'7WF V * f***! f* * * * * G* G* * * *****9! * U* U* * * ?G* * GV* * FV* ?f* * * ?J* !"#$%&$%*-7*'(|('7=*
?J*************?f**************?G***************U**************G**************f**************J****** *]*2V*W*[Ve.*G*3*L('7#*
GV**51%'^1(*%-O'L#*W*N#* FV**.'%.L,-%*D5171(*)$1O$#'.*%-O'L#* * * d5171(*MD5$%$**
FeG ".%'7WF V* W*SQGH*V*
GV* Q2/*/&!+72#(#!! B81'#!1*!//!/S! RO! Q2/*/&!M72#(#!!! ****%-O'L#*WFFeGV* !"#$%&$%*-7*'(|('7=*
GV* `..%$C1(*8'#/*8'#71%C1(* !"#$%&$%*-7*'(|('7=*
1;;(#>/&!)%+
FV* Flat space me image
Curved space me image at high inclina on
But …. no light from the Photon Sphere
-> Black hole shadow 45$*M5-O1Z*1;*-*+,-./*01,$* M'BL,-C1(#*
GR Model +0.6mm VLBI +1.3mm VLBI a=0.998 I=r-2
a=0 I=const
10 Rg=49-58 !as! (Falcke, Melia, Agol 2000, ApJL) u-%='()*75$*V1O$,#*
Infall: Jet: a=0.998 a=0.998 i=90º i=90º I=r-2 I=hollow
Infall: Jet: a=0 a=0 i=90º i=45º I=r-2 I=hollow
Agol, Falcke, Melia, et al. (2001), conf. proc. How to image a black hole
3/2 2 Photon sphere radius at infinit: 3 GM/c = 8 (M/Mo) km
-10 - Angular size (diameter): 1x10 (M/Mo)(kpc/D) arcsec , with D the distance:
-9 - 10 Mo galac c black hole in HMXB: < 1x10 arcsec 6 -6 - 4x10 Mo black hole (Sgr A*) in the galac c center (D=8 kpc): ~ 50 x 10 arcse 9 -6 - 6x10 Mo black hole in M87 (D=17 Mpc): ~ 40 x 10 arcsec
- Angular resolu on: lambda/L -> radio VLBI interferometry: resolu on ~ (1 cm/104 km) rad ~ 20 x 10-6arcsec The Astrophysical Journal Letters, 875:L1 (17pp), 2019 April 10 The EHT Collaboration et al. The array has a nominal angular resolution of λ/L,whereλ is the observing wavelength and L is the maximum projected baseline length between telescopes in the array (Thompson et al. 2017).In this way, VLBI creates a virtual telescope that spans nearly the full diameter of the Earth. To measure interferometric visibilities, the widely separated telescopes simultaneously sample and coherently record the radiation field from the source. Synchronization using the Event Horizon TelescopeGlobal Positioning System (EHT) typically achieves temporal align- ment of these recordings within tens of nanoseconds. Each station is equipped with a hydrogen maser frequency standard. With the atmospheric conditions during our observations the coherent integration time was typically 10 s (see Figure 2 in Paper II). Use of hydrogen maser frequency standards at all EHT sites ensures coherence across the array over this timescale. After observations, recordings are staged at a central location, aligned in time, and signals from each telescope-pair are cross-correlated. While VLBI is well established at centimeter and millimeter wavelengths (Boccardi et al. 2017; Thompson et al. 2017) and can be used to study the immediate environments of black holes (Krichbaum et al. 1993; Doeleman et al. 2001), the extension of VLBI to a wavelength of 1.3 mm has required long-term technical developments. Challenges at shorter wavelengths Figure 1. Eight stations of the EHT 2017 campaign over six geographic include increased noise in radio receiver electronics, higher locations as viewed from the equatorial plane. Solid baselines represent mutual atmospheric opacity, increased phase fluctuations caused by visibility on M87* (+12° declination). The dashed baselines were used for the atmospheric turbulence, and decreased efficiency and size of calibration source 3C279 (see Papers III and IV). radio telescopes in the millimeter and submillimeter observing bands. Started in 2009 (Doeleman et al. 2009a), the EHT began median zenith atmospheric opacities at 230 GHz ranging from a program to address these challenges by increasing array 0.03 to 0.28 over the different locations. The observations were sensitivity. Development and deployment of broadband VLBI systems (Whitney et al. 2013; Vertatschitsch et al. 2015) led to scheduled as a series of scans of three to seven minutes in duration, with M87* scans interleaved with those on the quasar data recording rates that now exceed those of typical cm-VLBI * arrays by more than an