Modeling the Accretion Flow Around the SMBH at the Galactic Center

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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.

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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

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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

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1. Observations on Polarizations
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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 ?ows.
(Balbus Hawley 1991, 1998).
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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).
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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).
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2. Modeling dynamical structure
E. g. , a well-fit model with a0.5 , bp0.05,
C10.272, Mdot0.6 e-8 Msol /yr
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2. Modeling radiative transfer
Line of sight
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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
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2. Modeling radiative transfer
LP base vs natural base
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2. Modeling radiative transfer
LP base vs natural base
CP modes
CP base
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2. Modeling radiative transfer
LP base vs natural base
CP base vs natural base
Total emission coefficient
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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.
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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).
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3. Reproduction of Observations --polarizations
The well-fit model with a0.5

Without external RM, T120 o
External depolarization
Data from Bower et al. (2002) Marrone et al.
(2006)
Without external T140 o
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3. Reproduction of Observations --1.3mm VLBI
Visibilities
Doeleman et al. (2008)
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3. Reproduction of Observations --1.3mm VLBI
Visibilities
The well-fit model with a0.5

Without external RM, T120 o
External depolarization
Without external T140 o
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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 a0.5, which can fit most
  polarization observations.
• The visibilities at 1.3mm predicted by the
  example fit recent VLBI measurements well.

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THANK YOU