AGN Jet Workshop 2020
"Active Galactic Nucleus Jets in the Event Horizon Telescope Era"Top

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12/5/2019

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

EventHorizonRadiogalaxyM87Telescope(Virgo A, 3C274)
The EHT Collaboration et al.

Event horizon apparent radius ranking

ObjectFigure 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).

VLBA 7mm(Junor+1999)

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
3C 279. The number of scans obtained on M87* per night
ranged from 7 (April 10) to 25 (April 6) as a result of different
observing schedules. A description of the M87* observations,
their correlation, calibration, and validated ﬁnal data products ispresented in Paper III and brieﬂy summarized here.
At each station, the astronomical signal in both polarizations
and two adjacent 2 GHz wide frequency bands centered at
227.1 and 229.1 GHz were converted to baseband using(108 Msun)

SgrA*

0.04

Sombrero

10

M87

1kpc (2 106Rs)

MBH

M84

Cen A

60

8.5
0.5

d
1Rs
(Mpc) (μas)
0.008

10

9.0

2.2

3.8

0.3

16.7
17

7
1

Photon ring~5 Rs• 1mas = 0.08pc = 140Rs• Technical developments for VLBI at 1.3 mm (230 GHz)
• Angular resolution q ~ 1.3 mm/104 km ~ 25 µas• “The Rosetta Stone of
AGN jets”

M87• Low-luminosity AGN with
Lg ~ 1042 erg/s ~ 10-6 LEdd(for MBH ~ 6 x 109 Msun)• Radiatively inefficient accretion
flow (RIAF)• rg ~ 1015 cm, rg/c ~ 10 hr• Radio jet (FR I type)
Ljet ~ 1042 – 1045 erg/s• BZ process?
• Ljet ~ Mdot c2 ?

Walker+2018

86 GHz (3.5mm); VLBA+GBT

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

Hada et al.

15 GHz;
VLBA+VLA(VSOP also detected
the triple-ridge)
Continuing
triple-ridge
structure(mas)

The Astrophysical Journal, 803:30 (12pp), 2015 April 10

z = 5mas
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

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

(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
Arons 1991), here we assume that minimum ener
electrons and positrons are the same for(mas)simplic
z = the15mas
z = SSA
30masfrequency, we obta
evaluating
emission at the-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,
Asada
Hada+2013,
2016,
2017;
Nakamura+2018;
Takahara+2015
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
9

g

B

5

g

6

g

v

()

GRMHD simulations• Magnetohydrodynamic
simulations in fixed Kerr
spacetime• Radiatively inefficientaccretion flow (RIAF)• Spinning BH-driven jet
where B2/rc2 >> 1 via
Blandford-Znajek process
Blandford & Znajek 1977;
KT & Takahara 2014;2016

e.g. Koide et al. 2000; Komissarov 2001;
McKinney & Gammie 2004; Noble+2006
Barkov & Komissarov 2008; Tchekhovskoy et al.
—Initial (left) and final (right) distribution of A . Level surfaces coincide with magnetic field lines, and field line density corresponds to poloidal field.
In the initial state field lines follow density contours if " > 0 :2 "2011; Ruiz et al. 2012; Contopoulos et al. 2013!

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

urnal, 777:13 (9pp), 2013 November 1

i = 30°Chan, Psalt

i = 60°5

i = 90°p
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8

0 a=0

0 a=0

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

-5a = 0.999-50α0-coordinate (M)5

a = 0.999-50
5Simulated
α0-coordinate(M)EHT observations-5

a = 0.999-50α0-coordinate (M)5round Kerr black holes with different spins aand observer inclinations i. The left, central, and right panels show the photon rings f• eachPhotons
will haveorbitedthe spins—from
BH
ly. Inpanel, different
colors represent
different
black being a= 0 •to red
being
a = 0.999.shape
For each inclination
The
shadow
does
very weakly
the black(nearhole spin.
Moreover,the photon ring retains its nearly circular shape even at high black hole spins; amanyontimes
theunstable
NOT strongly depend on
or a !orbit),
0.99 and picking
at large inclination
angles.brightness
up extra
BH spinfigure is available in the online journal.)

on their way to the observer

Holz & Wald 2019a Gralla,= 0.369043

a = 0.974881 R. Takahashi 2004; Chan,a =Psaltis
0.999& Ozel 2013; Pu+2016

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 di↵erent 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

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

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0

1

2

3

4

5

Brightness Temperature (109 K)

6

Paper V: Physical origin of the asymmetric ring
The Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10

The EHT Collaboration et al.

