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Accretion onto Black Hole : Advection Dominated Flow. K. Hayashida Osaka University. Free Fall & Escape Velocity. E=0 (at Infinite) E=1/2v 2 -GM/r=0 (at r ) v=sqrt(2GM/r) v=Free Fall Velocity=Escape Velocity v=c … r=r g =2GM/c 2 Schwartzshild radius

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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

### Free Fall & Escape Velocity

• 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

### Kepler Motion

• 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

### Viscosity

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)

### Effective Potential

• Stable Circular Orbit r>=3rg

• Binding Energy at r=3rg =0.0572c2

• … Mass conversion efficiency

### Accretion Flow (Disk) Models

• Start from Kepler Motion

• Optically Thick Standard Disk

• Optically Thin Disk

• Slim Disk (Optically Thick ADAF)

• Start from Free Fall

• Hydrodynamic Spherical Accretion Flow=Bondi Accretion … transonic flow

### Standard Accretion Disk Model

• Shakura and Sunyaev (1973)

• Optically Thick

• Geometrically Thin (r/H<<1)

• Rotation = Local Keplerian

• Viscosity is proportional to Pressure

### Standard Disk Model-2

• Mass Conservation

• Angular Velocity

• Angular Momentum Conservation

• Hydrostatic Balance

One zone approx.

### Standard Disk Model-3

• Energy Balance

• Equation of State

• Opacity

• Viscosity Prescription

a-disk model

### Standard Disk Thermal Equilibrium Curve

Corresponds

to L~0.1LEdd

• Double Valued Solutions for fixed S

### Standard Disk Heating and Cooling

• Low Temperature

• High Temperature

### Disk Blackbody Spectra

• Total Disk

(see Mitsuda et al., 1984)

### Optically Thin Disk

• 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

### Optically Thin Disk-2

• Energy Balance

• Disk

### Stability (Secular, Thermal)

• Energy Equation

• Energy Balance

### Optically Thin (& Low Density) ADAF

• Depending on S, Number of Solutions Changes.

### Thermal Equilibrium ADAF (Optically Thin)

ADAF (thick or thin)… H/r ~1

Conical Flow

### Optically Thin, Two Temperature ADAF

dM/dt is known from observation.

L is too low unless ADAF is considered.

### Presence of Event Horizon : BH vs NS

• Luminosity at Quiescence Lmin

• NS with Surface

• BH without Surface

Narayan et al., Theory of Black Hole

Accretion Discs, 1998, p.177

NLS1

### Slim　Disk　Model = Optically Thick ADAF

Mineshige et al., 2000