relativistic accretion disks: their dynamics and emission yuan, ye-fei （袁业飞） department of...

Relativistic accretion disks: their dynamics and emission

Yuan, Ye-Fei（袁业飞）Department of Astronomy, USTC

(2011.04.26)

Collaborators:

Cao, X.; Shen, Z.Q. (SHAO);

Li, Guangxing; Huang, L. (USTC)Ref.: ApJ, 699, 722-731(2009), ApJ, 715, 623-635(2010)

Outline

Relativistic Accretion Disks Ray Tracing Method Relativistic SSD/Slim Disks Images of Sgr A* ： Relativistic ADAF Main Conclusions

Relativistic Accretion Model

Kerr Metric:

Reference Frames: LNRF, CRF, LRF

LNRF(ZMAO) u

CRF

)(,2/12

)(

r

AVuLRF VV r )(

Four velocity of the fluid: uμ(Ω,V)

Basic Equations:

Fr

A

dr

dsTr

Mr2

,6

24

0 )(2

ADAF

SSD/Slim

Ray Tracing Methodβ

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,

MCD spectra Influenced by BH spin Prominent in XRBs

Relativistic SSD/Slim: One temperature disk

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

Global solution of the disk


Emergent Spectra


Implications For Spin Estimation


Measured Spin of GRS 1915+105

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

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 NatureFrom 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)

Radiation Transfer Equation

Radiation Transfer Equation

)(

),,(

)(

/),(

),(

~

),(~),(

~

30

0

3

00

xx

xkk

uk

xjj

x

II

xjIxukd

Id

obsem

emem

em

em

emem

em

θobs=0

Images of Sgr A*


θobs=90, 45, 0Images @ 7 mm

a=-9.998 -0.5 0 0.5 0.998

Yuan, Cao, Huang, Shen (2010 )

θobs=90, 45, 0

a=-9.998 -0.5 0 0.5 0.998

Images @ 3.5 mm


θobs=90, 45, 0

Images @ 1.3 mm

a=-9.998 -0.5 0 0.5 0.998


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?

Thanks!

relativistic accretion disks: their dynamics and emission yuan, ye-fei （袁业飞） department of...

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