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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Presentation Transcript
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
viscosity

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
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

Corresponds

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
advection terms
Advection Terms
  • Energy Equation
  • Energy Balance
optically thin low density adaf
Optically Thin (& Low Density) ADAF
  • Depending on S, Number of Solutions Changes.
thermal equilibrium adaf
Thermal Equilibrium ADAF

ADAF (thick or thin)… H/r ~1

Conical Flow

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

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