## Appendix A: Thermodynamic considerations for KSG -disksFor a KSG -disk, we have from Eq. 26 that If the disk is optically thick and advection is negligible, viscous dissipation leads to local effective temperature of with An essential thermodynamics requirement is that or that This condition is satisfied provided that and that the disk is selfgravitating in the vertical direction at . The latter condition leads to a second requirement on . For a standard Keplerian disk, the mass flow rate is given (Eqs. 8, 10, 43) by with the disk's mass. From Eq. 11, the condition that the disk is non-selfgravitating is and hence, from Eq. A5, that or A selfconsistent and physically acceptable solution can be obtained only if , that is the disk becomes selfgravitating at values of which are sufficiently high that thermodynamic requirements are not violated. This condition may then be written as Thus © European Southern Observatory (ESO) 2000 Online publication: June 5, 2000 |