order of magnitude. Parallel efforts to 3C 279. The number of scans obtained on M87 per night support infrastructure upgrades at additional VLBI sites, ranged from 7 (April 10) to 25 (April 6) as a result of different * including the Atacama Large Millimeter/submillimeter Array observing schedules. A description of the M87 observations, (ALMA; Matthews et al. 2018; Goddi et al. 2019) and the their correlation, calibration, and validated final data products is Atacama Pathfinder Experiment telescope (APEX) in Chile presented in Paper III and briefly summarized here. (Wagner et al. 2015), the Large Millimeter Telescope Alfonso At each station, the astronomical signal in both polarizations Serrano (LMT) in Mexico (Ortiz-León et al. 2016), the IRAM and two adjacent 2 GHz wide frequency bands centered at 30 m telescope on Pico Veleta (PV) in Spain (Greve et al. 1995), 227.1 and 229.1 GHz were converted to baseband using the Submillimeter Telescope Observatory in Arizona (SMT; standard heterodyne techniques, then digitized and recorded Baars et al. 1999), the James Clerk Maxwell Telescope (JCMT) at atotal rate of 32 Gbps. Correlation of the data was carried and the Submillimeter Array (SMA) in Hawai’i (Doeleman et al. out using a software correlator (Deller et al. 2007) at the MIT 2008; Primiani et al. 2016; Young et al. 2016), and the South Haystack Observatory and at the Max-Planck-Institut für Pole Telescope (SPT) in Antarctica (Kim et al. 2018a), extended Radioastronomie, each handling one of the two frequency the range of EHT baselines and coverage, and the overall bands. Differences between the two independent correlators collecting area of the array. These developments increased the were shown to be negligible through the exchange of a few sensitivity of the EHT by a factor of ∼30 over early experiments identical scans for cross comparison. At correlation, signals that confirmed horizon-scale structures in M87* and Sgr A* were aligned to a common time reference using an apriori (Doeleman et al. 2008, 2012; Akiyama et al. 2015; Johnson et al. Earth geometry and clock model. 2015; Fish et al. 2016; Lu et al. 2018). Asubsequentfringe-fitting step identified detections in For the observations at a wavelength of 1.3 mm presented correlated signal power while phase calibrating the data for here, the EHT collaboration fielded a global VLBI array of eight stations over six geographical locations. Baseline lengths residual delays and atmosphericeffects.UsingALMAasahighly ranged from 160 m to 10,700 km toward M87*, resulting in an sensitive reference station enabled critical corrections for iono- array with a theoretical diffraction-limit resolution of ∼25 μas spheric and tropospheric distortions at the other sites. Fringe (see Figures 1 and 2, and Paper II). fitting was performed with three independent automated pipelines, each tailored to the specificcharacteristicsoftheEHT observations, such as the wide bandwidth, susceptibility to 4. Observations, Correlation, and Calibration atmospheric turbulence, and array heterogeneity (Blackburn et al. We observed M87* on 2017 April 5, 6, 10, and 11 with the 2019;Janssenetal.2019,PaperIII).Thepipelinesmadeuseof EHT. Weather was uniformly good to excellent with nightly standard software for the processing of radio-interferometric data
3 M87: - massive ellip cal galaxy in Virgo Cluster, D ~ 16.8 Mpc, 9 9 - supermassive black hole M ~ 6.6x10 (3.5 x 10 ) Mo from stellar (gas) dynamics -> expected BH shadow (20-38) x 10-6 arcsec - bright compact radio source in center; 65 kpc long jet, flat 42-45 radio-mm synchrotron spectrum, Lkin~10 erg/s - photosphere of jets smaller and smaller when observed at higher and higher frequency -> jet base expected to be visible at mm wavelengths
- Previous VLBI observa on of M87 at 1.3mm saw variable structure on a scale of 40 x 10-6arcsec
- VLBI improved sensi vity (key role of ALMA): baseline ~104 km, resolu on ~ 25 x10-6 arcsec
- Observa ons from 8 sites ~ 4 days in April 2017: steady crescent seen !
