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Accretion onto Black Hole : Advection Dominated FlowPowerPoint Presentation

Accretion onto Black Hole : Advection Dominated Flow

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Accretion onto Black Hole : Advection Dominated Flow

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Accretion onto Black Hole : Advection Dominated Flow

K. Hayashida

Osaka University

- E=0 (at Infinite)
- E=1/2v2-GM/r=0 (at r )
- v=sqrt(2GM/r)
- v=Free Fall Velocity=Escape Velocity

- v=c … r=rg =2GM/c2 Schwartzshild radius
- 3km for 1Mo

- GM/r2 = v2/r = rW2
- v=sqrt(GM/r) ; W =sqrt(GM/r3)
- l (angular momentum) = vr = sqrt(GMr)
- E=1/2 v2 –GM/r = –GM/2r = –(GM)2/2l2
- To accrete from r1 to r2, particle must lose DE=GM/2r2 – GM/2r1 … e.g. Radiation
- Must lose Dl=sqrt(GMr1) - sqrt(GMr2) …Angular Momentum Transfer

Angular Momemtum

Flow

v(r)

r

- Viscosity force
- h: dynamical viscotiy
- h =rn (n: kinematic viscosity)
- ※Viscosity time scale >Hubble time unless turbulence or magnetic field exists.

r-Dr

v(r-Dr)

- Stable Circular Orbit r>=3rg
- Binding Energy at r=3rg =0.0572c2
- … Mass conversion efficiency

- Start from Kepler Motion
- Optically Thick Standard Disk
- Optically Thin Disk
- Irradiation Effect, Relativistic Correction, Advection etc.

- Slim Disk (Optically Thick ADAF)
- Optically Thin ADAF

- Start from Free Fall
- Hydrodynamic Spherical Accretion Flow=Bondi Accretion … transonic flow

- Shakura and Sunyaev (1973)
- Optically Thick
- Geometrically Thin (r/H<<1)
- Rotation = Local Keplerian
- Steady, Axisymmetric
- Viscosity is proportional to Pressure

- Mass Conservation
- Angular Velocity
- Angular Momentum Conservation
- Hydrostatic Balance

One zone approx.

- Energy Balance
- Equation of State
- Opacity
- Viscosity Prescription

a-disk model

Corresponds

to L~0.1LEdd

- Double Valued Solutions for fixed S

- Low Temperature
- High Temperature

- Total Disk

(see Mitsuda et al., 1984)

- Problem of Optically Thick Disk
- Fail to explain Hard X-ray, Gamma-ray Emission

- Optically Thin Disk (Shapiro-Lightman-Earley Disk) (1976)
- Radiation Temperature can reach Tvir

- Energy Balance
- Disk

- Energy Equation
- Energy Balance

ADAF

- Depending on S, Number of Solutions Changes.

ADAF (thick or thin)… H/r ~1

Conical Flow

dM/dt is known from observation.

L is too low unless ADAF is considered.

- Luminosity at Quiescence Lmin
- NS with Surface
- BH without Surface

Narayan et al., Theory of Black Hole

Accretion Discs, 1998, p.177

NLS1

Mineshige et al., 2000