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2019/7/30-8/2Outline1.
2.

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•  BH,
• MHD%3. Event Horizon Telescope (EHT)
4. EHT'+
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5. -# 

*($"&!&#( (BH jets)

BQ:P Cyg A

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• S

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• 9/E• D.1+<0R-4JWN

JWN"&$C7 2;?
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• OT>LX horizontal line represents the asymptotic line of the solid curve, which is locatedat 41 mas eastwards from the 43.2-GHz core in RA. At the distance of M87 of
16.7 Mpc and the mass of the black hole of 6.0 3 109 solar masses, 1 mascorresponds to a length of 0.08 pc or 140Rs projected on the plane of the sky.

RA

20
0

 
-0.2

0

20

40

60

80

0



 (AGN jets)

In Fig. 3 the upstream end of the jet corresponding to the dashed line
in Fig. 2 is overlaid on the 43-GHz intensity image as the shaded area. By
specifying the position angle of the M87 jet, we can also evaluate theJetofefficiency
for powerful radio sources
amount of the core shift in declination. On the basis
the 43-GHz imageof M87 in previous work that discusses the large direction uncertainty of
the inner jet region3, we set the allowed range of the jet position angle
47100

Frequency (GHz)

10

a

3.0
1 kpc

Declination offset from 43-GHz core (mas)

2.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0
1

0

b

erg/s

Figure 3 | VLBA image of M87 at 43 GHz
superimposed on the measured core-shift
positions. a, Global view of the radio jet on a
subparsec scale. b, Close-up view of the region
enclosed by the rectangle in a. The synthesized beamof the VLBA is 0.22 mas 3 0.46 mas at 25u (bottom
right in the upper image). The peak brightness and1s noise level are 724 mJy and 1.1 mJy per beam,
respectively. Contours are (21, 1, 2, 2.8 and4) 3 3.3 mJy per beam and thereafter increase byfactors of 21/2. Two broken red lines represent the
maximum possible range of the inner jet direction
centred on the 43.2-GHz core. A solid red arrow
represents the larger-scale jet direction. Red circles
indicate the core positions at 2.3, 5.0, 8.4, 15.2, 23.8
and 43.2 GHz relative to the 43.2-GHz core (thehigher the frequency of the core, the closer it
approaches the central engine). Core positions at
100Rs (0.06 pc)
each frequency are averaged over two epochs. We
assume that the core shift occurs along the largerscale jet direction. The positional uncertainties in
–2
–3
–4
–5
declination are due to uncertainties in the directionof the inner jet, which are shown by the verticalbroken arrows threading each core position. The
shaded area at the east of the 43.2-GHz core
represents the upstream end of the jet derived fromthe core-shift measurements. This area is enclosedby the 1s error in the core-shift value in RA, and the
direction of the inner jet defines uncertainties indeclination. A black circle (top left in b) shows thediameter 6Rs of the innermost stable orbit around a
non-rotating black hole. Inset in a, a 15-GHz VeryLarge-Array image showing kiloparsec-scale
Figure 4. Left-hand side panel: mid-IR (12 µm) rest-frame luminosity,
νLν12 µm , Nationalversus low-frequency
radio luminosity, Lν151 MHz . Symbols are as in Fig. 1.
structure. (CopyrightRadio Astronomy
The solid black line is the best-fitting line given by log10 (νLν12
log10 (Lν151Inc./National
Observatory/Associatedµm ) = (0.47 ± 0.13)Universities,
MHz ) + 25.0 ± 3.6. The Spearman correlation coefficient is
Scienceρ = 0.48 with a Spearman rank correlation probability of 98.8 percent.Foundation).
Righthand side panel: same plots as on the left-hand side panel overlaid with a sample ofbright optically selected quasars (OSQs) with 0.9 < z < 1.1 (blue cicles) from Falder et al. (2010). The top x-axes show the corresponding jet power, estimatedusing Qjet ≃ 3×1038 f 3/2 (Lν151 MHz /1028 )6/7 W (Willott et al. 1999), the left-hand y-axis shows bolometric luminosity, estimated using Lbol ≃ 8.5×νLν12 µm(Richards et al. 2006). The fact that these objects all lie above log10 (νLν12 µm ) ∼ 37.5 is due to the minimum IR luminosity corresponding to the opticalsensitivity limit of the Sloan Digital Sky Survey (SDSS). The vertical dot–dashed line shows the radio luminosity emitted by a starburst-forming massive stars(M ≥ 5 M⊙ ) at a rate of 1000 M⊙ yr1 (Condon 1992), equivalent to a total star formation rate of ∼4000 M⊙ yr−1 assuming a Salpeter initial mass function.
The vertical dotted line shows the radio luminosity emitted by a starburst-forming massive stars at a rate of 250 M⊙ yr−1 , equivalent to a total star formation
rate of ∼1000 M⊙ yr−1 assuming a Salpeter initial mass function. All quasars with flux < 2σ are represented as limits. The blue filled star represents theaverage of the stack of all the OSQs with limits. The red dashed line represents the maximum jet efficiency found for η ∼ 2.5.

Hada+2011

Lbol
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0.8

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–1

0.6

6Rs
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0.4

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Short GRBs Long GRBs

The peak luminosity–peak energy correlation?

Ghirlanda+2005

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(erg/s)L47• g > 100")

 

Lj = Ṁj c2 + Lth + LEM ⇠ const.
BH+

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or Lth<latexit sha1_base64="k6tO7GubqfxMf4rqb5RJHhg6tl4=">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</latexit>Ṁj c2   

LEM ! Ṁj c2
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 

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LEM ! LthṀj c2 ! Lth

 
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  B%2+K5$(GRMHD)
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e.g. Koide et al. 2000; Komissarov 2001;
McKinney & Gammie 2004;
Barkov & Komissarov 2008; Tchekhovskoy
et al. 2011; Ruiz et al. 2012; Contopoulos
et al. 2013
Initial (left) and final (right) distribution of A . Level surfaces coincide with magnetic field lines, and field line density corresponds to poloidal field!

the initial state field lines follow density contours if "0 > 0 :2 "0 ; max .




B




E=
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r·S=

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V

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J p ⇥ B'

1
E+ V⇥B=0c LEM ! Ṁj c2

r · Sp ==E · Jp✓1
J p ⇥ B'
c

B'
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Bp
Black Hole

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#

Z

J p ⇥ B'!

Jp · dS = r|B' |
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BpBp r2  
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(e.g. Begelman & Li 94; Takahashi & Shibata 98;
Fendt & Ouyed 04; KT & Takahara 13)

z
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3.1 The 3+1 decomposition of space–timeKerr
The space–time metric can be generally written as
ds 2 = gµν dx µ dx ν = −α 2 dt 2 + γij (β i dt + dx i )(β j dt + dx j ),Boyer-Lindquist a = J/(M rg )(12)p
a = 0.9
vector''and γ ij thewhere α is called the lapse function, β i the⌦shift↵/three-dimensional metric⌘ tensor⌦ of the space-like hypersurfaces.
The hypersurfaces are regarded as the absolute space at different instants of time t (cf. Thorne et al. 1986). For Kerr space–time, ∂t gµν = ∂ϕ gµν = 0. These correspond to the existences of

Event
(t,
ϕ, r, θ),the Killing vector fields ξ µ and χ µ . In the coordinateshorizonξ µ = (1, 0, 0, 0) and χ µ = (0, 1, 0, 0).
The local fiducial observer (FIDO; Bardeen et al. 1972; Thorneal.:1986),
whose
r !et1
a ! 1,⌦ !world
0 line is perpendicular to the absolute space,is described by the coordinate four-velocitygtt = ↵2 + '' ⌦2 > 0
r ! rH : !a ! 0( "! 0)
i
1
−β
2014
(13)
, 
, n = g nν = (−α, 0, 0, 0). Cf. KT & Takaharanµ =<latexit sha1_base64="lijY5VqTPW0GFW4lcIIWKBjbarE=">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</latexit>3.1 The 3+1 decomposition of space–timePenroseprocess
The space–time metric can be generally written as
ds 2 = gµν dx µ dx ν = −α 2 dt 2 + γij (β i dt + dx i )(β j dt + dx j ),Boyer-Lindquist a = J/(M rg )(12)<latexit sha1_base64="lijY5VqTPW0GFW4lcIIWKBjbarE=">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</latexit>

where α is called the lapse function, β i the shift vector and γ ij thee2 > e1three-dimensional metric⌘ tensor⌦ of the space-like hypersurfaces.
The hypersurfaces are regarded as the absolute space at different instants of time t (cf. Thorne et al. 1986). For Kerr space–time, ∂t gµν = ∂ϕ gµν = 0. These correspond to the existences of
the Killing vector fields ξ µ and χ µ . In the coordinates (t, ϕ, er,1 θ),• +*.!BH
$
µ
µ
e<0
ξ = (1,"' 0, 0, 0) and χ = (0, 1, 0, 0).
The local .!)
fiducial observer (FIDO; Bardeen et al. 1972; Thorne• "'txt) %whoseworld line is perpendicular to the absolute space,(e =et-al.
gttu1986),

is described by
the coordinate four-velocitygtt = ↵2 + '' ⌦2 > 0•
(#BH-"'&,

!
"
i
1 −β
µ
(13)
,
, n = g nν = (−α, 0, 0, 0).
n =Blandford-Znajek process• Slowly rotating Kerr BH• Steady, axisymmetric• Split-monopole B fieldFlat-space solution

H' =

Jp
E

• Force-free
approximation(Electromagneticallydominated)r · Sp = 0




2⇡⌦F B r

H' = 2⇡(⌦F     ⌦H )B r

p

p

sin ✓

E ⇥ H'Sp =4⇡sin ✓ Regularity at horizon
Blandford & Znajek 1977

BZ process,3B



BH'8D&15%

• Membrane!
&152: H. 
K. Thorne et al. 1986; see also Okamoto 2006

• ;2I"9*

EB' c/4⇡ 6= "v

KT & Takahara 2016

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M87• LLAGN with
Lg ~ 1042 erg/s ~ 10-6 LEdd(for MBH ~ 6 x 109 Msun)• FR-I type, but Lj ~ Mdot c2?
• Mechanism of a BH jet /accretion disk
• Imaging of a black holeshadow• Test of GR• BH as a central engine of AGN

Hada+2016

86 GHz (3.5mm); VLBA+GBT

The Astrophysical Journal, 817:131 (17pp), 2016 February 1

Hada et al.