The Astrophysical Journal Letters, 875:L1 (17pp), 2019 April 10 The EHT Collaboration et al. maximum likelihood (RML;e.g.,Narayan&Nityananda1986; Wiaux et al. 2009;Thiébaut2013). RML is a forward-modeling approach that searches for an image that is not only consistent with the observed data but also favors specified image properties (e.g., smoothness or compactness).AswithCLEAN, RML methods typically iterate between imagingandself-calibration,although they can also be used to image directly on robust closure quantities immune to station-based calibration errors. RML methods have been extensively developed for the EHT (e.g., Honma et al. 2014; Bouman et al. 2016;Akiyamaetal.2017;Chaeletal.2018b;see also Paper IV). Every imaging algorithm has a variety of free parameters that can significantly affect the final image. We adopted a two- stage imaging approach to control and evaluate biases in the reconstructions from our choices of these parameters. In the first stage, four teams worked independently to reconstruct the first EHT images of M87* using an early engineering data release. The teams worked without interaction to minimize shared bias, yet each produced an image with a similar prominent feature: a ring of diameter ∼38–44 μas with enhanced brightness to the south (see Figure 4 in Paper IV). In the second imaging stage, we developed three imaging pipelines, each using a different software package and associated methodology. Each pipeline surveyed a range of imaging parameters, producing between ∼103 and 104 images from different parameter combinations. We determined a “Top- Set” of parameter combinations that both produced images of M87* that were consistent with the observed data and that reconstructed accurate images from synthetic data sets corresponding to four known geometric models (ring, crescent, filled disk, and asymmetric double source). For all pipelines, the Top-Set images showed an asymmetric ring with a diameter of ∼40 μas, with differences arising primarily in the effective angular resolutions achieved by different methods. For each pipeline, we determined the single combination of Figure 3. Top: EHT image of M87* from observations on 2017 April 11 as a fiducial imaging parameters out of the Top-Set that performed representative example of the images collected in the 2017 campaign. The best across all the synthetic data sets and for each associated image is the average of three different imaging methods after convolving each imaging methodology (see Figure 11 in Paper IV).Becausethe with a circular Gaussian kernel to give matched resolutions. The largest of the three kernels (20 μas FWHM) is shown in the lower right. The image is shown angular resolutions of the reconstructed images vary among the 2 in units of brightness temperature, TSb 2 kB , where S is the flux density, pipelines, we blurred each image with a circular Gaussian to a λ is the observing wavelength, kB is the Boltzmann constant, and Ω is the solid common, conservative angular resolution of 20 μas. The top part angle of the resolution element. Bottom: similar images taken over different of Figure 3 shows an image of M87* on April11 obtained by days showing the stability of the basic image structure and the equivalence averaging the three pipelines’ blurred fiducial images. The image among different days. North is up and east is to the left. is dominated by a ring with an asymmetric azimuthal profile that is oriented at a position angle ∼170° east of north. Although the with the innermost stable circular orbit, or ISCO, and is instead measured position angle increases by ∼20° between the first two related to the lensed photon ring. To explore this scenario in great days and the last two days, the image features are broadly detail, we have built a library of synthetic images (Image Library) consistent across the differentimagingmethodsandacrossall describing magnetized accretion flows onto black holes in GR145 four observing days. This is shown in the bottom part of Figure 3, (Paper V). The images themselves are produced from a library which reports the images on different days (see also Figure 15 in of simulations (Simulation Library) collecting the results of Paper IV).Theseresultsarealsoconsistent with those obtained four codes solving the equations of GRMHD (Gammie et al. from visibility-domain fitting of geometric and general-relativistic 2003; Sadowski̧ et al. 2014; Porth et al. 2017; Liska et al. magnetohydrodynamics (GRMHD) models (Paper VI). 2018). The elements of the Simulation Library have been coupled to three different general-relativistic ray-tracing and radiative-transfer codes (GRRT, Bronzwaer et al. 2018; 6. Theoretical Modeling Mościbrodzka & Gammie 2018; Z. Younsi et al. 2019, in The appearance of M87* has been modeled successfully using preparation). We limit ourselves to providing here a brief GRMHD simulations, which describe a turbulent, hot, magnetized description of the initial setups and the physical scenarios disk orbiting a Kerr black hole. Theynaturallyproduceapowerful explored in the simulations; see Paper V for details on both the jet and can explain the broadband spectral energy distribution GRMHD and GRRT codes, which have been cross-validated observed in LLAGNs. At a wavelength of 1.3 mm, and as observed here, the simulations also predict a shadow and an 145 More exotic spacetimes, such as dilaton black holes, boson stars, and asymmetric emission ring. The latter does not necessarily coincide gravastars, have also been considered (Paper V).
5 BH shadow
The Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10 The EHT Collaboration et al.
The Astrophysical Journal Letters, 875:L1 (17pp), 2019 April 10 https://doi.org/10.3847/2041-8213/ab0ec7 © 2019. The American Astronomical Society.
