Relativistic accretion disks: their dynamics and emission Yuan, Ye-Fei （袁业飞） Department of Astronomy, USTC ( ) Collaborators: Cao, X.; Shen, Z.Q. (SHAO); Li, Guangxing; Huang, L. (USTC) Ref.: ApJ, 699, (2009), ApJ, 715, (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) CRF LRF Four velocity of the fluid: u μ (Ω,V)

Basic Equations: ADAF SSD/Slim

Ray Tracing Method β α (α,β)(α,β). Integral of motion of photons: Two impact parameters:

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, 60 0

Global solution of the disk Li, Yuan, Cao (2010)

Emergent Spectra Li, Yuan, Cao (2010)

Implications For Spin Estimation Li, Yuan, Cao (2010)

Measured Spin of GRS

Sgr A* --- The Black Hole Candidate in Milky Way Galaxy Mass : 4 x 10 6 M ⊙ D : 8 kpc Angular size of horizon : ~ 20 μas From: Lei Huang

UN beam 1.11 mas x o 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 Shen et al Nature From Zhiqiang Shen

Yuan, Shen, Huang, @3.5mm

Huang, Cai, Shen, Yuan, 2008, MNRAS θ obs =0 θ obs =45 θ obs =90

Global structure of ADAF Yuan, Cao, Huang, Shen (2009)

Radiation Transfer Equation

θ obs =0 Images of Sgr A* Yuan, Cao, Huang, Shen (2009)

θ obs =90, 45, 0 7 mm a= Yuan, Cao, Huang, Shen (2010 )

θ obs =90, 45, 0 a= mm Yuan, Cao, Huang, Shen (2009)

θ obs =90, 45, mm a= Yuan, Cao, Huang, Shen (2009)

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!