(mas)

ct
u
r
t
s
15 GHz; VLBA+VLA -ridgepleir(VSOP also detectedtThe
Astrophysical Journal, 803:30 (12pp), 2015 April 10
ingun
the triple-ridge)it
Con (nonthermal) electrons and positrons, respectively. A

electrons and positrons may have a different heating/ation process in e- e+ p mixed plasma (e.g., Hos(mas)s
Arons 1991), here we assume that0maminimum ener
3=
electrons and positrons are thez same for simplicsevaluating the emission
at the SSA frequency, we obta
5ma
z=1

16

Nakamura et al.

Jet axial distance (de-projected): z (pc)The
AstrophysicalJournal,803:30(12pp),
2015
April
Figure 3. VLBA+GBT
86 GHz false-color total intensity
image of the M87 jet.
The image is producedby combining
the visibility
data over the10
two epochs on 2014

February 11 and 26. The restoring beam (0.25 mas ×0.08 mas at PA 0°) is shown in the bottom-right corner of the image. The peak intensity is 500 mJy beam−1 and
-4
-3
-2
-1
1
2
the off-source rms noise level is 0.28 mJy beam−1, where the resulting dynamic range is greater than 1500 to 1.

106

10

10

10

10

1

10

10

z
103

Bondi radius

Jet radius: R (rg)Dc3C273 ~ Dc43 GHz + DcRM ~ 18 . Regarding M87, its
calibration procedure. The basic information of these data is
VLBA 15 GHz (AN12, H13)MERLIN 1.8 GHz (AN12)
also tabulated in Table 1.
EVPA uncertainty in 86 GHz images would be somewhat
1.6 GHz(AN12)VLBA 22 GHz (H13)larger than this value, since EVN
the lower
S/Nof polarization
signals (S/N∼4.5; see Section
3.4) from this source gives
VLBA 2.3 GHz (H13)
VLBA 43 GHz (AN12, H13)5another non-negligible
thermal
error
term.
This
can
be
3. RESULTS10
HSA 86 GHz (H16)(H13)
sp and P are~ sp 25PGHz
estimated as Dctherm (radian)VLBA
where
3.1. New 86 GHz Images
rms noise level and polarized
intensityinthepolarization
VLBA 8.4 GHz (H13)In Figure 3 we show a representative 86 GHz image of themap(e.g., Roberts et al. 1994). With S/N=P sp ∼4.5, we
VLBA Core that43 & 86(NA13)
M87 jet obtained by our VLBA+GBT observations. For a
DcGHz
and
obtain Dctherm,M87 ~ 6 . Assuming
3C273
betterthe image
independent,
weestimateatotal
Dctherm,M87 are statistically
VLBA Core 5, 8, 15, 24, 43, & 86 GHz (H13), visualization,
HSA Core 86 GHz(H16) is produced by combining the4visibility data over the two epochs, and restored with aerror budget for10
M87 to be DcM87∼± 20°.
EHT Core 230 GHz (D12, A15)
convolving beam of 0.25 mas ×0.08 mas at a position angle(PA) of 0°. A contour image with a natural weighting scheme is(Area) FFE parabolic jet (NMF07, TMN08)
also displayed in the top panel of Figure 4.
2.3. Lower-frequency Data
(Area) FFE genuine parabolic jet (NMF07,Thanks
TMN08)to the signiﬁcant improvement in sensitivity, aAs supplementary
data
sets,
we
additionallymade
VLBA0.5 (upper edge) - 0.99 (lower edge)detailed jet structure was clearly imaged down to the weaker
10of3 M87 at 24a =and
only observations
43 GHz close in time withemission regions. The resulting image rms noise of thethe 86 GHz sessions. The observations were carried out on
HST-1
combined image was ∼0.28 mJy beam−1. In this period the2014 March 8, 26, and May 8, where both 24 and 43 GHz wereextended jet was substantially bright down to ∼1 mas from theused quasi-simultaneously by alternating the receivers quickly.
core. The weak emission was detected (particularly in the
On March 26 and May 8, all the VLBA stations were present,
southern limb) down to ∼3 mas from the core at a level of 3σ,
2 antennas at Mauna Kea and Fort Daviswhile on March10
8 the
and another ∼1–2 mas at 2σ. The peak surface brightness of thewere absent. We received only RR polarization signals with aimage was 500 mJy beam−1 at this resolution, corresponding tototal bandwidth of 128 MHz (on March 8) or 256 MHz (onan image dynamic range greater than 1500 to 1 (the detailed
March 26 and May 8). Among these sessions, the data on
value varies slightly as a function of the weighting scheme andMarch 26 were the best in overall quality, while the data on
convolving beam). This is the highest image dynamic range
March 8 were relatively
poor.
The
initialdatacalibration
obtained so far at 86 GHz for this jet, and is quite comparable
1
10correction,(a priori amplitude
fringe-ﬁtting, and bandpass) wasto typical dynamic ranges in VLBA images at 43 GHz(e.g., Ly
made in AIPS, and the subsequent image reconstruction was
et al. 2007). We describe a comparison of our 86 and 43 GHz
performed in Difmap based on the usual CLEAN/selfimages in the next subsection.

5

1

104

as
= 5m

-2
æ n ssa,obs ö5 æ qobs ö÷4 æç Snssa,obs ö÷÷ ç
B^ = b (p) çç÷çè 1 GHz ÷÷ø ççè 1 mas ÷÷ø çççè 1 Kino
Jy ÷÷øet al.

æ d ö
÷,
´ çç
çè 1 + z ÷÷ø

where b (p) is tabulated in Marscher (1983), Hirotani
and K14. The term K is given byæ D A ö-1 æ n ssa,obs ö-2p - 3 æ qobs ö-2p
÷÷ ç
÷
÷
çç
K = k (p) çççè 1 Gpc ÷÷ø ççè 1 GHz ÷÷øçè 1 mas ÷÷øæ Snssa,obs ö p + 2 æ d ö-p - 3
÷÷
÷
çç
´ çç
,
çè 1 + z ÷÷øççè 1 Jy ÷÷ø

where k (p) is tabulated in K14. The cgs units of K a@onz =
datathedependp: 10
erg rpg-;1 fromcm−3. ItEHT2012
is useful to show
expression of the ratio U U B as follows:

Figure 1. Illustration of the jet base of M87 down to the EHTregion scale. The
right panel shows 1the actual
imageof M87
with 10VLBA
at 43 GHz
adopted
4
101
102
103
105
106
107
108
from Hada et al. (2013). The yellow–green circle shows the one-zone region
Jet axial distance (de-projected): z (r )with its diameter,110 μas, which is investigated in K14. g The EHTregion+2
detected
byDistribution
Doelemanet al.
isjetshownasz (de-projected
the bluewithcircle.
F IG . 15.—of the jet radius
R as (2012)
a function of theaxial distanceM = 6.2 ⇥BecauseHada
10 M and ✓ = 14 ) from the SMBH in
k p  -p,minæ D A ö-1 æ n ssa,obs ö-2p
U
16π
units of r (cf. Asada & Nakamura 2012; Nakamura & Asada 2013; Hada et al. 2013, labeled as AN12, NA13, and H13, respectively). Additional data points÷÷ ççç
et al.
(2011)
indicatethat
theet al.central
engine
M87
isA15,locatedat ∼41Theμas÷÷ byare taken
from Doeleman
et al. (2012);
Akiyama(2015); Hada
et al. (2016)of(labeled
as D12,and H16, respectively).
(vertical) dashed-dotted=Kino+2015
Asada
Hada+2013,
2016,
2017;
Nakamura+2018;
Figure 3. Allowed
region
of
and
(the
red
cross
points enclosedBgline denotes the &BondiNakamura
radius r , located at ' 6.9 ⇥2012;10 r and the HST-1
complex is around 10 r . Filled
black region denotes
the black hole(inside the event
tot
,min
ç
2
eastwardof thetheradiocore at
43 GHz,put thea =EHTregion
aroundThehorizon), while
hatchedarea represents
the ergosphere
for thewespin parameter
0.99. The light gray area
denotes thethere.
approximate
solution (e.g. NMF07,
U(p - 2) è 1 Gpc ÷÷ø ççè 1 GHz ÷ø(de-projected)
9

g

B

5

g

6

g

v

()