First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
The Event Horizon Telescope Collaboration (See the end matter for the full list of authors.) Received 2019 March 1; revised 2019 March 12; accepted 2019 March 12; published 2019 April 10
Abstract Figure 1. Left panel:When an surrounded EHT2017 image by ofa M87transparent from Paper emissionIV of this region, series ( blacksee their holes Figure are 15) expected. Middle panel: to reveal a simulated a dark image shadow based causedon a GRMHD by model. Right panel: the model image convolved with a 20as FWHM Gaussian beam. Although the most evident features of the model and data are similar, fine features in the model are not resolvedgravitational by EHT. light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission In Section 6 we combine EHT data with other constraints on the (e.g., Johannsen & Psaltis 2010). For an a fl 0 black hole firing with a diameter of 42±3 μas, which is circular and encompasses a central depression in brightness with a* ux radiative ef ciency,ratio 10:1. X-ray The luminosity, emission ring and is jet recovered power and using show different calibrationof mass M andand imaging distance schemes,D, the with photon its diameter ring angular and radius on that the latter constraint eliminates all a 0 models. In the sky is width remaining stable over four different* observationsfl carried out in different days. Overall, the observed image is Section 7 weconsistent discuss limitations with expectations of ourfor models the shadow and also of a brie Kerry black hole as predicted by general relativity. The asymmetry in discuss alternatives to Kerr black hole models. In Section 8 we 27 GM brightness in the ring can be explained in terms of relativistic beaming p of the emission from a plasma rotating close to summarize ourthe results speedand of light discuss around how a black further hole. analysis We compare of existing our images to an extensivecD library2 of ray-traced general-relativistic EHT data, future EHT data, and multiwavelength companion 9 1 magnetohydrodynamic simulations of black holes and derive a central mass of M⎛=(6.5M±0.7)×⎞10⎛ MeD.Ourradio-⎞ observations will sharpen constraints on the models. 18.8 as, 1 wave observations thus provide powerful evidence for the presence of supermassive⎜ black holes9 in⎟⎜ centers of galaxies⎟ () and as the central engines of active galactic nuclei. They also present a new tool to⎝ 6.2 explore 10 gravityM ⎠ in⎝ 16.9 its most Mpc extreme⎠ limit and on a mass scale that was so far not accessible. 2. Review and Estimates where we have scaled to the most likely mass from Gebhardt et al. Key words: accretion, accretion disks – black hole physics (–2011galaxies:) and active a distance– galaxies: of 16.9 individual Mpc (see(M87 also) EHT– Collaboration galaxies: jets – gravitation In EHT Collaboration et al. (2019d; hereafter Paper IV) we et al. 2019e, (hereafter Paper VI;Blakesleeetal.2009;Birdetal. present images generated from EHT2017 data (for details on 2010;Cantielloetal.2018).Thephotonringangularradiusfor the array, 2017 observing campaign, correlation, and calibra- tion, see Paper II and Paper1. IntroductionIII). A representative image is opticallyother inclinations thick accretion and values disk (Shakura of a* differs & Sunyaev by at1973 most; Sun 13% & from Malkan 1989). In contrast, most AGNs in the local universe, reproducedBlack in holes the left are apanel fundamental of Figure prediction1. of the theory of Equation (1),andmostofthisvariationoccursat11 ∣∣a including the Galactic center and M87, are associated with* general relativity (GR; Einstein 1915). A defining feature of (e.g., Takahashi 2004;Younsietal.2016).Evidentlytheangular Four features of the image in the left panel of Figure 1 play supermassive black holes fed by hot, tenuous accretion flows black holes is their event horizon, a one-way causal boundary in radius of the observed photon ring is approximately 20 as an important role in our analysis: (1) the ring-like geometry, (2) with much lower accretion rates (Ichimaru 1977; Narayan & Yi spacetime from which not even light can escapefl (Schwarzschild the peak brightness temperature, (3) the total ux density, and 1995(Figure; Blandford1 and Paper & BegelmanIV),whichisclosetothepredictionofthe1999; Yuan & Narayan 2014). 1916). The production of black holes is generic in GR (Penrose (4) the asymmetry of the ring. We now consider each in turn. blackIn many hole AGNs, model givencollimated in Equation relativistic(1). plasma jets (Bridle & 1965), and more than a century after Schwarzschild, they remain (1) The compact source shows a bright ring with a central Perley(2) The1984; observed Zensus 1997 peak) launched brightness by temperature the central black of the hole ring in at the heart of fundamental questions in unifying GR with 9 dark area without significant extended components. This bears contributeFigure 1 is T tob, pk the 6 observed 10 K emission.,whichisconsistentwithpastEHT These jets may be quantum physics (Hawking 1976; Giddings 2017). a remarkable similarity to the long-predicted structure for poweredmm-VLBI either measurements by