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

TL;DR

This paper revises the mathematical treatment of resonant excitation of disk oscillations in relativistic, deformed disks, ensuring rigorous analysis around resonant points while confirming the core results remain unchanged.

Contribution

It provides a more rigorous mathematical framework for analyzing resonant disk oscillations, emphasizing the importance of relativistic effects and improving numerical calculation methods.

Findings

Resonant excitation requires relativistic disks with non-monotonic epicyclic frequency.

The growth rate expression is reformulated for better numerical computation.

Core results of previous studies remain valid after correction.

Abstract

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