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

• Working hypothesis: Kerr BH with -1 < a = Jc/GM2 < 1

In Section 6 we combine EHT data with other constraints on the(e.g., Johannsen & Psaltis2010). For an a* = 0 black hole*radiative efﬁciency, X-ray luminosity, and jet power and showof mass M and distance D, the photon ring angular radius onØ constraint
GRMHD
simulations+ GRRTimagingIn
the sky isthat the latter
eliminates
all a* = 0 models.
Section 7 we discuss limitations of our models and also brieﬂy
27 GM
discuss alternatives to Kerr black hole models. In Section 8 we
qp ºsummarize our results and discuss how further analysis of existingc2D• Examine if the model is consistent with the EHT dataRough estimatesTi ⇠ 0.3 Ti,vir ' 1012
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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• Time-averaged images• i = 163 deg (Accretion disk
angular momentum)

SANE• Arrows: BH spin vector
projected onto the sky

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.

• So many models are
acceptable. This is likely
because the source
structure is dominated by
the photon ring
• Asymmetry is controlled
3.3. Image Library Summary
by the BH spin (except
The Image Library contains of order 60,000 images. We
generate images from 100 to 500 distinct output ﬁles from each of
the SANE Rhigh < 10)= 1, 10, 20, 40, 80 , and
the GRMHD models at each of R
high160. In comparing to the data we adjust the PA by rotation andThe Astrophysical Journal Letters, 875:L5 (31pp), 2019 April 10

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.

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=">AAACkXichVHLLgRBFD3ae7wGG4lNx4SMx0yqh8RjNWEjsfEaJIZJd6uho6e7dddM0JkfsLSxsCIRET9gi40fsPAJYkliY+FO60QQ3E5XnXvqnlunqjTHNDzB2EOVVF1TW1ff0Bhpam5pbYu2dyx5dtHVeUa3Tdtd0VSPm4bFM8IQJl9xXK4WNJMva9tTlfXlEnc9w7YWxZ7D1wrqpmXkDV0VROWiQ/m4mhvol7Oq47j2rkzJekqOK4NZb8cVvpIIiHL/up9IlXPRGEuyIOSfQAlBDGHM2tFzZLEBGzqKKIDDgiBsQoVH3yoUMDjErcEnziVkBOscZURIW6QqThUqsds0blK2GrIW5ZWeXqDWaReTfpeUMnrZPbtgz+yOXbJH9vZrLz/oUfGyR7P2oeVOru2ga+H1X1WBZoGtT9WfngXyGAu8GuTdCZjKKfQPfWn/6HlhYr7X72On7In8n7AHdksnsEov+tkcnz9GhB5A+X7dP8FSKqkMJ1NzI7H0ZPgUDehGD+J036NIYxqzyNC+h7jCNW6kTmlcSkthrVQVajrxJaSZd3JDmC0=</latexit>p1a2⇤ ) 2(for a* < 0.95)

Other constraints
Results: SANE model• EHT image, radiative efficiency, X-ray, jet power

nstraint: data fitting, radiative efficiency, X-ray, jet powera/Rhigh

1

10

20

40

80

160

-0.94

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

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

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

0.94

+-+-

+-+-

1

10

-++-

++-+

Results: MAD model+++- +++- ++++ ++++

nstraint: data fitting, radiative efficiency, X-ray, jet powera/Rhigh

20

40

80

SANE
Mdot/MdotEdd ~ 10-5 – 10-4
MdotEdd = 10 LEdd/c2

160

-0.94

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

-0.5

+-+-

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

0

+-+-

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

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

0.94+- -+ +-++ ++++ ++++ ++++ ++++

MAD
Mdot/MdotEdd ~ 10-6

EHT2017 Summary• EHT 2017 data are consistent with the hypothesis that• 1.3 mm emission arises within a few rg of a Kerr BH• Optically-thin synchrotron emission of thermal electron in RIAF
• Image is generated by strong grav. lensing & Doppler beaming• M = 6.5 +0.7-0.6 x 109 Msun (M/D = 3.8+0.4-0.3 µas), which isconsistent with previous estimate based on stellar
dynamics• The strongest evidence for the presence of SMBHs incenters of galaxies• Case of a* = 0 rejected by condition Pjet > 1042 erg/s• The jet is driven via BZ process in the models with a* ≠ 0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

Connection of the ring with the jet
Nakamura et al.
Nakamura+2018• 2D high-resolution MHD simulation• Stagnation surface• Relativistic blobs by MHD instability?

