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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

Accretion onto Black Hole : Advection Dominated Flow

K. Hayashida

Osaka University

Free fall escape velocity

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

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





  • Viscosity force

  • h: dynamical viscotiy

  • h =rn (n: kinematic viscosity)

  • ※Viscosity time scale >Hubble time unless turbulence or magnetic field exists.



Effective potential

Effective Potential

  • Stable Circular Orbit r>=3rg

  • Binding Energy at r=3rg =0.0572c2

    • … Mass conversion efficiency

Accretion flow disk models

Accretion Flow (Disk) Models

  • 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

Standard accretion disk model

Standard Accretion Disk Model

  • Shakura and Sunyaev (1973)

  • Optically Thick

  • Geometrically Thin (r/H<<1)

  • Rotation = Local Keplerian

  • Steady, Axisymmetric

  • Viscosity is proportional to Pressure

Standard disk model 2

Standard Disk Model-2

  • Mass Conservation

  • Angular Velocity

  • Angular Momentum Conservation

  • Hydrostatic Balance

One zone approx.

Standard disk model 3

Standard Disk Model-3

  • Energy Balance

  • Equation of State

  • Opacity

  • Viscosity Prescription

a-disk model

Standard disk thermal equilibrium curve

Standard Disk Thermal Equilibrium Curve


to L~0.1LEdd

  • Double Valued Solutions for fixed S

Standard disk heating and cooling

Standard Disk Heating and Cooling

  • Low Temperature

  • High Temperature

Disk blackbody spectra

Disk Blackbody Spectra

  • Total Disk

(see Mitsuda et al., 1984)

Optically thin disk

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

Optically Thin Disk-2

  • Energy Balance

  • Disk

Stability secular thermal

Stability (Secular, Thermal)

Advection terms

Advection Terms

  • Energy Equation

  • Energy Balance

Optically thick high dm dt adaf

Optically Thick (& High dM/dt) ADAF


Optically thin low density adaf

Optically Thin (& Low Density) ADAF

  • Depending on S, Number of Solutions Changes.

Thermal equilibrium adaf optically thin

Thermal Equilibrium ADAF (Optically Thin)

Thermal equilibrium adaf

Thermal Equilibrium ADAF

ADAF (thick or thin)… H/r ~1

Conical Flow

Adaf opticallt thick and thin

ADAF (Opticallt Thick and Thin)

Optically thin two temperature adaf

Optically Thin, Two Temperature ADAF

Optically thin two temperature adaf model fit to sgra

dM/dt is known from observation.

L is too low unless ADAF is considered.

Optically Thin, Two Temperature ADAF (Model fit to SgrA)

Presence of event horizon bh vs ns

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

Slim disk model optically thick adaf


Slim Disk Model = Optically Thick ADAF

Mineshige et al., 2000



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