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Modeling the Accretion Flow Around the SMBH at the Galactic Center

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. Outline. 1. Observations on Polarizations of Sgr A* 2. Modeling of MRI-driven Keplerian Accretion Flow

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Modeling the Accretion Flow Around the SMBH at the Galactic Center

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  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. 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 Muduleya LEI HUANG @SINO-GERMAN

  3. EAT,N TALK Falcke et al. 1998 I’m inactive Macquart et al. 2006 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 Muduleya LEI HUANG @SINO-GERMAN

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

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

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

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

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

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

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

  14. 2. Modeling – radiative transfer Faraday rotation : (Melrose, 1997; Quataert & Gruzinov, 2000) LP & CP emission coefficients : Huang et al. (2008) : 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. Muduleya LEI HUANG @SINO-GERMAN

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

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

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

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

  20. THANK YOU Muduleya LEI HUANG @SINO-GERMAN

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