Accretion onto Black Hole : Advection Dominated Flow

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Accretion onto Black Hole : Advection Dominated Flow. K. Hayashida Osaka University. Free Fall &amp; 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

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

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
• Energy Equation
• Energy Balance
Optically Thin (& Low Density) ADAF
• Depending on S, Number of Solutions Changes.