The Event Horizon Telescope Collaboration
Kazunori Akiyama1,2,3,4 , Antxon Alberdi5 , Walter Alef6, Keiichi Asada7, Rebecca Azulay8,9,6 , Anne-Kathrin Baczko6 ,David Ball10, Mislav Baloković4,11 , John Barrett2 , Dan Bintley12, Lindy Blackburn4,11 , Wilfred Boland13,
Katherine L. Bouman4,11,14 , Geoffrey C. Bower15 , Michael Bremer16, Christiaan D. Brinkerink17 , Roger Brissenden4,11 ,Silke Britzen6 , Avery E. Broderick18,19,20 , Dominique Broguiere16, Thomas Bronzwaer17, Do-Young Byun21,22 ,John E. Carlstrom23,24,25,26, Andrew Chael4,11 , Chi-kwan Chan10,27 , Shami Chatterjee28 , Koushik Chatterjee29,
Ming-Tang Chen15, Yongjun Chen (陈永军)30,31, Ilje Cho21,22 , Pierre Christian10,11 , John E. Conway32 , James M. Cordes28,
Geoffrey B. Crew2 , Yuzhu Cui33,34 , Jordy Davelaar17 , Mariafelicia De Laurentis35,36,37 , Roger Deane38,39 ,Jessica Dempsey12 , Gregory Desvignes6 , Jason Dexter40 , Sheperd S. Doeleman4,11 , Ralph P. Eatough6 ,Heino Falcke17 , Vincent L. Fish2 , Ed Fomalont1, Raquel Fraga-Encinas17 , Per Friberg12, Christian M. Fromm36,
José L. Gómez5 , Peter Galisonl,41,42 , Charles F. Gammie43,44 , Roberto García16, Olivier Gentaz16, Boris Georgiev19,20 ,Ciriaco Goddi17,45, Roman Gold36 , Minfeng Gu (顾敏峰)30,46 , Mark Gurwell11 , Kazuhiro Hada33,34 , Michael H. Hecht2,
Ronald Hesper47 , Luis C. Ho (何子山)48,49 , Paul Ho7, Mareki Honma33,34 , Chih-Wei L. Huang7 , Lei Huang (黄磊)30,46,
David H. Hughes50, Shiro Ikeda3,51,52,53 , Makoto Inoue7, Sara Issaoun17 , David J. James4,11 , Buell T. Jannuzi10,
Michael Janssen17 , Britton Jeter19,20 , Wu Jiang (江悟)30 , Michael D. Johnson4,11 , Svetlana Jorstad54,55 ,Taehyun Jung21,22 , Mansour Karami18,19 , Ramesh Karuppusamy6 , Tomohisa Kawashima3 , Garrett K. Keating11 ,Mark Kettenis56 , Jae-Young Kim6 , Junhan Kim10 , Jongsoo Kim21, Motoki Kino3,57 , Jun Yi Koay7 ,Patrick M. Koch7 , Shoko Koyama7 , Michael Kramer6 , Carsten Kramer16 , Thomas P. Krichbaum6 , Cheng-Yu Kuo58,
Tod R. Lauer59 , Sang-Sung Lee21 , Yan-Rong Li (李彦荣)60 , Zhiyuan Li (李志远)61,62 , Michael Lindqvist32 ,Kuo Liu6 , Elisabetta Liuzzo63 , Wen-Ping Lo7,64, Andrei P. Lobanov6, Laurent Loinard65,66 , Colin Lonsdale2, Ru-Sen Lu(路如森)30,6 , Nicholas R. MacDonald6 , Jirong Mao (毛基荣)67,68,69 , Sera Markoff29,70 , Daniel P. Marrone10 ,Alan P. Marscher54 , Iván Martí-Vidal32,71 , Satoki Matsushita7, Lynn D. Matthews2 , Lia Medeiros10,72 ,Karl M. Menten6 , Yosuke Mizuno36 , Izumi Mizuno12 , James M. Moran4,11 , Kotaro Moriyama33,2 ,̈ 6,17 , Hiroshi Nagai3,34 , Neil M. Nagar73 , Masanori Nakamura7 ,Monika Moscibrodzka17 , Cornelia Muller
4,1174
Ramesh Narayan, Gopal Narayanan , Iniyan Natarajan39 , Roberto Neri16, Chunchong Ni19,20 , Aristeidis Noutsos6 ,33,75
Hiroki Okino, Héctor Olivares36 , Tomoaki Oyama33, Feryal Özel10, Daniel C. M. Palumbo4,11 , Nimesh Patel11,
76,77,78,18
Ue-Li Pen
, Dominic W. Pesce4,11 , Vincent Piétu16, Richard Plambeck79, Aleksandar PopStefanija74,
36,29
Oliver Porth, Ben Prather43 , Jorge A. Preciado-López18 , Dimitrios Psaltis10, Hung-Yi Pu18 ,73
Venkatessh Ramakrishnan, Ramprasad Rao15 , Mark G. Rawlings12, Alexander W. Raymond4,11 , Luciano Rezzolla36,
36
Bart Ripperda, Freek Roelofs17 , Alan Rogers2, Eduardo Ros6 , Mel Rose10 , Arash Roshanineshat10, Helge Rottmann6,
Alan L. Roy6 , Chet Ruszczyk2 , Benjamin R. Ryan80,81 , Kazi L. J. Rygl63 , Salvador Sánchez82,
David Sánchez-Arguelles50,83 , Mahito Sasada33,84 , Tuomas Savolainen6,85,86 , F. Peter Schloerb74, Karl-Friedrich Schuster16,
Lijing Shao6,49 , Zhiqiang Shen (沈志强)30,31 , Des Small56 , Bong Won Sohn21,22,87 , Jason SooHoo2 , Fumie Tazaki33 ,Paul Tiede19,20 , Remo P. J. Tilanus17,45,88 , Michael Titus2 , Kenji Toma89,90 , Pablo Torne6,82 , Tyler Trent10,
Sascha Trippe91 , Shuichiro Tsuda33, Ilse van Bemmel56 , Huib Jan van Langevelde56,92 , Daniel R. van Rossum17 ,Jan Wagner6, John Wardle93 , Jonathan Weintroub4,11 , Norbert Wex6 , Robert Wharton6 , Maciek Wielgus4,11 ,George N. Wong43 , Qingwen Wu (吴庆文)94 , André Young17 , Ken Young11 , Ziri Younsi95,36 , Feng Yuan(袁峰)30,46,96 , Ye-Fei Yuan (袁业飞)97, J. Anton Zensus6 , Guangyao Zhao21 , Shan-Shan Zhao17,61 , Ziyan Zhu42,
Jadyn Anczarski98 , Frederick K. Baganoff99 , Andreas Eckart6,100 , Joseph R. Farah11,101,4 , Daryl Haggard102,103,104 ,Zheng Meyer-Zhao7,105, Daniel Michalik106,107 , Andrew Nadolski44 , Joseph Neilsen98 , Hiroaki Nishioka7,
Michael A. Nowak108 , Nicolas Pradel7, Rurik A. Primiani109 , Kamal Souccar74, Laura Vertatschitsch11,109,
Paul Yamaguchi11 , and Shuo Zhang99
1

M87*

EHT images

April 11, 2017

• Central depression inbrightness with a flux ratio>~ 10:1• Ring shape• no extended component(jet / accretion disk)-> EHT 2020

• Flux ~ 0.5 Jy• Asymmetry• Stable in different daysF⌫ ' 0.5 Jy
✓
◆2 ⇣
⌘2
✓
⌫
Tb
⇥
40µas
230GHz 6 ⇥ 109 K

50 µasApril 5

April 6

April 10<latexit sha1_base64="DprUuUpWtNMjaF4djB6i96E9uKQ=">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</latexit><latexit sha1_base64="KbKWo+ujGDGE08Rs4iF7MzgNtuU=">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</latexit>

0

1

2

3

4

5

Brightness Temperature (109 K)

6

Black hole shadow & photon ringZero-spin BH with emitting plane

77:13 (9pp), 2013 November 1°

Chan, Psaltis, & Öze

i = 60°5

i = 90°p
3 3 rg5<latexit sha1_base64="FF6yOlP/eX7vXxC9M8m8AKWGEF8=">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</latexit>

8

0 a=0

0 a=0

Event Horizon Telescope Collaboration
GRMHD models
SANE, a = 0, Rhigh = 10

-5a = 0.999

0-coordinate (M)5

a = 0.999-505α0-coordinateSimulated(M) EHT observations-5

a = 0.999-50α0-coordinate (M)5rr black holes with different spins aand observer inclinations i. The left, central, and right panels show the photon rings for i = 30
• "((r= 3spins—fromrg)
h panel,different colors
represent different
black being a= 0 to•red
being a = 0.999.#
For each
inclination, the size
BH
akly on the blackhole spin. "!
Moreover, the photon ring retains its nearly circular shape even at high black hole spins; a significa'$
99 andat large inclination
angles.
%&vailable in the online journal.)R.accretion
Takahashi
2004;
Chan,
Psaltis& Ozel 2013; Pu+2016
Gralla, Holz & Wald 2019
for April 11 corresponding to di↵erent spin parameters andflows. Bottom:
sametheoreticalmodels, processed
369043a =simulation
0.974881
aThe=weather
0.999
through a VLBI
pipeline with the same schedule, telescope characteristics,
andparameters as in the April
Figure 4. Top: Three example models of some of the best-fitting snapshots from the image library of GRMHD simulations

that we are imaging only those regions that have relaxed,
we draw snapshots for comparison with the data from5 ´ 103 £ t rg c-1 £ 10 4 .
GRMHD models have two key physical parameters. The ﬁrst
is the black hole spin a*, -1 < a* < 1. The second parameter is
FBH -0.5,
crossing
one 0.75,
hemispherethethe absolute• BHmagnetic
spin: a* ﬂux= -0.94,
0, 0.5,0.97 &ofmore
event horizon (see Tchekhovskoy et al. 2011; O. Porth et al.
r <~ 10 rg for!%"$2019, in• preparationa deﬁnition). It is convenient to recast
˙ g2 c )-1 2 .110
FBH in •dimensionlessform f º FBH (MrBH-.,The magnetic
ﬂux f (fis ~nonzero
SANE models
3), MADbecausemodelsmagnetic(f > 50) ﬁeld
is advected into the event horizon by the accretion ﬂow
and sustained by currents in the surrounding plasma.
highnumerical Rsimulations
show that the
At f >• fmax*~ 15,111
accumulated magnetic
the accretion
Ti ﬂux erupts,p2 pushes aside1R ⌘ (Tchekhovskoy= Rhigh+ﬂow, and escapes
et al.
2Te
1 +et p2al. 2011;
1 + McKinneyp2012). Models with f ~ 1 are conventionally referred to as
Standard• andNormal Evolution
Narayan et al. 2012;
Funnel'&( (SANE;

