Close binary systems Jean-Pierre Lasota Lecture 5 Accretion discs II

4. Energy conservation equation (cdn) accounts for the heating by the mass-transfer stream and tidal forces. in stationary geometrically thin discs one can neglect radial gradients and in the bulk of the disc the energy equation is:

(Turbulent) viscous heating (Power = Torque x angular_velocity) Navier-Stokes equations: - the Shakura-Sunyaev ansatz for Keplerian discs equivalent to

Viscous heating In thermal equilibrium hence independent of viscosity !

Effective temperature Inner temperature

r -3/4

Eddington luminosity Gravitational force = radiative force Accretion luminosity

Disc luminosity and spectrum

Vertical structure equations for radiative energy transport:

Shakura – Sunyaev solution

Radiative flux Vertical mechanical equilibrium Radial velocity

Radiative vertical structure Boundary conditions

Radiative vertical structure 2

Thermal (and viscous) stability

The S-curve  max  min Hameury et al Thermal equilibria: heating=cooling Unstable 3 heating<cooling heating>cooling

Local limit-cycle Menou, Hameury, Stehle 1998 quiescence

 max  min irr Dubus et al. 2001a

SS Cygni

Guillaume Dubus Outbursts of an irradiated accretion disc around a 10 M O black hole