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

2. Free Fall & Escape Velocity
E= (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. Viscosity Viscosity force h: dynamical viscotiy
Angular Momemtum
Flow
Viscosity r
v(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

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

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

26. Summary