magnetic atfields 230 threading GHz (Doeleman the event horizon,et al. 2012; Black holes are common in astrophysics and are found over optically thin emission from a hot plasma surrounding a black extractingAkiyama et the al. rotational2015),andGMVA3 energy from the mm-VLBImeasurementsof black hole (Blandford a wide range of masses. Evidence for stellar-mass black holes hole (Falcke et al. 2000). The central hole surrounded by a &the Znajek core region1977)(,Kim or fromet al. 2018 the accretion).Expressedinelectronrest-massflow (Blandford & comes from X-ray (Webster & Murdin 1972; Remillard & bright ring arises because of strong gravitational lensing (e.g., Payne(m ) units,1982 ). The near-horizonkT mc emission2 1,where from low-luminosityk is Boltzmann’s McClintock 2006) and gravitational-wave measurements e b,B, pk b pk() e B active galactic nuclei (LLAGNs; Ho 1999) is produced by Hilbert(Abbott1917 et; von al. 2016 Laue).1921 Supermassive; Bardeen black1973 holes,; Luminet with masses1979). constant. The true peak brightness temperature of the source is synchrotron radiation that peaks from the radio through the far- Thefrom so-called millions“photon to tens ring of billions” corresponds of solar masses,to lines are of thoughtsight that to higher if the ring is unresolved by EHT, as is the case for the infrared. This emission may be produced either in the accretion passexist close in to the(unstable centers of) photon nearly all orbits galaxies(see( TeoLynden-Bell2003), linger1969; model image in the center panel of Figure 1. flow (Narayan et al. 1995), the jet (Falcke et al. 1993), or both nearKormendy the photon & orbit,Richstone and1995 therefore; Miyoshi have et a al. long1995 path), including length The 1.3 mm emission from M87 shown in Figure 1 is (Yuan et al. 2002). throughin the the Galactic emitting center plasma.(Eckart These & Genzel lines1997 of sight; Ghez will et al. appear1998; expected to be generated by the synchrotron process (see Yuan When viewed from infinity, a nonrotating Schwarzschild comparativelyGravity Collaboration bright if the et al. emitting2018a) plasmaand in the is optically nucleus of thin. the & Narayan 2014, and references therein) and thus depends on The central flux depression is the so-called black hole (the1916 electron) black distribution hole has a photon function capture(eDF) radius. If theR emittingcg 27 plasmar , nearby elliptical galaxy M87 (Gebhardt et al. 2011; Walsh et al. 2 “shadow2013”). (Falcke et al. 2000), and corresponds to lines of wherehas arg thermal GM eDF,c is the then characteristic it is characterized lengthscale by of an a black electron hole. The photon capture radius is larger than the Schwarzschild2 sight thatActive terminate galactic on nuclei the event(AGNs horizon.) are central The bright shadow regions could that be temperature TTeb , or eee kTB () mc 1, because radius RS that marks the event horizon of a nonrotating black seencan in outshine contrast the to entiresurrounding stellar population emission fromof their the host accretion galaxy. e b, pk if the ring is unresolved or optically thin. flowSome or lensed of these counter-jet objects, quasars,in M87 are(Broderick the most & luminous Loeb 2009 steady). hole,Is theRS ≡ observed2 rg. Photons brightness approaching temperature the black consistent hole with with an what impact parameter b R are captured and plunge into the black Thesources photon in the ring universe is nearly(Schmidt circular1963 for; all Sanders black ethole al. spins1989) andand one would expect< fromc phenomenological models of the hole (Hilbert 1917); photons with b>R escape to infinity; all inclinationsare thought of to the be black powered hole by spin supermassive axis to the line black of sightholes source? Radiatively inefficient accretionc flow models of M87 accreting matter at very high rates through a geometrically thin, photons with b=Rc are captured on an unstable circular orbit and produce what is commonly referred to as the lensed “photon 2 ring.” In the Kerr (1963) metric, which describes black holes Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further with spin angular momentum, Rc changes with the ray’s distribution of this work must maintain attribution to the author(s) and the title orientation relative to the angular-momentum vector, and of the work, journal citation and DOI. the black hole’s cross section is not necessarily circular
1 The Astrophysical Journal Letters, 875:L1 (17pp), 2019 April 10 The EHT Collaboration et al.
Figure 4. Top: three example models of some of the best-fitting snapshots from the image library of GRMHD simulations for April 11 corresponding to different spin parameters and accretion flows. Bottom: the same theoretical models, processed through a VLBI simulation pipeline with the same schedule, telescope characteristics, and weather parameters as in the April 11 run and imaged in the same way as Figure 3. Note that although the fit to the observations is equally good in the three cases, they refer to radically different physical scenarios; this highlights that a single good fit does not imply that a model is preferred over others (see Paper V).
