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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. 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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  1. Accretion onto Black Hole : Advection Dominated Flow K. Hayashida Osaka University

  2. 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

  3. 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

  4. 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)

  5. Effective Potential • Stable Circular Orbit r>=3rg • Binding Energy at r=3rg =0.0572c2 • … Mass conversion efficiency

  6. 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

  7. 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

  8. Standard Disk Model-2 • Mass Conservation • Angular Velocity • Angular Momentum Conservation • Hydrostatic Balance One zone approx.

  9. Standard Disk Model-3 • Energy Balance • Equation of State • Opacity • Viscosity Prescription a-disk model

  10. Standard Disk Thermal Equilibrium Curve Corresponds to L~0.1LEdd • Double Valued Solutions for fixed S

  11. Standard Disk Heating and Cooling • Low Temperature • High Temperature

  12. Disk Blackbody Spectra • Total Disk (see Mitsuda et al., 1984)

  13. 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

  14. Optically Thin Disk-2 • Energy Balance • Disk

  15. Stability (Secular, Thermal)

  16. Advection Terms • Energy Equation • Energy Balance

  17. Optically Thick (& High dM/dt) ADAF ADAF

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

  19. Thermal Equilibrium ADAF (Optically Thin)

  20. Thermal Equilibrium ADAF ADAF (thick or thin)… H/r ~1 Conical Flow

  21. ADAF (Opticallt Thick and Thin)

  22. Optically Thin, Two Temperature ADAF

  23. dM/dt is known from observation. L is too low unless ADAF is considered. Optically Thin, Two Temperature ADAF (Model fit to SgrA)

  24. 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

  25. NLS1 Slim　Disk　Model = Optically Thick ADAF Mineshige et al., 2000

  26. Summary

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