Eigenmodes of trapped horizontal oscillations in accretion disks

TL;DR

This paper calculates eigenfrequencies and eigenfunctions of trapped oscillations in accretion disks around black holes and stars, providing detailed mode data and approximations for the lowest modes.

Contribution

It extends previous models by computing specific eigenmodes for different azimuthal numbers in accretion disks around Schwarzschild black holes and rotating stars.

Findings

Eigenfrequencies and eigenfunctions for five azimuthal modes are provided.

Lowest mode frequencies can be approximated by Airy functions.

Results are applicable to thin accretion disks in astrophysical contexts.

Abstract

We present eigenfrequencies and eigenfunctions of trapped acoustic-inertial oscillations of thin accretion disks for a Schwarzschild black hole and a rapidly rotating Newtonian star (a Maclaurin spheroid). The results are derived in the formalism of Nowak and Wagoner (1991) with the assumption that the oscillatory motion is parallel to the midplane of the disk. The first four radial modes for each of five azimuthal modes $m = 0$ through $m = 4$ are presented. The frequencies and wavefunctions of the lowest modes may be accurately approximated by the Airy function.