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Emission from relativistic
accretion disks probing the strong gravity near the event
horizon of BHs
Yuan, Ye-Fei（袁业飞）
Department of Astronomy, USTC
(NAOC, 03/27/2013)
Collaborators:
Li, G.X., Cui, Y.D. (USTC)
Shen,Z.Q., Cao, X., Huang, L., You, B. (SHAO)
Wang, J.M., Li, Y.L., Zhang, S. (IHEP), Wang, J.C.(YNAO)
Outline
Dynamics of Accretion Flows
Emission from Flows: Ray Tracing Method
Probes of Strong Gravity
Part I:
Dynamics of Accretion Flows
Description of motion of the fluid
in accretion flows Kerr Metric:
Reference Frames: LNRF, CRF, LRF
LNRF(ZMAO) u
CRF
)(,2/12
)(
r
AVu
LRF
VV r )(
Four velocity of the fluid: uμ(Ω,V)
Energy-momentum tensor and viscous stress tensor
Energy-momentum tensor
Viscous stress tensor
Alpha-viscosity (just one slide)
Sadowski, A., 2011, arXiv:1108.0396
Relativistic thin disk (Novikov & Thorne 1973)
M conservation:
L conservation:
Specific L
Comoving stress tensor
Keplerian ang. vel.
Viscous heating
Vertical structure:
Energy balance:
(radiation transfer)
Relativistic ADAF/Slim disk
Fr
A
dr
dsT
r
Mr
2
,6
24
0 )(2
ADAF
SSD/Slim
GRMHD—3+1 Form (Baumgarte, T.W. & Shapiro, S.L. 2003)
Einstein’s Field Eqs in 3+1 Form
Time vector
Metric:
Eric Gourgoulhon gr-qc/0703035
Maxwell Eqs.:
Maxwell Eqs. in 3+1 form:
e.g. Thorn & MacDonald 1982
Part II:
Emission from Flows:
Ray Tracing Method
Ray Tracing Method β
α
(α,β) . Integral of motion of photons:
EQqEL
ppH
LEapQ
PL
pE
z
z
z
t
/,/
1,0,2
1
2
1
cotcos
2/1
222222
Two impact parameters:
obspaq obsobs
obs
2/1222 )cotcos(
sin
Equation of photon trajectroy:
Analytic solution of photon’s trajectory:
where,
Part III:
Probes of Strong Gravity
Probes of Strong Gravity
Continuous spectra
Broad emission lines
Reverberation
Images of accretion flows
Polarization
X-ray Microlensing
TeV variation from M87
MCD spectra
Influenced by BH spin
Prominent in XRBs
Relativistic SSD/Slim: One temperature disk
3.1 Continuous spectra
Why XRB?
•Mass Estimation
•Inclination Angle (Superluminal Motion)
•Bright, Easy to Observe
What can MCD tell us about Spin?
•Effect of Spin
•Degeneracy Between Spin and Inclination Angle
Li.L.X .et. al 2006, Shafee. R .et.al 2006
Our motivations
•Study the spectra from slim accretion disks
•Study the influence of spin and Inclination angle
on the emergent spectra
•Quantify the error of Standard Accretion Disk
model in estimating spin
Physical Effects: Heat Advection
Li, Yuan, Cao (2010)
Physical Effects: Disk Thickness
•Left: No Thickness, Right: With Thickness, M_dot=2, a=0.98, 600
Emergent Spectra
Li, Yuan, Cao (2010)
Implications for Accretion Rate Estimation
Li, Yuan, Cao (2010)
Accretion disks with coronae
You, Cao, Yuan, 2012, ApJ
the spectral index in the infrared waveband depends on the mass accretion rate
and the black hole spin a, which deviates from the f(ν) ∝ ν1/3
X-Ray Reflection Spectra
Reynolds (1996)
Fabian et al. (2000)
Relativstic broad Fe K alpha line 3.2 Relativistic broad Fe K alpha line
Reynolds (1996)
Fabian et al. (2000)
MCG 6-30-15
AGNs
Fabian et al. (2009)
3.3 REVERBERATION
Time lag: ~ 30 s inner disk radius ~ Rg
Location of the hard X-ray emitters?
