Kinematic Density Waves in Accretion Disks

TL;DR

This paper investigates long-lived, non-intersecting density wave modes in accretion disks around black holes, classifying their frequencies and exploring their potential link to observed high-frequency quasi-periodic oscillations.

Contribution

It identifies a discrete set of stable, long-lived perturbation modes in accretion disks and relates their frequencies to disk properties, extending understanding of diskoseismic waves.

Findings

Modes are concentrated near radii with vanishing radial derivative of pattern speed.

Long-lived modes coincide with diskoseismic waves at small sound speeds.

These modes do not match the observed frequencies of high-frequency QPOs.

Abstract

When thin accretion disks around black holes are perturbed, the main restoring force is gravity. If gas pressure, magnetic stresses, and radiation pressure are neglected, the disk remains thin as long as orbits do not intersect. Intersections would result in pressure forces which limit the growth of perturbations. We find that a discrete set of perturbations is possible for which orbits remain non-intersecting for arbitrarily long times. These modes define a discrete set of frequencies. We classify all long-lived perturbations for arbitrary potentials and show how their mode frequencies are related to pattern speeds computed from the azimuthal and epicyclic frequencies. We show that modes are concentrated near radii where the pattern speed has vanishing radial derivative. We explore these modes around Kerr black holes as a possible explanation for the high-frequency quasi-periodic oscillations of black hole binaries such as GRO J1655-40. The long-lived modes are shown to coincide with diskoseismic waves in the limit of small sound speed. While the waves have long lifetime, they have the wrong frequencies to explain the pairs of high-frequency quasi-periodic oscillations observed in black hole binaries.