Sa̧dowski et al (2013a)) models; models with f ~ fmax are• inclination i = 12, 17, 22, 158, 163, 168GRMHD + GRRT calculations<latexit sha1_base64="WpH6Fz9xQ4faXP92w4+ungucbZM=">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</latexit>

Porth+ 2019110

f is determined by the outcome of the simulation and cannot be triviallypredicted from the initial conditions, but by repeated experiment it is possible• #
MtorusBH andto manipulate
the size of the initialM
torus
strength and geometry of the
initial ﬁeld to
produce a target f.  +)
111
In Heaviside units, where a factor of 4p is absorbed into the deﬁnition ofB, f  15. In the Gaussian units used in some earlier papers, f  50 .

SANE

inclination i = 163

The Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10

The EHT Collaboration et al.

Figure 2. Time-averaged 1.3 mm images generated by ﬁve SANE GRMHD simulations with varying spin (a* = -0.94 to a* = +0.97 from left to right) and Rhigh(Rhigh = 1 to Rhigh = 160 from top to bottom; increasing Rhigh corresponds to decreasing electron temperature). The colormap is linear. All models are imaged ati=163°. The jet that is approaching Earth is on the right (west) in all the images. The black hole spin vector projected onto the plane of the sky is marked with anarrow and aligned in the east–west direction. When the arrow is pointing left the black hole rotates in a clockwise direction, and when the arrow is pointing right theblack hole rotates in a counterclockwise direction. The ﬁeld of view for each model image is 80 m as (half of that used for the image libraries) with resolution equal to1mas /pixel (20 times ﬁner than the nominal resolution of EHT2017, and the same employed in the library images).

using a simple model:

MAD

Te =

2m pu
3 k r (2 + R )

,

(7 )

where we have assumed that the plasma is composed ofhydrogen, the ions are nonrelativistic, and the electrons are
relativistic. Here R º Ti Te and
R = Rhighb 2p
1 + b 2p+

1.
1 + b 2p(8 )This prescription has one parameter, Rhigh , and sets Te  Ti in
low b p regions and Te  Ti Rhigh in the midplane of the disk. It
is adapted from Mościbrodzka et al. (2016) and motivated bymodels for electron heating in a turbulent, collisionless plasmathat preferentially heats the ions for b p 2 1 (e.g., Howes 2010;
Kawazura et al. 2018).
(3) We must specify the observer inclination i, theorientation of the observer through the position angle PA , theblack hole mass M , and the distance D to the source. Non-EHT
constraints on i, PA , and M are considered below; we have

have examined, including Ṁ , are insensitive to small changes
in i. The image morphology does depend on whether i isgreater than or less than 90°, as we will show below.
The model images are generated with a 160 ´ 160 mas ﬁeldof view and 1mas pixels, which are small compared to the~20 mas nominal resolution of EHT2017. Our analysis isinsensitive to changes in the ﬁeld of view and the pixel scale.
For M we use the most likely value from the stellar
absorption-line work, 6.2 ´ 109M: (Gebhardt et al. 2011). For
the distance D we use 16.9 Mpc, which is very close to that
employed in Paper VI. The ratio GM (c 2D) = 3.62 mas(hereafter M/D) determines the angular scale of the images.
For some models we have also generated images with
M = 3.5 ´ 109 M: to check that the analysis results are notpredetermined by the input black hole mass.
3.3. Image Library Summary
The Image Library contains of order 60,000 images. We
generate images from 100 to 500 distinct output ﬁles from each of
the GRMHD models at each of Rhigh = 1, 10, 20, 40, 80 , and160. In comparing to the data we adjust the PA by rotation and•B

EHT`f&$>ULi• &$Mh[Y3:

• 1.3mmXdKerr7VFrgG;4 • RIAFe:J<optically-thin 10'01Xd• BHCI=/1#]QSj@5U:(,1• `f .1a\*-#+DZg^ PE • 2c@5UKOSMBH^TR9• M = 6.5 +0.7-0.6 x 109 Msun (M/D = 3.8+0.4-0.3 µas). G8bNA`f_9Y3:• BH")1BW • !%'6H `f?90#/Ongoing work
• Polarization: further constraints on ne, B• Combination of EHT data and lower freq. VLBI data
(Nakamura+18; Chael+19; Kino+14, 15; K. Takahashi+18)• EHT 2020: more stations• imaging extended component• time variability?

• Future EHT 345 GHz campaigns• Green Land Telescope constructed by ASIAA, Taiwan• Lower optical depth & higher spatial resolution-> Kawashima+2019; Nakamura+2019 in prep.

Connection of the ring with the jet
Nakamura et al.

• BZ process
p 

#"

 

p PBZ = PBZ(a*, FBH)
p !"

• Stagnation surface• Blob formation found in 2D highresolution simulations• The most upstream of blobs may not be
the stagnation surface• But MHD simulations do not include paircreation gaps

Nakamura+2018

Figure 19. Innermost jet radii displayed as the FWHM/2 of millimeter VLBI
cores at 43, 86, and 230 GHz, by utilizing the VLBI core shift. Our GRMHD

⇠

c

=
2
B

c

1
Large-scale jet emission
model
⇠p
.
1

[g(✓, ⌫)]2That is, the fluid velocity is dominatedpoloidal compone
Consistentby
withthenumerical
unity. We note here that, as g(✓,FF⌫)simulations! 1, the leading terms in Eqs
relations in steady axisymmetric cold outflows in ideal MHD (Tom
✓
◆ 2
1
R⌦F
cf.
Tchekhovskoy+2008
⇠ 1,
p ⇠1
2
c
!
✓
◆ 1"
R̃2 ⌦2F
R|⌦F |=
11cc2
which holds for R|⌦F |/c

1 and

v

˜ ⇠ 1, where the letters wi

Approaching MHD velocity
at far zone

B

A.4. Non-thermal El
The number density of the non-thermal electrons, n, is assumer · (nv) = 0, by following BL09, although it is not so obvious wh
For RB⌦FM.6=Nakamura
0, the& continuity
equation is reduced to
K. Takahashi,
KT, Kino,
Hada 2018BP type: 

BZ type: BP type:

 
vf

BZ type: 

Ogihara, Takahashi, & Toma

Triple-ridge image
The Astrophysical Journal, 877:19 (12pp), 2019 May 20

Ogihara, Takahashi, & Toma

15 GHz; VLBA+VLA
z = 30mas
Continuing triple-ridge
structurez = 30mas

z = 15mas

Continuing triple-ridge structurez = 15mas

z = 30mas

z = 15mas

z = 5masz = 5masz = 5masContinuing triple-ridge structure

The Astrophysical Journal, 877:19 (12pp), 2019 May 20
nuing triple-ridge structure

Hada et al. 2017z = 15mas

z = 30mas

Figure 1. Left panel: the computed image with the computational resolution of 3 R . Right panel: the image convolved with the beam size (1.14 mas×0.55 mas),S
3 for Θ=15° in the northern
G2circle(1 -inbm
Figure 2. Spatial distributionof B′,sizen′,is vplottedandhemisphere.
B′ and n′value,
are normalized
byrepresent
each maximum
p/vf, aswhere the beam
the 1graythe )bottom
left corner. The intensity is normalizedby each maximum
and the contours
the intensity value. The
white solid lines are thez axis,represent
ﬁeld
throughthe BHhorizonat isthelines are the(k=1,and
2, 3,theK,gray27 fordashedthe left lines
panel andk=1, 2,the
3, K,
21 lines
for thepassing
right panel).
The numberof contour
lines
notequatorial
the same as plane.
in T18. The
Note dottedthat 1 mas
at 2−k
−2
−2.5
−3
−3.5
−4
−5
−6
≈136
, 10 , toand
10 RS. in the upper left panel, 10 , 10 , and 10 in the upper right panel, 1 and 10 in the lower left panel, and 1000, 2000,
contours of 10 , 10 corresponds
3000, and 4000 in the lower right panel. Note that 1 RS corresponds to ≈7.3μas.

• • 
 











we normalize the intensity by the value at X=0 of each line in
As for the dependence on the parameters related to the
4. Discussion
the axis
is debeamed. This leads to the asymmetry of the inner
Figure 3. The upper left panel represents the intensity proﬁlesdensity distribution, we examine only the dependence on Δ
ridgeincomputed
image,
we havein pointed
becausethe dependence
on whichRp was discussed
T18. As out forin theValleys
case ofbetween
Θ=7°, Ridges
10°, 15°, 20°, and 75°, with theand z1our
4.1.
panel orofz1Figure
1 indecreases,
the Section
density in 3.
the jet edge increases
Δ increases
other parameters unchanged. For smaller Θ, the relation the left

Ogihara, K. Takahashi, & KT 2019

GMVA + ALMA 2020 forecast

Fig. 2: GRMHD+GR Ray-Tracing (GRRT) images and simulated GMVA(+ALMA) observations of the M 87
jet. Topbottom:jet formation withALMA
high [22,14]
and lowmagnetic
flux (BH spin a ⇠ 0.9).
• and
EHT
Collaboration,Cycle
7 [21,8]+ GMVA
Proposal
From left to right: Simulated jet emission, simulated observation with GMVA+ALMA, and without ALMA.

