1. Muduleya LEI HUANG @SINO-GERMAN 1 Modeling the Accretion Flow Around the SMBH at the Galactic Center Lei Huang Center for Astrophysics, USTC Collaborators: Zhi-Qiang Shen, Rohta Takahashi, Siming Liu, Ye-Fei Yuan.

2. Muduleya LEI HUANG @SINO-GERMAN 2 Outline 1. Observations on Polarizations of Sgr A* 2. Modeling of MRI-driven Keplerian Accretion Flow -- dynamical structure -- radiative transfer 3. Reproduction of Observations -- polarizations -- 1.3mm VLBI visibilities 4. Summary

3. Muduleya LEI HUANG @SINO-GERMAN 3 Sgr A* is the best super- massive black hole candidate Sub-millimeter bump in spectrum... High LP in sub- millimeter bump … Accretion flow with low mass accretion rate … Inactive jet I ’ m inactive Falcke et al. 1998 Macquart et al. 2006 EAT,N TALK

4. Muduleya LEI HUANG @SINO-GERMAN 4 1. Observations on Polarizations Sgr A* Macquart et al. 2006 Eckart et al. 2006, NIR

5. Muduleya LEI HUANG @SINO-GERMAN 5 2. Modeling of MRI-driven Keplerian Accretion Flow Magneto-Rotational-Instability (MRI) Mechanism --- The primary mechanism for generation of turbulence and viscous stress in accretion flows. (Balbus & Hawley 1991, 1998).

6. Muduleya LEI HUANG @SINO-GERMAN 6 2. Modeling – dynamical structure Keplerian rotation accretion flow assumed : All physical quantities are measured on the equatorial plane. Any value A(r, z) is assmed = A(r, 0).

7. Muduleya LEI HUANG @SINO-GERMAN 7 2. Modeling – dynamical structure Viscous tensor component : Heating mechanism by turbulent plasma waves : PLASMA WAVE TURBULENCE Particles are accelerated from a background plasma to high energies by interacting resonantly with PLASMA WAVE TURBULENCE (Petrosian & Liu 2004; Liu et al. 2006).

8. Muduleya LEI HUANG @SINO-GERMAN 8 2. Modeling – dynamical structure E. g., a well-fit model with a=0.5, bp=0.05, C1=0.272, Mdot=0.6 e-8 Msol /yr :

9. Muduleya LEI HUANG @SINO-GERMAN 9 2. Modeling – radiative transfer B B Line of sight

10. Muduleya LEI HUANG @SINO-GERMAN 10 2. Modeling – radiative transfer LP modes : Commonly used, but not the natural ones. Natural modes : Dieletric tensor : Electric field : Dispersion relation & eigenvalues : Eigenvectors : Natural base : (Pacholczyk 1970; Melrose 1971)

11. Muduleya LEI HUANG @SINO-GERMAN 11 2. Modeling – radiative transfer LP base vs natural base :

12. Muduleya LEI HUANG @SINO-GERMAN 12 2. Modeling – radiative transfer LP base vs natural base : CP modes : CP base :

13. Muduleya LEI HUANG @SINO-GERMAN 13 2. Modeling – radiative transfer LP base vs natural base : CP base vs natural base : Total emission coefficient :

14. Muduleya LEI HUANG @SINO-GERMAN 14 2. Modeling – radiative transfer LP & CP emission coefficients : Definitions of rotation components (Melrose 1997) Melrose (1997) & Shcherbakov (2008) derived the three emission coefficients and two Faraday coefficients separately. Neither appears exactly in agreement the above relation. Faraday rotation : (Melrose, 1997; Quataert & Gruzinov, 2000) Huang et al. (2008) :

15. Muduleya LEI HUANG @SINO-GERMAN 15 North East North The four-vectors of reference coordinates (a µ, b µ ) are calculated according to the parallel transport in general relativistic theory (Chandrasekhar 1983). Rotation matrix : 2. Modeling – radiative transfer

16. Muduleya LEI HUANG @SINO-GERMAN 16 3. Reproduction of Observations --polarizations Without external RM, Θ=120 o Without external Θ=140 o Data from Bower et al. (2002) & Marrone et al. (2006) The well-fit model with a=0.5 : External depolarization

17. Muduleya LEI HUANG @SINO-GERMAN 17 3. Reproduction of Observations --1.3mm VLBI Visibilities JCMT CARMA ARO/SMT Doeleman et al. (2008) :

18. Muduleya LEI HUANG @SINO-GERMAN 18 Without external RM, Θ=120 o Without external Θ=140 o The well-fit model with a=0.5 : 3. Reproduction of Observations --1.3mm VLBI Visibilities External depolarization

19. Muduleya LEI HUANG @SINO-GERMAN 19 4. Summary We establish a general relativistic model based on the MRI-driven Keplerian accretion flow. The effects of relativity and birefringence are considered self-consistent in the radiative transfer. We show an example with a=0.5, which can fit most polarization observations. The visibilities at 1.3mm predicted by the example fit recent VLBI measurements well.

20. Muduleya LEI HUANG @SINO-GERMAN 20 THANK YOU