The Astrophysical Journal Letters, 875:L1 (17pp), 2019 April 10 The EHT Collaboration et al. spin energy through mechanisms akin to the Blandford–Znajek The diameters of the geometric crescent models measure the Table 1 our measurement of the black hole mass in M87* is not process. characteristic sizes of the emitting regions that surround the Parameters of M87* inconsistent with all of the prior mass measurements, this allows Modelshadows and not and the sizes derived of the shadows themselvesparameters(see, e.g., Parameter Estimate us to conclude that the null hypothesis of the Kerr metric a (Psaltis et al. 2015; Johannsen et al. 2016), namely, the Ring diameter d 42±3 μas assumption that the black hole is described by the Kerr metric, Psaltis et al. 2015; Johannsen et al. 2016; Kuramochi et al. Ring width a 20 as 7. Model Comparison and Parameter Estimation has not been violated. Fourth, the observed emission ring 2018, for potential biases). Crescent contrast b >10:1 a reconstructed in our images is close to circular with an axial fi Axial ratio <4:3 In Paper VI, the black hole mass is derived from tting to the We model the crescent angular diameter d in terms of the Orientation PA 150°–200° east of north ratio 4:3; similarly, the time average images from our 2 2 c GRMHD simulations also show a circular shape. After visibility data of geometric and GRMHD models, as well as gravitational radius and distance, g GM c D,asd=αθg, g GM Dc 3.8±0.4 μas d 0.5 associating to the shape of the shadow a deviation from the from measurements of the ring diameter in the image domain. – d g 11 0.3 where α is a function of spin, inclination, and Rhigh (α;9.6 10.4 c 9 circularity—measured in terms of root-mean-square distance M (6.5±0.7)×10 Me Our measurements remain consistent across methodologies, corresponds to emission from the lensed photon ring only).We from an average radius in the image—that is 10%, we can set Parameter Prior Estimate algorithms, data representations, and observed data sets. calibrate α by fitting the geometric crescent models to a large an initial limit of order four on relative deviations of the D e (16.8±0.8) Mpc quadrupole moment from the Kerr value (Johannsen & Psaltis Motivated by the asymmetric emission ring structures seen in e 1.1 9 number of visibility data generatedfromtheImageLibrary.We M(stars) 6.2 0.6 10 Me 2010). Stated differently, if Q is the quadrupole moment of a the reconstructed images (Section 5) and the similar emission e 0.9 9 can also fitthemodelvisibilitiesgenerated from the Image Library M(gas) 3.5 0.3 10 Me Kerr black hole and ΔQ the deviation as deduced from * circularity, our measurement—and the fact that the inclination structures seen in the images from GRMHD simulations toThe the Astrophysical M87 Journaldata, Letters, which875:L5 (31pp allows), 2019 April us 10 to measure θ directly. The EHT Collaboration et al. g Notes. angle is assumed to be small—implies that ΔQ/Q4 (Section 6),wedevelopedafamilyofgeometriccrescent a However, such a procedure is complicated by the stochastic nature Derived from the image domain. (ΔQ/Q=ε in Johannsen & Psaltis 2010). models(see, e.g., Kamruddin & Dexter 2013) to compare directly b Derived from crescent model fitting. Finally, when comparing the visibility amplitudes of M87* of the emission in the accretion flow(see, e.g., Kim et al. 2016). c to the visibility data. We used two distinct Bayesian-inference The mass and systematic errors are averages of the three methods (geometric with 2009 and 2012 data(Doeleman et al. 2012; Akiyama et al. To account for this turbulent structure, we developed a formalism models, GRMHD models, and image domain ring extraction). d fl 2015), the overall radio core size at a wavelength of 1.3 mm algorithms and demonstrate that such crescent models are The exact value depends on the method used to extract d, which is re ected has not changed appreciably, despite variability in total flux and multiple algorithms that estimate the statistics of the stochastic in the range given. statistically preferred over other comparably complex geometric e Rederived from likelihood distributions (Paper VI). density. This stability is consistent with the expectation that the models that we have explored. We find that the crescent models components using ensembles of images from individual GRMHD size of the shadow is a feature tied to the mass of the black hole fi simulations. We find that the visibility data are not inconsistent and not to properties of a variable plasma flow. provide ts to the data that are statistically comparable to those of It is also straightforward to reject some alternative astrophysical the reconstructed images presented in Section 5,allowingusto with being a realization of many of the GRMHD simulations. We procedure, we