• GMVA = Europe telescopes + VLBA & more [at 86 GHz]

2 Immediate Objectives :• Provinghigh-/low-magnetization
jet launching via
imaging the jet base
: New state-of-the-art nu• Brightcounter-jet emission& asymmetriclimb-brightening
merical simulations predict bright ring-like synchrotron emission at the jet base (Fig. 2). Standard jetin the small f model
formation theory posits that these outflows are collimated and launched by magnetic fields, which extract
angular momentum from the spinning BH [3]. From this it follows that a stronger e↵ective magnetic flux2

!  















 "
 



→ 


BH + accretion flow

Relativistic jet

Afterglow

Gamma-ray

Photosphere Internaldissipation
Prompt emission (~100 keV)
GAP, INTEGRAL(Yonetoku+11;12; Gotz+09;13)
Prompt Opt? (Troja+17)

Reverseshock

Forwardshock

Late-time Opt afterglow
PL ~ 1-3% (Covino+03)
PC ~ 0.6 % (Wiersema+14)
Radio: ALMA?

Early-time Opt afterglow: Liverpool, Kanata
PL ~ 30% (Mundell+13), PL ~ 10% (Steele+09),
PL ~ 10% (Uehara, KT, Kawabata+12)
PL < 8% (Mundell+07)

degree and direction, E2 would be higher abound on j"j would be tighter. Without
nature of the intrinsic polarization of the so
&1)CPT0
the one that gives the weakest bound on j"j amdo not exhibit the• accidental
cancellation me + ($ )the.#For GRB 110721A,
2& lower limits %$ > 35% in the whole energy band (E⇠ 2Emax ¼ 300 keV) lead!± to
' Ek2±’ 120 kkeV. Se
plin j#!ðE2 ; zÞ " #!ðEmin ; zÞj ) M
#=2,
we o
straint from GRB 110721A as j"j < 7 ( 10More accurate
constraints
are obtain
•
!&1)"
%
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ$, where N
ing that
Q2•þ%U2 =N >/,REmax %
  *
Q ¼ Emin E $i cos½2#!ðE;zÞ', and U ¼
'1)
sin ½2#!ðE; zÞ' with the intrinsic polari$i ¼ 1. Using •$P(70-300keV)> 0:35 and> %>(2s)"0:98,
35%
constraint from GRB
110721A as(D > 2.5Gpc)
for GRB110721A<latexit sha1_base64="(null)">(null)</latexit>

KT, Mukohyama, Yonetoku et al. 2012;
Myers & Pospelov 2003

j"j < 2 ( 10"15 ;θ(t, T ) ≈ 2 × 10−2 sin Ξ sin(mt + Ξneously broken by the axion field. This photon birengence caused by the axion background leads to thetation of the linear polarization plane.
Provided that a photon propagating along the z-axis isearly polarized into the x-direction at the initial time

where g ≡ g /(10 GeV ), m
and we used the dark matter d<latexit sha1_base64="(null)">(null)</latexit>

1!± ' k ±
ga ˙
2

• "(

• #

12

aγ

−12

−1

ρDM = m2 φ20 /2 ≈ 0.3 GeV/cm3 [2t

t+T$& )'*$

 %! l Letters, 729:L17 (6pp), 2011 March 10

Hashimoto et al.

600
0

1″

Axion effect?

AB Aurigae
0

1″

q

Number200
400

Number
200
400

600

The Astrophysical Journal Letters, 729:L17 (6pp), 2011 March 10

80

85
90
95
Angle (degree)

100

Figure 3. Polarization vector pattern of AB Aur. Left: polarization vectors superposed on the PI image of AB Aur in the H band. The plott



gag

ACK

−9
CAST

log10 (gaγ /GeV−1 )−10

SN 1987A−11

Quasor polarization

−12
−13

ALPS-II
IAXO
Soft X-ray
γ−ray transparency
This work (optimistic)
This work (conservative)

−14
−15
−25

−24

−23

−22

−21

−20

−19

log10 (m/eV)

−18

−17

−16

−15

We are gratefulworkshop ‘Essentia
ogy’ held on Juneversity, where we cter. We would li
Fukushima, Mikhai
Tanaka, Jun Hashim
sky and Ken’ichi Sa
ments. This work i
in-Aid for JSPS R
and No. 17J02411
for Scientific Resea

FIG.
2: Constraint on the coupling constant g for varying-21• m < 10
mass of eV
the axion
dark matter m. The black solidline indicates the upper bound derived in eq. (14), whereas the graysolid line is the conservative upper bound. Blue, green, and~ [14]) and[1]22R. D. Peccei andred regions are rejected by the experiment
(CAST
t
⇠
⇠
1.3/(m/10eV) yr• "!
 p mcQuasor(1977).
2
astronomical observations (SN 1987A [17] andpolaraγ[2] E. Witten, Phys
ization [18]). Black broken lines are the expected sensitivities
E. Witten,
JHEP& KT 2019of future projects (ALPS-II [16] and IAXO [15]) and red bro- Fujita, Tazaki<latexit sha1_base64="(null)">(null)</latexit>

Summary• BH$&A4^'+(Q@;GL• xCKeySE7Ht|~9Ke• ls2i v

d1:;?

• g3Tu>Nnls}b(,#)$-*56z_YB• Event Horizon TelescopeMDIX• 0pA4^PVFm/UBH• }bTw• hr{JOK, 345GHzls

k]



 Z7

• BZ processls8V= • }b"(!qocIBRaf• 0%(`<   \j[.W
(Goldreich & Julian 1969)

E ⇥ B'
Sp =
4⇡

r⇥E=0

Jp
V'

Steady, axisymmetric

E

Electric field screened by plasma

E·B=0

E=
E=

V' ⇥ Br · Sp =E · Jp > 0

E= r
E' = 0r⌦Fe' ⇥ Bc⌦F = ⌦pulsar

M87(VirgoA,
3C274)
BHs with largest angular sizes
Event horizon apparent radius ranking

ObjectSgrA*
M87

Sombrero

M84

Cen A

MBH

(108 Msun)

0.04

d
1Rs
(Mpc) (μas)
0.008

10

10

9.0

2.2

0.5

3.8

0.3

(30?)
60
16.7
Stellar dynamics (gas dynamics)

8.5

17

7
1

(= 2rg = 2GM/c2)

0.0

Where
the engine
central engine?
Location
ofisthe-0.5-1.0

100 Rs (0.06 pc)

1

(Hada
et al. -12011)
0-2
MilliARC SEC

-3

-0.4
-0.6
MilliARC SEC

-0.8

-4

-5

VLBA 7mm

0.8
6 Rs
0.01 pc

0.6

MilliARC SEC

0.4

0.2

0.0

-0.2

Core-shift(Blandford & Konigl 1979)

-0.4

0.4

0.2

0.0

-0.2

-1.0

-1.2

-1.4

• High-accuracy core-shift measurement suggests the central
engine resides very close to 7mm core
Hada+20111979A&A....75..228L

Image models

General relati• Standard disk model
Luminet 1979; Bardeen 1973

Figure 5. Images from total (top row), disc (middle row) and jet (bottom row) components for thcolumns) at 1.3 mm (first and third columns) and 0.87 mm (second and fourth columns). The colours
with a dynamic range of 60. The panel size is 100 × 100 µas. The images are taken from the samerotated 90◦ to roughly align with the position angle of the large-scale jet at 7 mm. Both fiducial model• RIAF + jet models (GRMHD simulations + GRRT calculations)
Falke, Melia & Agol 2000; Dexter+2012; Moscibrozka+2016

Photon ring
Azimuthal angle change

Schwarzschild BH

Impact parameter• Photons which are seen near the critical curve will have orbitedthe BH many times and then pick up extra brightness on their way
to the observer• Photon ring (+ lensing ring) is bright in the optically-thin caseGralla, Holz & Wald 2019

Rough estimatesTi ⇠ 0.3 Ti,vir ' 1012
<latexit sha1_base64="PtyyT/6rhxEwIQFit+T4l4J+D4Y=">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</latexit>

⇣r ⌘
g

r

K

ni kB Ti + ne kB Te = p B 2 /8⇡

✓ ◆
1
3
2
p
⌫
4⇡r ne
e ⌫s
⌫
3
(
)
⌫
s
F⌫ =
2⇡
e
2
2
3D
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B'5<latexit sha1_base64="BImJBPWV3IN50BzS69tdb9n1Sfo=">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</latexit>

✓

r
rg

4

✓

r
rg

◆ 0.63

◆ 1.3
p

0.19

✓

0.62
p

Ti
3Te

✓

Ti
3Te

✓

⇥e
10

◆2

◆ 0.47 ✓◆0.14 ✓Te
10Tb

Optically-thinthermal e synchrotron(Leung+2011)

