Resonant Excitation of Disk Oscillations in Deformed Disks III: Revision of Mathematical Treatment

Abstract

In previous studies, we have examined a resonant excitation of disk oscillations in deformed disks. In these studies, however, the mathematical treatment around the resonant points was not rigorous. In this paper the inadequate point is corrected, but with no essential changes in the final results. For this excitation process to work, disks must be general relativistic. That is, a non-monotonic radial distribution of the epicyclic frequency in relativistic disks is essential for the presence of the resonance, and for trapping oscillations. In this paper, the growth rate of resonant oscillations is expressed in a form more suitable for numerical calculations.