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=1/2v 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

      • 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

  • 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

  • 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)


Advection Terms

  • Energy Equation

  • Energy Balance


Optically Thick (& High dM/dt) ADAF

ADAF


Optically Thin (& Low Density) ADAF

  • Depending on S, Number of Solutions Changes.


Thermal Equilibrium ADAF (Optically Thin)


Thermal Equilibrium ADAF

ADAF (thick or thin)… H/r ~1

Conical Flow


ADAF (Opticallt Thick and Thin)


Optically Thin, Two Temperature ADAF


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

  • 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


Summary


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