A Dynamic Model of Magnetic Coupling of a Black Hole with its surrounding Accretion Disk Huazhong University of Science & Technology ( , Beijing) Ding-Xiong Wang

1. A review of the coexistence of the BZ and MC processes Fig. 1. Different types of magnetic field lines in BH magnetosphere. Blandford (2002)

Fig. 2. Magnetic field Configuration with the BZ and MC processes (Wang et al. 2002, 2003, 2004).

Energy and angular momentum are transferred from the BH to the disk (MacDonald & Thorne 1982)

Fig. 3. —Equivalent circuit for a unified model for the BZ and MC processes

2. Effects of the MC process on accretion rate 2.1 Magnetic coupling of a rotating black hole with its surrounding disk results in a suspended accretion state for Accretion rate can be written as

It is assumed that the magnetic field on the disk varies with the radial coordinate r as follows: where n is a power-law index indicating the degree of concentration of the magnetic field in the central region of the disk. It is found that the sign of depends on the BH spin, the power-law index n and the disk radius r.

Fig.4. The curves of versus the BH spin with and n = 4, 5 and 6 in (a), (b) and (c), respectively. (a) (b) (c)

3. The possibility for a thin disk evolving to a thick disk (torus) are located outside and inside respectively. The accreting flows with A thin disk might evolve to a thick disk (torus) ???

Fig.5. A BH surrounded by a torus, which is adapted from Li 2000 and van Putten 2003 in (a) and (b), respectively. (a) (b)

Thus the time scale for a thin disk evolving to a thick one can be estimated as The average accretion rate can be estimated as

where is a function derived based on the effects of the MC effects on the accretion rate The concerning parameters are given in Wang et al. (2003) It is found that

It is believed that then we have (Camenzind M and Khanna 1996))

For a given ratio of the BH mass to that of the torus with we have

(1)The vertical component of radiative force acting on each electron where and are the radiation fluxes due to disk accretion and the MC process, respectively. (Page & Thorne 1974)

Li (2002); Wang et al. (2003) Function is the flux of the angular momentum transferred from the BH to the disk.

(2) The vertical component of gravitational force acting on a proton: The ratio of to is

Discussion (2) Setting the initial configuration of the disk Thin disk cannot evolve to the thick disk; (1) i.e.,

4. A possible scenario for the X-ray flares in GRB early afterglows 4.1 The detection of X-ray flares in GRB early afterglows by Swift suggests that GRB central engine is very likely still active after the prompt gamma-ray emission is over, but with a reduced activity at later times.

A scenario for X-ray flares in GRB early afterglows Stage 1 A GRB is driven by the BZ process with clean electromagnetic energy; Stage 2 Energy and angular momentum are transferred from a spinning BH to the disk in the MC process, (1)Resulting in a state of suspended accretion; (2) Providing energy for SN; (3) Leading to a torus from a thin disk after the prompt gamma-ray emission is over

It is believed that then we have (Camenzind M and Khanna 1996)) For we have A thin disk has evolved to a thick disk before X-ray flares.

Stage 3 Magnetic field instability starts B-bomb provided that the following criterion is satisfied (van Putten 2003): and are the kenetic energy of the torus and the energy of the magnetic field, respectively.

We assume a ratio based on the following consideration: most of energy transferred to the torus is radiated as gravitational wave rather than magnetic energy.

4.2 Accretion starts to drive X-ray flares Taking the following parameters in fittings, ，，， The instability leads to the disrupt of the MC between the BH and the torus, and disk accretion starts to drive X-ray flares. we have

4.3 Fitting the energy and time-scale of the X-ray flares where

5. A possible scenario for state transition in BH X-ray Binaries Multi-wavelength observations for GRS (Mirabel 1998)

Belloni et al. (2000) interpret the transition between State C and States A/B as being caused by the disappearance and reappearance of the inner accretion disk due to a disk instability mechanism.

Livio et al. (2003) proposed that during State C, the inner accretion disk is still present, and is still accreting at essentially the same rate as before, but, rather, the energy liberated in the accretion is converted efficiently into magnetic energy and is emitted in the form of a magnetically dominated outflow or jet. Brown et al. (2000) argued that the material in the inner disk will move outwards due to the magnetic transfer from a rotating black hole. The viscous inflow time is estimated to be

A possible scenario for state transition, which is switched between the state dominated by accretion and by the MC processes. A state dominated by MC Process (SDMC) A state dominated by Disk Accretion (SDDA)

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