• What is an observational evidence of the
BZ process for the jet production?
• Observed relativistic blobs --- s > a few• B strength estimates from core size (Kino)• Sharp limb-brightening (K. Takahashi)• Only jet edge shines?
• No effective particle injection (Shigeo)• Gap formation – null surface (Kisaka)nGJ ~ B/(4p e rg) ~ 10-5 B2/M9 cm-3
• Gamma-ray origin?

• Spine emission? (Ogihara; Shuta)

30

25

20

15

10

5

0

-4 -3 -2 -1 0 1 2 3 4X(mas)

dence of the image on the free parameters on
ometry of the jet ⇥ and ⌫ and those on the espatial distribution
and z1 .

3.1. Triple-ridge Structure

Figure 1 shows the resultant image with the ctional resolution (left panel) and the one convol
the Gaussian beam (right panel). The Gaussi
size is represented as the gray circle in the bocorner of the right panel. For both of the im

Figure 1. Left panel: The computed image with the computational resolution of 3RS . Right panel: The image convo
the beam size (1.14 mas ⇥ 0.55 mas), where the beam size is plotted as the gray circle at the bottom left corner. The
is normalized by each maximum value, and the contours represent the intensity at 2 k (k = 1, 2, 3, ..., 27 for the left p
k = 1, 2, 3, ..., 21 for the right panel). The number of the contour lines is not the same as in T18. Note that 1 mas coto ⇡ 136RS .

model such as the radiative cooling and reaccelerationof electrons. In this paper, we treat A and n0 arbitrarily
and focus on the relative intensity along the transverse
direction of jets in order to simply illustrate our novelidea on the mechanism for the triple-ridge images.

3. RESULTS

In Section 3.1, we show the resultant image of thetriple-ridge structure, and figure out its physical origin.
In Section 3.2, we demonstrate the parameter depen-b ~ b p ~ g (q , n ) ,ccagnetic ﬁeld conﬁguration is not much different
ere
B and
E denotethe magnetic
andﬁelds,
a general
relativistic
treatmenteven
neartheelectric
hole a=0.1⎛ Ra=0.998⎞-1Keplerian
disk
Kerr
BH
with
Kerr BH with∣∣WF
⎟ [g (q , n )bf ~ ⎜
pectively.
Here, Thethe images
standardwill
cylindrical(R, fresultant, z ) are radio
Narayan 2007).
⎝ c ⎠rdinates,thesubscript
pis
assignedforthepoloidal
antly changed as long as we focus on the limbβ denotes the speed normalized
ures seenf̂far
the centralunit
warpedregion.
We
is from
the azimuthal
vector,and W
mponent,
Y)
F = WF (wherethat is an order of tenth and appro
desponds
formulation
Appendixfrequency
A and brieﬂy
explain ﬁelds.factor
to theinrotationalof magneticItults
jet axis (θ=0, π; see Figure 12). That i
uld below.
be noted that the magnetic ﬁeld is wound up andby the poloidal component an
idal dominant, B ~ ∣Bf∣, for R∣WF ∣ c  1, while it dominatedisElectromagnetic
B ~ ∣Bp ∣, Field
oidal2.1.1.
dominant,for R∣WF ∣ c  1.
around the jet axis if R∣WF ∣ c  1. For
other hand, the following relations are oaxisymmetric force-free ﬁeld, a stream function Ψ
2.1.2. Fluid BL09,
Velocitywe assume aromagnetic ﬁeld. Following
R∣WF ∣,
b~b~
controlled
paraboloid-likejet determined
instead of anf
he ﬂuid velocity
cannot bein exact
the force-freeTakahashi
etal.
triple-ridge structure corce-freeﬁeld. since
The stream
functionis givenbyt in principle,
the inertia
is totallyneglected.
InContinuing
this⎛ RWF ⎞2 1
2WF Y v, as the ﬂuid
er,following drift velocity,
en we use then⎟
Y = Ar (1 B cos q ). Bf = B
, (1)
(3 )
bp ~ ⎜
ng by following BL09:ocity⎝ c ⎠ g (q , n )Rcor2F(r, q, f ) denote thexpression,
1Bf standard sphericalRBWpmb- v = E ´ B c =E-=RW
W