GHz

Te
10Tb

◆ 0.71

G

◆ 2.4

cm 3

Tb ~ 6 x 109 K

following we discuss eplerian orbital frequency, a corona with gas-to-magneticinterested in a high-lev
ssure ratio b p º pgas pmag ~ 1, and a strongly magnetizedskip ahead to Section
ion over both poles of the black hole with B2 rc 2  1. We(1) GRMHD modeler to the strongly magnetized region as the funnel, and thethe plasma ﬂow. N• Kerr
BH thewithfunnel
fixed andM &thea* corona as the funnel wallundarybetweeninvariant, however, unde Villiersal. 2005;• 3Detideal
MHDHawleymodels& Krolik 2006). All models in
4 r c-1
M. In particular, thet=10.
libraryareevolved
from
t=0
to
g
• Codes: BHAC (Porth+17), H-AMR (Liska+18),
M1 2B,
strength B
The simulation
outcomedependsontheinitialmagneticﬁeldiharm (Gammie+03), KORAL (Sadowski+13)
Alfvén speed B r1 2 aength and geometry insofar as these affect the magnetic ﬂux
That is, there is no intr
ough the disk, as discussed below. Once the simulation is
Initialcondition:hydrodynamicallytorusloses
as long as the mass
iated• thedisktransitions
to a turbulent staticstate and+poloidalB
field
mory of most of the details of the initial conditions. This
comparison to M .112 W• Accretionflow
AM ||inside
BH spinaxed turbulent
state isfounda characteristic radius
the average image fromt grows
over the courseof the simulation.
• Outflow-onlyboundary
condition To be conﬁdent
density ≈0.5 Jy (see Pt we• areimaging
internal energy, and m
Densityflooronly those regions that have relaxed,
draw snapshots for comparison with the data from
The mass unit M de´ 103 £ t rg c-1 £ 10 4 .
Ṁ ranges Porth+2´1from 2019
-1
4
GRMHD
models have state
two key
The ﬁrst• Quasi-steadyat rphysical<~ 10 rparameters.
g: 5000 <~ t/rg c <~ 10 rates vary by model-6
he black hole spin a*, -1 < a* < 1. The second parameter is~
10
MAD
modelsis• 2 key parameters: normalized magnetic flux & BH spin
-5M
absolute magnetic ﬂux FBH crossing one hemisphere of the
˙
~
5
´
10
is
• SANE models (f ~ 3): a* = -0.94, -0.5, 0, 0.5, 0.75, 0.88, 0.94, 0.97, 0.98Edd ; annt horizon (see Tchekhovskoy et al. 2011; O. Porth et al.
(2) The observed rad•MADmodels
(f
>
50):
a
=
-0.94,
-0.5,
0,
0.5,
0.75,
0.94
*
19, in preparation for a deﬁnition). It is convenient to recast
and the polarization c
2 -1 2 110
˙.
H in dimensionless form f º FBH (Mrg c )that the 1.3 mm emissi

GRMHD simulation library

GR Ray-Tracing calculations• Thermal electrons assumed, with one parameter Rhigh(cf. Howes 2006; Kawazura+2018)

2
Ti
1
p
R⌘
= Rhigh+2
Te1+ p
1 + p2

Howes 2010<latexit sha1_base64="WpH6Fz9xQ4faXP92w4+ungucbZM=">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</latexit>• Emission from regions with B2 > rc2 (i.e. funnel region) is set to zeroFig. 1. The ion-to-electron heating ratio Qi /Qe vs. i (left) and T i /T e (right). We take the timescale. The error bars show the standard deviation of the time series. The dotted lines in the r
calculated via the model proposed in [7], based on linear theory: note the much lower ion hea
the case of cold ions (low T i /T e ) from the general trend.

• 100-500 images from each GRMHD models,each of Rhigh = 1, 10, 20, 40, 80, 160
are ordered out). We also assume that ions and electrons individually Met
are near Maxwellian equilibria, but at di↵erent temperatures. This ex- phy
inclination i = 12, 17, 22, 158, 163, 168
(nothighlycludesany heating
mechanisms affectassociated withimage)pressure anisotropies sim[21–23] or significant non-thermal tails in the particle distributionfunctions [24, 25]. Furthermore, it can be shown that in such a turbulence, Alfvénic and compressive (slow-wave-like) perturbations
decouple energetically in the inertial range [6]. In the solar wind,
the compressive perturbations are energetically subdominant in theinertial range [17], although it is not known how generic a situation
this is. At low i , it can be shown rigorously that the energy carried by
the compressive cascade will always1/2
end up as ion heat [26]. Here weshall ignore this heating channel and focus on the Alfvénic cascade
only.

• Various codes that include RAIKOU (Kawashima+)

2• C is adjusted for Fn ~ 0.5 Jy, then M determines ring size & Ṁ ⇠ 4⇡r ⇢v
Numerical Approach<latexit sha1_base64="sHXHnHSVUehgj59i1ihIiZx1QRw=">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</latexit>

Ene

The
the
heat
incr
(1, 1
in th
MH
mor
dom

R

• MHD velocity field is invariant under scaling r -> Cr, B -> C B, u -> Cu

in th
num

An Alfvénic turbulent cascade starts in the magnetohydrodynamicrPhotonorbitsグと円盤内縁リングの中心のズレ：光子軌道から観測者スクリーンリング

赤道面に射影observer screen

内縁リング• 光子リングは大きさはスピンに依存しない
Credit: Kawashima (cf. Kawashima+2019)
が、位置はスピンに依存(横にシフト)。

これは光子球軌道はスピンに対して順回
Johnson+2019

• Time-averaged images

SANE• i = 163 deg (Accretion
disk angular momentum)• Arrows: BH spin vector
projected onto the sky

The Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10• Asymmetry is controlled
by the BH spin (except
the SANE Rhigh < 10)• Doppler beaming

using a simple model:
Te =

2m pu
3 k r (2 + R )

,

(7 )

where we have assumed that the plasma is composed ofhydrogen, the ions are nonrelativistic, and the electrons are
relativistic. Here R º Ti Te and
R = Rhighb 2p
1 + b 2p+

1.
1 + b 2p(8 )This prescription has one parameter, Rhigh , and sets Te  Ti in
low b p regions and Te  Ti Rhigh in the midplane of the disk. It
is adapted from Mościbrodzka et al. (2016) and motivated bymodels for electron heating in a turbulent, collisionless plasmathat preferentially heats the ions for b p 2 1 (e.g., Howes 2010;
Kawazura et al. 2018).
(3) We must specify the observer inclination i, theorientation of the observer through the position angle PA , theblack hole mass M , and the distance D to the source. Non-EHT
constraints on i, PA , and M are considered below; we have

have examined, including Ṁ , are insensitive to small changes
in i. The image morphology does depend on whether i isgreater than or less than 90°, as we will show below.
The model images are generated with a 160 ´ 160 mas ﬁeldof view and 1mas pixels, which are small compared to the~20 mas nominal resolution of EHT2017. Our analysis isinsensitive to changes in the ﬁeld of view and the pixel scale.
For M we use the most likely value from the stellar
absorption-line work, 6.2 ´ 109M: (Gebhardt et al. 2011). For
the distance D we use 16.9 Mpc, which is very close to that
employed in Paper VI. The ratio GM (c 2D) = 3.62 mas(hereafter M/D) determines the angular scale of the images.
For some models we have also generated images with
M = 3.5 ´ 109 M: to check that the analysis results are notpredetermined by the input black hole mass.

MAD• Much emission comesfrom the funnel wall thatrotates in a similar way
as the BH

The EHT Collaboration et al.

Figure 2. Time-averaged 1.3 mm images generated by ﬁve SANE GRMHD simulations with varying spin (a* = -0.94 to a* = +0.97 from left to right) and Rhigh(Rhigh = 1 to Rhigh = 160 from top to bottom; increasing Rhigh corresponds to decreasing electron temperature). The colormap is linear. All models are imaged ati=163°. The jet that is approaching Earth is on the right (west) in all the images. The black hole spin vector projected onto the plane of the sky is marked with anarrow and aligned in the east–west direction. When the arrow is pointing left the black hole rotates in a clockwise direction, and when the arrow is pointing right theblack hole rotates in a counterclockwise direction. The ﬁeld of view for each model image is 80 m as (half of that used for the image libraries) with resolution equal to1mas /pixel (20 times ﬁner than the nominal resolution of EHT2017, and the same employed in the library images).

3.3. Image Library Summary
The Image Library contains of order 60,000 images. We
generate images from 100 to 500 distinct output ﬁles from each of
the GRMHD models at each of Rhigh = 1, 10, 20, 40, 80 , and160. In comparing to the data we adjust the PA by rotation andThe Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10

a* = +0.94

The EHT Collaboration et• Prograde models: a* > 0• Location of the origin for
all photons that make up
an image• Emission at 1 < r/rg < 4(unstable photon orbit
region) dominant• The funnel wall is brightfor high Rhigh cases• Funnel is wider for MAD
than for SANE

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

• Retrograde models: a* < 0Rhigh = 160

6MAD• MAD funnel widths are
similar in pro- and retrograde cases

4

4

2

2

0

0

2

2

4

4

6

(cf. Tchekhovskoy & McKinney
2012)

MAD

[GM/c2 ][GM/c2 ]

0

2

4

6
[GM/c2 ]

8

10

6

12

6

0

2

4

6
[GM/c2 ]8

SANE[GM/c2 ]• Even in SANE models,funnel is wide

12

SANE

4

4

2

2

0

0

2

2

4

4

6

10

6

[GM/c2 ]• ISCO radius is muchlargerRhigh = 10

6

0

2

4

6
[GM/c2 ]

8

10

12

6

0

2

4

6
[GM/c2 ]

8

10

12

The Astrophysical Journal Letters, 875:L6 (44pp), 2019 April 10

Th

Model fitting• Probability distribution of parameters M/D, C,
and PA via MCMC method• Each simulation code derive similar
distribution
The Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10

The EHT Collaboration et al.