infer values of θg and α for regularized interpretations. For instance, the image is unlikely to be produced fi conclude that the recovered model parameters are consistent maximum likelihood and CLEAN reconstructed images. by a jet-feature as multi-epoch VLBI observations of the plasma determine the basic parameters of the crescents. The best- t Combining results from all methods, we measure emission jet in M87 (Walker et al. 2018) on scales outside the horizon do across algorithms. region diameters of 42 3 μas, angular sizes of the gravita- models for the asymmetric emission ring have diameters of ± not show circular rings. The same is typically true for AGN jets in tional radius θ =3.8±0.4 μas, and scaling factors in the 43±0.9 μas and fractional widths relative to the diameter of Finally, we extract ring diameter, width, and shape directly g large VLBI surveys (Lister et al. 2018).Similarly,werethe range α=10.7–11.5, with associated errors of ∼10%. For the from reconstructed images (see Section 5). The results are apparent ring a random alignment of emission blobs, they should <0.5. The emission drops sharply interior to the asymmetric distance of 16.8±0.8 Mpc adopted here, the black hole mass −1 9 also have moved away at relativistic speeds, i.e., at ∼5 μas day emission ring with the central depression having a brightness consistent with the parameter estimates from geometric is M=(6.5±0.7)×10 Me; the systematic error refers to the 68% confidence level and is much larger than the statistical (Kim et al. 2018b),leadingtomeasurablestructuralchangesand <10% of the average brightness in the ring. crescent models. Following the same GRMHD calibration 9 sizes. GRMHD models of hollow jet cones could show under error of 0.2×10 Me. Moreover, by tracing the peak of the emission in the ring we can determine the shape of the image extreme conditions stable ring features (Pu et al. 2017),butthis and obtain a ratio between major and minor axis of the ring that effect is included to a certain extent in our Simulation Library for 7 Figure 5. Illustration of the effect of black hole and disk angular momentum on ring asymmetry. The asymmetry is produced primarily by Doppler beaming: the bright models with R >10. Finally, an Einstein ring formed by region corresponds to the approaching side. In GRMHD models that fit the data comparatively well, the asymmetry arises in emission generatedis in4:3; the funnel thiscorresponds wall. to a 10% deviation from circularity high The sense of rotation of both the jet and funnel wall are controlled by the black hole spin. If the black hole spin axis is aligned with the large-scalein terms jet, which of points root-mean-square to distance from an average radius. gravitational lensing of a bright region in the counter-jet would the right, then the asymmetry implies that the black hole spin is pointing away from Earth (rotation of the black hole is clockwise as viewed from Earth). The blue require a fine-tuned alignment and a size larger than that measured ribbon arrow shows the sense of disk rotation, and the black ribbon arrow shows black hole spin. Inclination i is defined as the angle betweenTable the disk1 summarizes angular the measured parameters of the image momentum vector and the line of sight. features and the inferred black hole properties based on data in 2012 and 2009. fi from all bands and all days combined. The inferred black hole At the same time, it is more dif cult to rule out alternatives give each image every opportunity to fit the data. The best-fit particular, we can assign a probability p thatmass the data strongly is drawn favors the measurement based on stellar to black holes in GR, because a shadow can be produced by fi any compact object with a spacetime characterized by unstable parameters (MDF,,PA ) for each snapshot are found by two from a speci cmodel’sdistribution. dynamics(Gebhardt et al. 2011). The size, asymmetry, bright- pipelines independently: the THEMISpipeline using a Markov In this Letter we focus on comparisons withness a single contrast, data set, and circularity of the reconstructed images and circular photon orbits(Mizuno et al. 2018). Indeed, while the chain Monte Carlo method (A. E. Broderick et al. 2019a, in the 2017 April 6 high-band data (PapergeometricIII). The models, eight as well as the success of the GRMHD Kerr metric remains a solution in some alternative theories of preparation), and the GENA pipeline using an evolutionary EHT2017 data sets, spanning four days with two bands on gravity (Barausse & Sotiriou 2008; Psaltis et al. 2008), non- each day, are highly correlated. Assessingsimulations what correlation in isdescribing the interferometric data, are consis- algorithm for multidimensional minimization (Fromm et al. * fi expected in the models is