Y
=
f.ˆ 0
´ B , (That(4)ﬂuid velocity is not relativisti
FB +areˆR5) is, theWfz.
nd the minus 2and plus signaturesforFc 2 pF c2
eldY(mas)
the toroidal component.
B
B
B
pectively.
Here,
ν
is
the
parameter
tocontrol
the
he
where
B holds
and Ethedenotethe magnetic
andelectricﬁelds,
velocity
followingconditionsforthez = 15mas
z = 30mas
ere
ν=1
gives
paraboloidal
jets,
and
A
is
a
z = 5masjetaboverespectively.
Here,
are
the
standard
cylindrical
(
R
,
f
,
z
)
2.1.3.
NonthermalElect•
Fasterrotation,
v
>>
v
,
2 -by
npB],Equations
ftromagnetic
ﬁeld ofgiven(2)–(4):(1) thehas
the dimension
with
B
being
the
[
r
cal
coordinates,
the subscript
p is assigned for the poloidalLessasymmetric
&
ocity
does
not
exceed
the
speed
of
light
in theentire regionMotivated by the limb-brightened jets,ka
The electromagnetic
ﬁeld
is
then
given
by
f̂ is the azimuthal unit vector, and wherecomponent,
W =W
)
F (Y
counter-jet
thenonthermal
electrons are distriburen - 2Dimmer, (2) the electricﬁeld vanishes in the ﬂuid rest frameF
corresponds
totherotationalfrequencyofmagneticﬁelds.
It
1 is notbeaxis, in contrast to BL09, who assumed th• BButlimb
frozen-in
condition),(3)sharp
the velocity is asymptotically
ˆ ,so
=
´and
f
(2) is woundpshould 
beY notedthat the magnetic ﬁeld
up and to the axis. Such a spatial di
are clinging
same as in Rcold, ideal MHD when R∣WF ∣ c  1 (seeB ~ ∣Hada
Bf∣, 2018;
1, while& itKT istoroidaldominant,for R∣WF ∣ c 
K. Takahashi,
KT, Kino,
Takahashi
2019
ourpendixA.3). Figure
1Nakamurasketches&an
exampleOgihara,of the K.
twistedM87 proper motion
The Astrophysical Journal, 868:146 (28pp), 2018 December 1

Nakamura et al.

Figure 16. Distribution of Γβ as a function of the jet axial distance z (deprojected with M=6.2×109 Me and θv=14°) from the SMBH in units of rg. The data ofproper motions are taken from the literature (Reid et al. 1989; Biretta et al. 1995, 1999; Kellermann et al. 2004; Cheung et al. 2007; Kovalev et al. 2007; Ly et al.
2007; Giroletti et al. 2012; Meyer et al. 2013; Asada et al. 2014; Hada et al. 2016; Mertens et al. 2016; Hada et al. 2017, labeled as R89, B95, B99, K04, C07, K07,
L07, G12, M13, A14, H16, M16, and H17, respectively). Theoretical expectation by utilizing the FFE parabolic (z∝R1.8) jet solutions (NMF07; TMN08) is also
displayed with varying Kerr parameters (a=0.5: dotted line; a=0.7: dashed line; a=0.9: triple-dot-dashed line; a=0.99: solid line). The vertical solid line with

Jet edge: mass mixing reduces velocity?
2

1.6

M87 spectrum

No. 1, 200910

FERMI-LAT γ -RAY D

-10

-11

-2

10

-1

• Jet SSC modelr ~ 1016 cm
B ~ 55 mG• Matter dominant
at 10 rg?

νFν [erg s cm ]

10

-12

-13

10
10

-14

-15

10
10

-16
8

10

10 10

12

10

10

14

16

10

18

20

22

10 10 10
ν [Hz]

24

10

26

10

10

28

30

10

Figure 4. SED of M87 with the LAT spectrum and the 2009 January 7 MOJAVEVLBA 15 GHz and Chandra X-ray measurements of the core indicated in red.
The non-simultaneous 2004 TeV spectrum described in Figure 2 and Swift/
BAT hard X-ray limits (Section 3) of the integrated emission are shown in lightbrown. Historical measurements of the core from VLA 1.5, 5, 15 GHz (Biretta
et al. 1991), IRAM 89 GHz (Despringre et al. 1996), SMA 230 GHz (Tan et al.
2008), Spitzer 70, 24 µm (Shi et al. 2007), Gemini 10.8 µm (Perlman et al. 2001),
Hubble Space Telescope HST) optical/UV (Sparks et al. 1996), and Chandra
1 keV from Marshall et al. (2002, hidden behind the new measurements) areplotted as black circles. The VLBA 15 GHz flux is systematically lower than thehistorical arcsec-resolution radio to infrared measurements due to the presenceof intermediate scale emission (see, e.g., Kovalev et al. 2007). The blue line
shows the one-zone SSC model fit for the core described in Section 3.