Figure 9. Illustration of the parameters of the SSM described in Section 6.2. Both the original GRMHD simulation (left) and the correspo
set of parameter values, (ﬂux rescaling, stretching of the image, and rotation; right) are shown. In both panels, the gray arrow indi
forward jet.

GRMHD ﬁtting to mm-VLBI data of Sgr A* (e.g., Dexter et al.
230 GHz ﬂux density is ∼0.5Jy. The
2010; Kim et al. 2016). We further develop and apply a method
between snapshots is selected such thatfor testing the consistency of the M87 data with the simulation
weakly correlated.
models (Section 6.4) and ﬁnd that the majority of the simulation
library models is consistent with the data. We use the results to
6.2. Single Snapshot Modeestimate physical parameters, including the black hole angular
Each snapshot image generates aradius GM Dc 2 (Section 6.5). The implications of our results
deﬁnedby the total compact ﬂux (CF), a
for the physical properties of the emission region are discussedorientation (deﬁned to be the position an
in more detail in Paper V. From EHT data alone it is difﬁcult tomeasured east of north, PAFJ). Variation
rule out many of the broad range of possible models for theapproximately
correspond to variations
black hole and plasma properties. However, in combination
black hole mass, and orientation ofwith other data (especially the observed jet power), ultimately
respectively.
Variations
in massareandasso
Figure 7. Distribution of M/D obtainedmore
by ﬁttingto thebe2017
April 6 data, in mas, measured independently
using
the (left panel)
THEMIS
thanImagehalf Libraryof the snapshots
models can
excluded.
+0.7
9
the diameterof thering,
a generi(right panel) GENA pipelines with qualitatively
similar results.
The threelinesphoton
show thebest-ﬁt1%-0.6
sun Smooth lines were drawn with a Gaussian kernel density estimator.
M imagesD = 2.04in(dashed)mas
and 3.62image
within each model (solid); the best-ﬁt 10% within each model (dashed); and all model images (dotted). The vertical lines
allshowof thethe GRMHD(solid), corresponding to M=3.5 and 6.2 ´ 109 M: . The 6.1.
distribution
uses aofsubset
of models for which spectra and jet power
estimates
are available
Section 6).
Eachsnapshot
image is(seecharacterized
Summary
Simulations
Only images with a* > 0 , i>90° and a* < 0 , i<90° (see also the left panel of Figure 5) are considered.
normalized intensity map of the im
As described in detail in Paper V, we have constructed acorresponding nominal total intensity Cˆ
large
image
libraryofhorizon-scale
synchrotron
emission
Because the emission is produced in front of the black hole,away from Earth. If the ﬂuctuations
are such that the ﬁtted PA forˆ• M ~ 6.5

x10 M

(derived in paper VI)• Consistent with the previous estimates based on stellar dynamics

PA ~ 288, large-scale jet orientationThe EHT Collaboration et al.

The Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10

i < 90, a* < 0i > 90, a* > 0
These cases are
more likely

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

turbulent dissipation, and Coulomb heating, which transfers energy
from the hot ions to the cooler electrons. In our suite of simulations
the parameter Rhigh can be thought of as a proxy for the sum ofthese processes. In a fully self-consistent treatment, some models

Eliminating all MAD models with a* . 0 and Rhigh = 1 does notchange any of our earlier conclusions.
6.2. X-Ray Constraints

include all scattering orders in the Monte Carlo calculation).
Increasing Rhigh at ﬁxed Fn (230 GHz) tends to increase Ṁ andtherefore τT and decrease Te. The increase in Te dominates in our
ensemble of models, and so models with small Rhigh have larger
Event Horizon
Telescope
Collaboration
Rhigh have
LX , while models
with large
smaller LX . The effect is
GRMHD
modelsnot strictly monotonic, however, because of noise in our sampling
SANE, a = -0.94, R= 80
SANE, a = 0, R
= 10
MAD, a = 0.94, R= 10
process and the highly variable nature of the X-ray emission.
The overluminous models are mostly SANE models with
Rhigh - 20 . The model with the highest áLXñ = 4.2 ´
10 42 erg s-1 is a SANE, a* = 0, Rhigh = 10 model. The
corresponding model with Rhigh = 1 has áLXñ = 2.1 ´
10 41 erg s-1, and the difference between these two indicates thelevel of variability and the sensitivity of the average to the brightest
50 µassnapshot. The upshotof applicationof the LX constraints is that LX
Simulated
EHT observations
is sensitive to Rhigh . Very low values of Rhigh are disfavored. LX
thus most directly constrains the electron temperature model.
high

40

30

20

10

Brightness Temperature (109 K)

high

Fluxb

6

5

6.3. Jet Power

4Brightness Temperature (109 K)

high

Table 1
Average Image Scoringa Summary

SANE
SANE
SANE
SANE
SANE
SANE
SANE
SANE
MAD
MAD
MAD
MAD
MAD
MAD

a*c
−0.94
−0.5
0
0.5
0.75
0.88
0.94
0.97
−0.94
−0.5
0
0.5
0.75
0.94

á p ñdNmodel e

MIN( p )f

MAX( p )g

0.33
0.19
0.23
0.51
0.74
0.65
0.49
0.12
0.01
0.75
0.22
0.17
0.28
0.21

24
24
24
30
6
6
24
6
18
18
18
18
18
18

0.01
0.01
0.01
0.02
0.48
0.26
0.01
0.06
0.01
0.34
0.01
0.02
0.01
0.02

0.88
0.73
0.92
0.97
0.98
0.94
0.92
0.40
0.04
0.98
0.62
0.54
0.72
0.50

Average of snapshot images

Notes.
a
The Average Image Scoring (THEMIS-AIS) is introduced in Section 4.
Estimates of M87ʼs jet power (Pjet ) have been reviewed in2
2b ﬂux: net magnetic ﬂux on the black hole (MAD or SANE).
Reynolds et al. (1996), Li et al. (2009), de Gasperin et al.
ca : dimensionless black hole spin.
1d *(2012), Broderick et al. (2015), and Prieto et al. (2016). Theáp ñ: mean of the p value for the aggregated models.
eestimates range from 1042 to 10 45 erg s-1. This wide range is a
Nmodel : number of aggregated models.
re 4. Top: Three example models of some of the best-fitting snapshots from the image library of GRMHD simulationsfconsequence of both physical uncertainties in the models used2
MIN( p ): minimum p value among the aggregated models.
pril 11 corresponding to di↵erent spin parameters and accretion flows. Bottom: The same theoretical models, processedgugh a VLBI simulation
pipeline withsame theschedule,telescopecharacteristics,
and weather
parameters as in the April
Pjettheand
wide
range
in length
and timescales
to estimate
MAX( p ): maximum p value among the aggregated models.
3

c dist. of snapshotspc

1 obs.
probed by the observations. Some estimates may sample adifferent epoch and thus provide little information on thestate ofions
thewithcentral
engineduringNevertheless,posed of non-relativistic
temperature
Ti
As an EHT2017.
example, the top
row of Fig. 4 shows three• Overall,
the
image
consistent
44
relativistic
electronswith temperature
Tobserved
simmodelsnapshotsfromtheImage Library withwith expectations for thee . A yield
PjetGRMHD
~ 10
erg
s-1is
(e.g.,
Stawarzobservationsof HST-1
rescription for the ratio of the temperatures of thedi↵erent spins and flow type, which fitted closure phasesby changing
the eDF. The eDF and Pout are coupled because Pout is~70
pc predictedof theofcentral
engineand,et al. 2006). of
HST-1
iswithinaa single
Kerrbyrelativity
species can shadow
then be imposed in termsofpa- BHsand amplitudes
the April 11 data
best.general
For these modṀ , and Ṁ is adjusted to produce the observed
determinedbytakingaccountofrelativistic
time
foreshortening,
may
be
ter Rhigh (Mościbrodzka et al. 2016), such that theels we produced simulated visibilities for the April 11
andtheweatherand calibrated themof the emissionsamplingcomes either fromaccretionengine
disk
compact mm ﬂux. The relationship between Ṁ and mm ﬂux
Pschedule
lastparameters,
few decades.
the thecentraljet over•, TSomany
modelsareThislikely because the sourcell Rhighwith aacceptable.
synthetic data generation andcalibrationis
pipelinee ' Ti ) or from the jet (large Rhigh ,Furthermore,
the
1.3
mm
light
curve
of
M87
as
observed
depends upon the eDF. If the eDF is altered to produce mm
Ti /Rhigh ) . While this prescription is not the only
(Blecher et al. 2017; Roelofs et al. 2019a). The simulated
150%
over
decadetimescalesby
SMA showsless efﬁciently (for example, by lowering Te in a thermal
structure
is simple,
dominatedthephotonring
possible, it has
the advantage
of being
suffi- variability
data wereby
then imaged
withthesame pipeline
usedphotons
forly generic, and(Bower
robust (seeet
Paper
for a discussion
observed
images. The similarities
between the simal. V2015).
Based onthethese
considerations
it seems
model), then Ṁ and therefore Pout increase. A typical nonthermal
on-thermal particles and radiative cooling).
ulated images (bottom row of Fig. 4) and the observed
reasonable
to
adopt
a
very
conservative
lower
limit
on
jet
eDF,
by contrast, is thenlikely to the
producemm photons with greater• GRMHDIf powertheBH
andscale jet are aligned,
BH
nce eachsimulation
canspinbe used42
todeare remarkable.
-M87’s1images (Fig. 3)large
º
P
=
10
erg
s
.
efﬁciency by shifting electrons out of the thermal core and into ae several di↵erent physical jet,min
scenarios by changing
Overall, when combining all the information contained
spine
vectorispointedaway
prescribed electron
function,
we have
both theSimulation
Library
and Earth
Image
thePjet Library, nonthermal
Todistribution
apply
this
constraint
weinmust
deﬁneandfrommeasuretail. It will therefore lower Ṁ and thus Pout . A thermal
the SimulationinLibraryto generate
morethan 420 is discussed
physical origin
the emission
features ofA.
the image obour models.
Our
procedure
in ofdetailin Appendix
eDF with lower T could have higher Pout , as is evident in the largen and imaged in the same way as Fig. 3. Note that although the fit to the observations is equally good in the three cases,
refer to radically di↵erent physical scenarios; this highlights that a single good fit does not imply that a model is preferredothers (see Paper V).

