Stability of radiation-pressure dominated disks. I. The dispersion relation for a delayed heating alpha-viscosity prescription

Understand

We derive and investigate the dispersion relation for accretion disks with retarded or advanced heating.

• We follow the alpha-prescription but allow for a time offset (\tau) between heating and pressure perturbations, as well as for a diminished response of heating to pressure variations.
• We study in detail solutions of the dispersion relation for disks with radiation-pressure fraction 1 - \beta .
• For \tau <0 (delayed heating) the number and sign of real solutions for the growth rate depend on the values of the time lag and the ratio of heating response to pressure perturbations, \xi .