Effects of strong gravity: Shapiro delay …
Dynamics of the disk
REVERBERATION: Stellar BHs
•Time scale is too short: statistics, S/N
•1day@GRAVITAS ~ 1year@XMM-Newton
•Line redshift,…
MAPPING THE INNERMOST ACCRETION FLOW
Global simulations of accreting black holes
i=80
Armitage & Reynolds (2003)
http://jila.colorado.edu/~pja/black_hole.html
i=30
Armitage & Reynolds (2003)
http://jila.colorado.edu/~pja/black_hole.html
Variation of the emission line
(NGC 3516)
Iwasawa, Miniutti & Fabian (2004)
Sgr A* --- The Black Hole Candidate in Milky Way Galaxy
Mass : 4 x 106 M⊙
D : 8 kpc
Angular size of horizon : ~ 20 μas
From: Lei Huang
3.4 Images of accretion flows (BH shadow)
UN beam 1.11 mas x 0.32 mas @ 9o
Super-resolution 0.02 mas
unresolved (no extended structure) → single component
zero closure phases → symmetrical structure
(~E-W) elongated emission → consistent with λ≥ 7mm data
The first image of Sgr A* @3.5mm
Shen et al. 2005 Nature From Zhiqiang Shen
Yuan, Shen, Huang, 2006, ApJL
@7mm
@1.3mm
@3.5mm
Huang, Cai, Shen, Yuan, 2008, MNRAS
@1.3mm @3.5mm
θobs=0
θobs=45
θobs=90
Global structure of ADAF
Yuan, Cao, Huang, Shen, 2009, ApJ
Radiation Transfer Equation
Radiation Transfer Equation
)(
),,(
)(
/),(
),(
~
),(~
),(
~
3
0
0
3
00
xx
xkk
uk
xjj
x
II
xjIxukd
Id
obsem
emem
em
em
emem
em
θobs=0
Images of Sgr A*
Yuan, Cao, Huang, Shen, 2009, ApJ
θobs=90, 45, 0
Images @ 7 mm
a=-9.998 -0.5 0 0.5 0.998
Yuan, Cao, Huang, Shen, 2009, ApJ
θobs=90, 45, 0
a=-9.998 -0.5 0 0.5 0.998
Images @ 3.5 mm
Yuan, Cao, Huang, Shen, 2009, ApJ
θobs=90, 45, 0
Images @ 1.3 mm
a=-9.998 -0.5 0 0.5 0.998
Yuan, Cao, Huang, Shen, 2009, ApJ
Yuan, Cao, Huang, Shen, 2009, ApJ
Main conclusions
•Effects of BH spin:
For a>0, the larger the spin, the smaller the shadow
of BH, and the brighter the inner part of the disk.
For a<0, there is no significant difference.
•Effects of the viewing angles:
The larger the viewing angles, the smaller the BH
shadow which is even obscured at edge on case,
and the brighter the inner part of the disk.
•Effects of the observing wavelength:
The shorter the observing wavelength, the smaller of
the images.
•Application to SgrA*: fast spin or large inclination?
Laor, A. et al. 1990
3.5 X-Ray polarization
Comptonized disc’s thermal radiation
Comptonized disc’s thermal radiation
Schnittman and Krolik 2009
Reflection from the accretion disc
Scattered by the corona
Schnittman and Krolik 2010
Polarization of relativistic Ka line
Ogura, Ohuo & Kojima (2000)
3.6 X-Ray Microlensing
Direct measurement of size of emission
region: X-rays from 10 Rg (Optical 70
Rg)
Chartas et al. 2009
Dai et al. 2009
(Li, Yuan,Wang,Wang,Zhang 2010)
3.7 TeV Variation--Spin of the SMBH in M87
The source can be very close to the BH (Li, Yuan,Wang,Wang,Zhang 2010)
(Li, Yuan,Wang,Wang,Zhang 2010)
TeV from M87
(Cui, Yuan,Li & Wang 2012)
•The larger the spin, the deeper the TeV photons
could be from
•The larger the spin, the more symmetric of the
contour of tau
•The deeper the TeV source, the stronger the TeV
emission.
•Different response of the TeV flux to the spins (<20
Rg or >20 Rg)
2008 2005
2004
2008
2005
Thanks!
