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!