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

3. 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:

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

6. Viscous heating In thermal equilibrium hence independent of viscosity !

7. Effective temperature Inner temperature

8. r -3/4

9. Eddington luminosity Gravitational force = radiative force Accretion luminosity

10. Disc luminosity and spectrum

13. Vertical structure equations for radiative energy transport:

14. Shakura – Sunyaev solution

15. Radiative flux Vertical mechanical equilibrium Radial velocity

16. Radiative vertical structure Boundary conditions

17. Radiative vertical structure 2

19. Thermal (and viscous) stability

20. The S-curve  max  min Hameury et al. 1998 Thermal equilibria: heating=cooling Unstable 3 heating<cooling heating>cooling

21. Local limit-cycle Menou, Hameury, Stehle 1998 quiescence

22.  max  min irr Dubus et al. 2001a

23. SS Cygni

26. Guillaume Dubus Outbursts of an irradiated accretion disc around a 10 M O black hole http://www.oa.uj.edu.pl/~lasota/Close%20Binaries/output.mpg