Appendix A: Thermodynamic considerations for KSG -disks
For 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 m the mass of the central star in solar units and the radius in astronomical units.
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 .
with the disk's mass. From Eq. 11, the condition that the disk is non-selfgravitating is and hence, from Eq. A5, that
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 thin KSG -disks appear to be inconsistent with basic thermodynamic requirements if , . There is no inconsistency if either or both of these quantities are sufficiently large.
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000