1. 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)

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

3. Relativistic Accretion Model Kerr Metric:

4. Reference Frames: LNRF, CRF, LRF LNRF(ZMAO) CRF LRF Four velocity of the fluid: u μ (Ω,V)

9. Basic Equations: ADAF SSD/Slim

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

11. Equation of photon trajectroy: Analytic solution of photon’s trajectory: where,

12.  MCD spectra  Influenced by BH spin  Prominent in XRBs Relativistic SSD/Slim: One temperature disk

13. Why XRB? Mass Estimation Inclination Angle (Superluminal Motion) Bright, Easy to Observe

14. 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

15. 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

16. Physical Effects: Heat Advection Li, Yuan, Cao (2010)

17. Physical Effects: Disk Thickness Left: No Thickness, Right: With Thickness, M_dot=2, a=0.98, 60 0

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

19. Emergent Spectra Li, Yuan, Cao (2010)

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

21. Measured Spin of GRS 1915+105

22. 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

23. UN beam 1.11 mas x 0.32 mas @ 9 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 A* @3.5mm Shen et al. 2005 Nature From Zhiqiang Shen

24. Yuan, Shen, Huang, 2006, ApJL @7mm @1.3mm @3.5mm

25. Huang, Cai, Shen, Yuan, 2008, MNRAS @1.3mm@3.5mm θ obs =0 θ obs =45 θ obs =90

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

27. Radiation Transfer Equation

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

32. θ obs =90, 45, 0 Images @ 7 mm a=-9.998 -0.5 0 0.5 0.998 Yuan, Cao, Huang, Shen (2010 )

33. θ obs =90, 45, 0 a=-9.998 -0.5 0 0.5 0.998 Images @ 3.5 mm Yuan, Cao, Huang, Shen (2009)

34. θ obs =90, 45, 0 Images @ 1.3 mm a=-9.998 -0.5 0 0.5 0.998 Yuan, Cao, Huang, Shen (2009)

36. 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?

37. Thanks!