Luminous accretion disks with optically thick/thin transition A. S. Klepnev,G. S. Bisnovatyi-Kogan

Problem statement Nonrotating black hole We use pseudo-Newtonial approach to describe the disk structure in the vicinity of the black hole. In the approach general relativistic effects are simulated by using the Paczynski-Wiita potential( Paczynski &Wiita, 1980) When the gravitational radius.

We consider steady, geometrically thin accretion disk. The self-gravity of the disk is neglected. Basic equation Equation of equilibrium in the vertical direction midplane “isotermal” sound speed

Basic equation The mass conservation equation The radial momentum equation is accretion rate

Basic equation The angular momentum equation when Is the component viscous stress tensor is the specific angular momentum

Internal energy equation. Advection heat advection viscous dissipation radiative cooling rates per units disk surface is the specific angular momentum in the horizon black hole Advection is energy carrying over to a radial direction together with matter.

Plasma parameters The total Thomson scattering depth of the disk The optical depth with respect to bremssatrahlung absorption The effective optical depth

The equation of state of the accreting matter The gas pressure The radiation pressure The internal energy density

Differential equation N and D to denote algebraic expression then depend only

Numerical method We use a finite-difference method to solve the system of ordinary differential equations The presence of the outer singular point does not require the explicit of the regularity condition in this point. The numerical solution, which follows the separatrix, passes the outer singular point without special numerical treatment.

Inner singular point To correctly approximate the differential equation in the first grid interval (inner singular points) we expand the solution in this point

Radial velocity

Effective optical depth

Midplane temperature