Frequency spectrum of axisymmetric horizontal oscillations in accretion disks

TL;DR

This paper analyzes the eigenfrequency spectrum of axisymmetric oscillations in thin accretion disks around Schwarzschild black holes, identifying discrete trapped modes and a continuum of eigenmodes.

Contribution

It provides a detailed calculation of the eigenfrequencies of axisymmetric oscillations in accretion disks using a pseudo-potential model, highlighting the spectrum of trapped modes and continuum.

Findings

Nine discrete eigenfrequencies corresponding to trapped modes.

Eigenmodes with nine or more radial nodes belong to the continuum.

The spectrum includes a range of frequencies starting below the maximum radial epicyclic frequency.

Abstract

We present the spectrum of eigenfrequencies of axisymmetric acoustic-inertial oscillations of thin accretion disks for a Schwarzschild black hole modeled with a pseudo-potential. There are nine discrete frequencies, corresponding to trapped modes. Eigenmodes with nine or more radial nodes in the inner disk belong to the continuum, whose frequency range starts somewhat below the maximum value of the radial epicyclic frequency. The results are derived under the assumption that the oscillatory motion is parallel to the midplane of the disk.