Abdo+09

VLBA measurements of the core. Also plotted are historical
radio-to-X-ray fluxes of the core (see Sparks et al. 1996; Tan

lsyn
3me c
=
rg
4 T U B c ± rg✓
◆ 3/2 ⇣
B
⌫syn ⌘ 1/2
⇠1
,
20 G
230 GHz(⌦/⌦H ) ' 0.24, 0.23, 0.33, and 0.4, for a⇤ = 0.5, 0.7, 0.9,
and 0.99, respectively, where ⌦H = a⇤ c/2 is the anglularvelocity of the BH. These values are roughly consistent(6)
with those in Tchekhovskoy et al. (2010).
Using the above model, we calculate the image of thewhere we have assumed that the Lorentz factor of bulk
stagantion ring. We assume that it is vacuum outside
motion
is
⇠
1
at
the
stagnation
surface,
and
⌫
=
syn
stagnation ring
because photon
we focus onring
the theoreti• We
consider a toy model of emission thering• Clearis2eB ±/2⇡me c.
cal image of the localized emission due to the stagnaat the deepest stagnation regions
observed more easily intion ring, which might mimic the ring-like image obcaseof diffuse,nonserved in M87. The thegeneralrelativistic
radiative transfer
equations are solvedlocalized
by using RAIKOU.
We integrate theemission
geodesic equations of photons by solving the Hamilton’s
stagnation
canonical equationsof motionin the model
Boyer–Lindquist• The
simplering
coordinate which are discribed in Schnittman & Krolik
indicates the ring at(2013), using the 8th-order Runge–Kutta method withapproaching
jet appears
adoptive stepsize control(Press et al. 2002).
For theradiative process, we
Synchrotron emistoincorporate
be toothebrightBH
sion and absorption via the non-thermal electrons. We
use the coefficient of emissivity and the absoption in
Legg & Westfold (1968), which we numerate and tab22ulate without assuming min⌫p Kawashima+⌧ ⌫ ⌧ max⌫ini.e.,p , prep.
2
2
without assuming min ⌫p ! 0 and max ⌫p ! 1 (seeWestfold 1959; Dexter 2016, in detail), where ⌫p =Figure 1. Location and geometry of the stagnation ring for
3eB sin ✓B /4⇡me c. Following some works based on semithe model with a⇤ = 0.5, 0.7, 0.9 and 0.99. Blue, filled circle
display the stagnation ring. Gray curve present the funnel
analitic models (e.g., Pu et al. 2016), we fix the angle
wall with= b2 /⇢ = 1, which is well described by the
between the ray and the magnetic field ✓B to be ⇡/6 formagnetic stream function (r, ✓) = (r/rH ) (1 p cos ✓) = 1,
the sake of the simplicity.
where radius of the outer horizon rH = rg (1 + 1 a2⇤ ) For
Throughout this work, the mass of the BH is set tothe location of the stagnation surface based on the GRMHD
be 6.5⇥109 M . As discribed above, we parameterizesimulations, see Figure 14 in ?.
the BH spin to be a⇤ = 0.5, 0.7, 0.9, and 0.99. The
observer screen, which has field of view 160µas ⇥ 160µas
The physical quantities of stagnation ring is demondivided by 2400⇥2400 pixels, is located at 104 rg withstrated as follows. We set the magnetic field strengthviewing angle i = 163 . To calculate the radiative flux,
B =100 G, which is consistent with the estimated value
we assume that the distance from the BH to the Earth
fu n

ne
lw

all

Stagnation ring model (Preliminary)Photon ring
2

Michael D. Johnson et al.

a = 0.94, R= 10

Figure 1. Time-averaged image of a GRMHD simulation of M87
with parameters chosen to be consistent with the 2017 EHT data.
This model corresponds to the high magnetic flux “Magnetically
Arrested Disk” accretion state with parameters M = 6.2 ⇥ 109 M ,a/M = 0.94, ✓obs = 163 , rhigh = 10, and mass accretion rate
matching the 1.3 mm flux density (see Paper V for details). The

