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Modeling the Accretion Modeling the Accretion Flow Around the SMBH Flow Around the SMBH at the Galactic Centerat the Galactic Center

Lei HuangLei HuangCenter for Astrophysics, USTCCenter for Astrophysics, USTC

Collaborators: Zhi-Qiang Shen, Collaborators: Zhi-Qiang Shen,

Rohta Takahashi, Siming Liu, Ye-Fei Yuan.Rohta Takahashi, Siming Liu, Ye-Fei Yuan.

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OutlineOutline1. Observations on Polarizations of Sgr A* 1. Observations on Polarizations of Sgr A*

2. Modeling of MRI-driven Keplerian 2. Modeling of MRI-driven Keplerian Accretion Flow Accretion Flow -- dynamical structure -- radiative transfer

3. Reproduction of Observations 3. Reproduction of Observations -- polarizations -- 1.3mm VLBI visibilities

4. Summary 4. Summary

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Sgr A* is the best super-Sgr A* is the best super-massive black hole candidatemassive black hole candidate

Sub-millimeter bump in Sub-millimeter bump in spectrum ...spectrum ...

High LP in sub-High LP in sub-millimeter bump …millimeter bump …

Accretion flow with low Accretion flow with low mass accretion rate …mass accretion rate …

Inactive jetInactive jet

I’m inactive

Falcke et al. 1998

Macquart et al. 2006EAT,N TALK

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1. Observations on 1. Observations on PolarizationsPolarizations

Sgr A*

Macquart et al. 2006

Macquart et al. 2006

Macquart et al. 2006

Eckart et al. 2006, NIR

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2. Modeling of MRI-driven 2. Modeling of MRI-driven Keplerian Accretion FlowKeplerian Accretion FlowMagneto-Rotational-Instability (MRI) Mechanism --- The primary mechanism for generation of turbulence and viscous stress in accretion flows. (Balbus & Hawley 1991, 1998).

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2. Modeling 2. Modeling – dynamical structure– 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 2. Modeling – dynamical structure– 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 PLASMA WAVE TURBULENCETURBULENCE (Petrosian & Liu 2004; Liu et al. 2006).

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2. Modeling 2. Modeling – dynamical structure– 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 :

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2. Modeling 2. Modeling – radiative transfer– radiative transfer

B

B

Line of sight

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2. Modeling 2. Modeling – radiative transfer– radiative transfer

LP modes : Commonly used, but not the natural ones.

Natural modes :Natural modes :

Dieletric tensor :

Electric field :

Dispersion relation & eigenvalues :

Eigenvectors :

Natural base :

(Pacholczyk 1970; Melrose 1971)

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2. Modeling 2. Modeling – radiative transfer– radiative transfer

LP base vs natural base :

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2. Modeling 2. Modeling – radiative transfer– radiative transfer

LP base vs natural base :

CP modes :

CP base :

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2. Modeling 2. Modeling – radiative transfer– radiative transfer

LP base vs natural base :

CP base vs natural base :

Total emission coefficient :

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2. Modeling 2. Modeling – radiative transfer– radiative transfer

LP & CP emission coefficients :

Definitions of rotation components (Melrose 1997) Melrose (1997) & Shcherbakov (2008) derived Melrose (1997) & Shcherbakov (2008) derived the three emission coefficients and two the three emission coefficients and two Faraday coefficients separately. Faraday coefficients separately. NeitherNeither appears exactly in agreement the above appears exactly in agreement the above relation. relation.

Faraday rotation : (Melrose, 1997; Quataert & Gruzinov, 2000)

Huang et al. (2008) :

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North

EastNorth

The four-vectors of reference coordinates The four-vectors of reference coordinates (a(aµµ , b , bµµ ) are calculated according to the ) are calculated according to the parallel transport in general relativistic parallel transport in general relativistic theory (Chandrasekhar 1983).theory (Chandrasekhar 1983).

Rotation matrix :

2. Modeling 2. Modeling – radiative transfer– radiative transfer

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3. Reproduction of 3. Reproduction of Observations --polarizationsObservations --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

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3. Reproduction of Observations 3. Reproduction of Observations

--1.3mm VLBI Visibilities--1.3mm VLBI Visibilities

JCMT CARMA

ARO/SMT

Doeleman et al. (2008) :

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Without external RM, Θ=120 o

Without external

Θ=140 o

The well-fit model with a=0.5 :

3. Reproduction of Observations 3. Reproduction of Observations --1.3mm VLBI Visibilities--1.3mm VLBI Visibilities

External

depolarization

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4. Summary4. 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-GERMANMuduleya LEI HUANG @SINO-GERMAN 2020

THANK YOUTHANK YOU