Astron. Astrophys. 357, 1123-1132 (2000)

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 .

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 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
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