Johnson+2019-

Figure 2. Photon shell and photon ring of a Kerr black hole withspin a/M = 0.94. Top: cross section of the photon shell in the (r, ✓)plane in Boyer-Lindquist coordinates. The spin axis is vertical andthe color varies with r. The intersection of an observer’s line ofsight with the photon shell boundaries at r = r± determines then,M87 jet observations (activated by
Whereis the central engine?
East-Asia
researchers)
0.0

-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

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)

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

Ongoing & future works• Polarization: further constraints on ne, B• Need parameter survey• 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 developed by ASIAA, Taiwan• Lower optical depth & higher spatial resolution• -> Kawashima+2019; Nakamura+2019 in prep.

EHT data + EAVN data

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

GMVA + ALMA 2020 forecast

Fig. 2: GRMHD+GR Ray-Tracing (GRRT) images and simulated GMVA(+ALMA) observations of the M 87
jet. Top and bottom: jet formation with high [22,14] and low [21,8] magnetic flux (BH spin a ⇠ 0.9).
• toEHT
7 +withGMVA
Proposal
From leftright: Collaboration,
Simulated jet emission,ALMA
simulatedCycle
observation
GMVA+ALMA,
and without ALMA.
2 Immediate Objectives :• GMVA = Europe telescopes + VLBA & more [at 86 GHz]
• Proving high-/low-magnetization jet launching via imaging the jet base : New state-of-the-art numerical •simulations
predict brightring-like synchrotron
the jet base (Fig.emission2). Standard jet
Asymmetricapproaching-jet&emissionbrightatcounter-jet
formation intheorythat theseoutflows are collimated and launched by magnetic fields, which extract
theposits
small
f modelangular momentum from the spinning BH [3]. From this it follows that a stronger e↵ective magnetic flux2

The first EHT results: 6 ApJ Letters
Paper I: The Shadow of the Supermassive Black Hole (Summary Paper)
Coordinators: G. Bower, H. Falke & D. Psaltis

Paper II: Array and Instrumentation
Coordinators: S. Doeleman, V. Fish & R. Tilanus

Paper III: Data Processing and Calibration
Coordinators:L. Blackburn, S. Issaoun & M. Wielgus

Paper IV: Imaging of the Central Black Hole in M87
Coordinators:K. Akiyama, K. Bouman, A. Chael, J. Gomez & M. Johnson

Paper V: Physical Origin of the Asymmetric Ring
Coordinators: C. Gammie, Y. Mizuno & H.-Y. Pu

Paper VI: The Shadow and Mass of the Central Black HoleCoordinators: K. Asada, A. Broderick, J. Dexter & F. Ozel

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*

• 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+0.7
obtainedmore
by ﬁttingto thebe2017
April 6 data, in mas, measured independently
using
the (left panel)
THEMIS
thanImageof the snapshots
models can
excluded.
9half Library
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
high
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• Small bump: a*< 0, SANE, R= 1, rejected by jet luminosity

Large-scale jet orientation PA~288 The 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* < 0Figure 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).

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• Parameter fitting results for
M87 are consistent indifferent codes

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

Participants to Paper V from East Asia region

T. Kawashima(NAOJ)

K. Toma(Tohoku)

M. Kino(NAOJ/Kogakuin)

We will connect jet-ring!

M. Nakamura(ASIAA)BHシャドウのスピン依存性
a=0

BH shadow

a=0.998
a = 0, 0.5, 0.998

BH

event horizon
analytic solution of shadow-surface• BH質量依存性：光子リング(BHシャドウ)のサイズはBH質量に比例。
• BHスピン依存性：サイズはわずか約±5%のずれ。
光子リング( シャドウ)の位置がスピン軸に垂直方向にずれるのみ。
• BH質量を決めるのには適している。一方でスピンを決めるのは困難。
Kawashima’s slide

64

観測者スクリーン

光子リング

2

0
-2

赤道面に射影-4

observer screen

-6
6
4
2

• 光子リングは大きさはスピンに依存しない

円盤内縁リング

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

0

転、逆回転で大きく半径が変わるため。

-2• 円盤内縁リングを形成する光子は光子球に乗る必要がないので角運動量の正負にあま

-4
-6
-6

observer screen
-4

-2

0

2

4

6

り依存しない。

Kawashima, Kino & Akiyama 2019

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