Other constraints• Radiative efficiency• Lbol/Mdot c2 < thin disk radiative efficiency• Simultaneous X-ray observation (2-10 keV)
• Single IC scattering of synchrotron photons• Pjet ~ 1042 – 1045 erg/s• Conservative lower limit: 1042 erg/s• All a*=0 models rejected• SANE models with |a*|=0.5 rejected
2

PBZ ⇡ 2.8f (a⇤ )( /50) Ṁ c<latexit sha1_base64="odQsJErxXmIa2nnkDOp2/mNB9u8=">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</latexit>2f (a⇤ ) ⇡ a2⇤ (1 +<latexit sha1_base64="e37W8XAsplDMrUes1IlXXlv+7JA=">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</latexit>p1a2⇤ ) 2(for a* < 0.95)

Other constraints

Results: SANE model

raint:
data models:fitting, radiative
efficiency,
X-ray,efficiency,
jet power X-ray, jet power• SANE
EHT image,radiative
a/Rhigh

1

10

20

40

80

160

-0.94

-+++ ++++ ++++ ++++ ++++ -+++

-0.5++- - ++- - +++- +++-

0+++- +++- ++- - +++- ++- - ++- -0.5+++- +++- +++- +++- +++- +++-

0.94

+-+-

+-+-

-++-

++-+

+++- +++- ++++ ++++
Mdot/MdotEdd ~ 10-5 – 10-4

Other constraints

Results: MAD model• MAD
EHT image,radiative
efficiency,
X-ray, jet power
traint:datamodels:fitting, radiative
efficiency,
X-ray,
jet power
a/Rhigh

1

10

20

40

80

160

-0.94

- -++ -+++ -+++ -+++ -+++ -+++

-0.5

+-+-

+++- ++++ ++++ ++++ ++++

0

+-+-

+++- +++- +++- +++- +++-

0.5+-+- ++++ ++++ ++++ ++++ ++++

0.94+- -+ +-++ ++++ ++++ ++++ ++++
Mdot/MdotEdd ~ 10-6

Discussion• Radiative effects: GRMHD vs radiation GRMHD• Non-thermal electrons• Analysis limitations• Fast light approximation• Untilted disks• Pair production• Floors• Alternatives to Kerr BHs

EHT data + EAVN data

, (,• High cadence observations of M87/SgrA*• Data quality comparable to VLBA
• 22/43 GHz à spectral index),

EHT 2020 forecast• EHT Collaboration, ALMA Cycle 7 M87 Proposal• 3 more telescopes including Green Land Telescope will
make it so sensitive as to detect extended component

Event Horizon Telescope
The EHT Collaboration et al.

The Astrophysical Journal Letters, 875:L1 (17pp), 2019 April 10

the
ine
In
the

ted
the
the
gnach
rd.
the
in
all
his
ral
air

ter
nd
les
of
rm
ths
her
by
of
ng
gan
ray
BI
to
BI

Figure 1. Eight stations of the EHT 2017 campaign over six geographic
locations as viewed from the equatorial plane. Solid baselines represent mutual
visibility on M87* (+ 12° declination). The dashed baselines were used for thecalibration source 3C279 (see Papers III and IV).

• Angular resolution q ~ 1.3 mm/104 km ~ 25 µas

median zenith atmospheric opacities at 230 GHz ranging from0.03 to 0.28 over the different locations. The observations werescheduled as a series of scans of three to seven minutes induration, with M87* scans interleaved with those on the quasar*

olds for R|⌦F |/c

1 and=

holds for R|⌦F |/c

1 and

1
˜
R̃2 ⌦2F withR|⌦˜ F⇠| 1, where the letters
tilde
1
1
⇠
2
which holds forcR|⌦
1
c
F |/c

Parametrize electron
A.4.distribution
Non-thermal Electrons˜ ⇠ 1, where the letters with tilde dnumber density of the non-thermal electrons, n, is assumed to b
numberdensityof thet) = 0, by following BL09, although itA.4.
isThe
not
so
obviouswhether
Non-thermal
ElectronsBL
r
·
(nv)
=
0,
by
following⌦F 6= 0, the continuity equation is reduced to
For RBn,⌦Fis 6=assumed
number density of the non-thermal electrons,
to be g
⇣ n0, ⌘the continuitv) = 0, by following BL09, although it is not so obvious whether the
B·r
= 0,
2
B ⌦F 6= 0, the continuity equation is reduced toB⇣ n ⌘means that n scales with B along a given
field.
In this
which
that
n
scaleswi
Bmagnetic·meansr=
0,
2
A constantfraction
electronstion of the non-thermal electrons on theplaneszBof=ofthe
±z
(zare
0)
1
1
distribution
non-therma
assumed to have power-law energy2 In this pa
distributionmeans that n scales with B along a given
magnetic field.
(R Rp )
bution of the non-thermal electrons n(R,on the±zplanes
z
=
±z
(z
0):
1
1 ) = n0 exp 1
2 22
(R Rp )
exp
where
Rnp0planeisthe andradius where
1) =Rp is the radius where n have then(R,peak±z
on
the
gives
2
2
density at
the R
peak.
We noteat the peak. We note that BL09 consideredonly
p = 0, wherejetaxis
at z =gives±z1 . theRpaxisis then have the peakon=the
the
plane
and
et
at radiusz = ±zwhere
1.
- zon
Δ
=
5
r
:
fixed
1
g
Equations
and
(A31)
y
at
the
peak.
We
note
that
BL09
considered
only
R(A30)= 0,non-therm
where
th
pthe
tions (A30) and (A31) give the number
densityofR:varied0pfieldlabeled by
as follows:
0 z = ±z1 .
eeled
jet axisatby
as follows:2Turbulence cascade• Alfven turbulent cascade• MHD inertial range-> ion Larmor scale(conversion to ion heating)-> kinetic Alfven waves(ultimately heating electrons)

Howes 2010

• For low beta, ion thermal
speed << Alfven speed, sothat ions cannot interact with
Alfvenic perturbations-electron heating ratio Qi /Qe vs. i (left) and T i /T e (right). We take the time average in the steady state for a period & 5tA , where tA is Alfvén t
barsKawazura,show the standard
deviationof the time series. 2018
The dotted lines in the right panel show the fitting formula (2). The inset in the left panel is
Barnes& Schekochihinmodel proposed in [7], based on linear theory: note the much lower ion heating at low i , absence of a “ceiling” at high i and a more dramat

GRMHD code comparison

Porth+2019

has a much higher net polarization (≃15 per cent compared to ≃1 per cent forRH40), which is not seen in SMA observations of M87* (Kuo et al. 2014).

Polarization

Faraday rotated is depolarized, and we pick up signals only fromthe polarized emission in front of the accretion disc that experiencesa much weaker Faraday rotation. As a consequence, the measured
RM is fairly independent of the disc density (Ṁ) or temperature(Rhigh ).

Synchrotron radiation is intrinsically highly polarized (up to
100 per cent, e.g. Pandya et al. 2016), but in our images the brightest regions (in Stokes I) are depolarized to 10 per cent and the total
linear polarization degree is 1 per cent on average (in all models except in model RH1, see the last column in Table 1). What is causing
the strong depolarization? We recompute model RH40 using lower
and upper hemispheres of the GRMHD simulations to investigate!
thepolarimetricof light
comingthethecounterjet andFigure 5. First and second panels: polarized
emissioneach pixel originatingfrom below(blue) andfrom
above (red)mid-plane together
with
Q2 + U 2 for properties
polarization ticks for model RH40. Third and fourth panels: same as first and second panels but with Faraday effects switched off. The model without Faraday
forwardjet,andrespectively.
Fig. 5 shows the structure of linear poeffects shows coherent polarization signals fromboth counter
forward jets.
larization intensity and orientation of the polarization plane of thecounter jet and forward jet. In Fig. 5, the counter-jet polarization
MNRAS 468, 2214–2221 (2017)(first panel) is evidently significantly scrambled compared to thecoherent signal from the forward jet (second panel). The total LP
g from below (blue) anddegree from the counter jet is 1 per cent. This is smaller than theL09 (right) models. Each
total polarization degree of the forward jet which is 3.1 per cent.
The forward jet, above
The forward
counter jet LP flux ratio is about 2.2. In the third andssion
in the BL09 Dexter,
case. Davelaar
Moscibrodzka,& Falke to2017Black Hole Shadow
Non-spinning Black HoleMaximumly Rotating Black Hole

~4.8 Rs~5.2 Rs

Figure credit: H.-Y. Pu