Radial modes of pressure bumps and dips in astrophysical discs

TL;DR

This paper explores how pressure extrema in astrophysical discs influence global oscillations, revealing new wave modes and their potential for discoseismology applications.

Contribution

It introduces a generalized dispersion relation including pressure gradients and identifies topological modes associated with pressure bumps and dips.

Findings

Pressure extrema act as wave guides for specific modes.

Fundamental modes at pressure bumps can resonate at any frequency.

Modes at pressure gaps propagate at fixed frequencies.

Abstract

This study investigates the signatures of pressure extrema on global oscillations in discs. To this end, we use the framework of wave topology to establish a generalised local dispersion relation that includes pressure gradients. We highlight the influence of a previously unrecognized epicyclic-acoustic frequency and derive an analytical criterion for the existence of a branch of modes transiting between the inertial and the pressure bands. We find that pressure extrema consist of wave guides in which such topological modes propagate. The fundamental mode trapped at a pressure bump can propagate at all frequencies, allowing it to resonate with any temporal forcing, while the mode associated with a pressure gap propagates at a fixed frequency, propagates with arbitrary vertical phase velocity. These specific features make them attractive candidates for future discoseismology.