a complicated tasktent that with we defer the to EHT images of M87 being associated with Kerr black hole solutions do exist in a variety of such modi ed 2019a; C. Fromm et al. 2019b, in preparation; see also theories (Berti et al. 2015). Furthermore, exotic alternatives to Section 4 of Paper VI for details). The best-fit parameters later publications. The 2017 April 6 datastrongly set has the lensed largest emission from the vicinity of a Kerr black hole. contain information about the source and we use the number of scans, 284 detections in 25 scans (see Paper III) and black holes, such as naked singularities(Shaikh et al. 2019), is therefore expected to be the most constraining.116 distribution of best-fit parameters to test the model by asking boson stars (Kaup 1968; Liebling & Palenzuela 2012), and whether or not they are consistent with existing measurements 8. Discussion gravastars (Mazur & Mottola 2004; Chirenti & Rezzolla 2007), of M/D and estimates of the jet PA on larger scales. 5. Model Constraints: EHT2017 AloneA number of elements reinforce the robustness of our image are admissible solutions within GR and provide concrete, albeit The 2 comparison alone does not provide a sharp test of the The resolved ring-like structure obtainedand from the the EHT2017conclusion that it is consistent with the shadow of a contrived, models. Some of such exotic compact objects can models. Fluctuations in the underlying GRMHD model, com- data provides an estimate of M/D (discussed inblack detail hole in Paper asVI predicted) by GR. First, our analysis has used already be shown to be incompatible with our observations bined with the high signal-to-noise ratio for EHT2017 data, imply and the jet PA from the immediate environmentmultiple of the independent central calibration and imaging techniques, as given our maximum mass prior. For example, the shadows of that individual snapshots are highly unlikely to provide a formally black hole. As a first test of the models we can ask whether or not fi 2 well as four independent data sets taken on four different days naked singularities associated with Kerr spacetimes with acceptable twith 1.Thisisborneoutinpracticewiththe these are consistent with what is known from other mass 2 in two separate frequency bands. Second, the image structure ∣a ∣ 1 are substantially smaller and very asymmetric minimum 1.79 over the entire set of the more than 60,000 measurements and from the orientation of the large-scale jet. * individual images in the Image Library. Nevertheless, it is Figure 7 shows the distributions of best-fimatchest values of M previous/D for predictions well (Dexter et al. 2012; compared to those of Kerr black holes(Bambi & Freese 2009). 2 fi a subset of the models for which spectra and jet power possible to test if the from the ttothedataisconsistentwith Mościbrodzka et al. 2016) and is well reproduced by our Also, some commonly used types of wormholes (Bambi 2013) the underlying model, using “Average Image Scoring” with estimates are available (see below). The threeextensive lines show modeling the effort presented in Section 6. Third, because predict much smaller shadows than we have measured. fi THEMIS(THEMIS-AIS),asdescribedindetailinAppendixFof M/D distribution for all snapshots (dotted lines), the best- t fi THEMIS 2 10% of snapshots (dashed lines), and the best- t 1% of Paper VI). -AIS measures a distance (on the space of 8 visibility amplitudes and closure phases) between a trial image snapshots (solid lines) within each model. Evidently, as better fits are required, the distribution narrows and peaks close to and the data. In practice we use the average of the images from a MD 3.6 as with a width of about 0.5 as. given model as the trial image (hence THEMIS-AIS),butother The distribution of M/D for the best-fit 10% of snapshots 2 choices are possible. We compute the distance between the is qualitatively similar if we include only MAD or SANE trial image and synthetic data produced from each snapshot. The 2 models, only models produced by individual codes (BHAC, model can then be tested by asking whether the data’s is likely 2 116 to have been drawn from the model’sdistributionof .In Paper I and Paper IV focus instead on the April 11 data set. 8 I have a dream!
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+0* GRAVITY FROM EXPERIMENTS
Strong fields •Mergers, GRBs •Accreting binaries BH formation Psaltis •(2008) potential •New missions ahead •LIGO/Virgo curvature Extremely weak fields*6$$O'()*+,-./*01,$#* •LaboratoryMessy environment •Cosmology: ! STRONG CURVATURES WEAK CURVATURES Weak fields •NGO/LISA
WEAK FIELD •Galactic center, M87 •SKA ms radio pulsar •Solar system STRONG FIELD Event horizon telescope
• DYNAMIC SPACE TIME •Binary ms pulsars @ Sgr A* STATIONARY SPACE TIME