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

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)

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

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

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

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 Mineshige et al., 2000 NLS1

Summary