Density waves in debris discs and galactic nuclei

TL;DR

This paper investigates the linear perturbations and normal modes of collisionless near-Keplerian discs, revealing the existence of large-scale slow modes that could explain observed features in debris discs without invoking planets.

Contribution

It introduces a finite-element method to solve the linearized collisionless Boltzmann and Poisson equations, characterizing slow modes and their origins in debris and galactic nuclei discs.

Findings

Discs support large-scale slow modes with frequencies proportional to disc mass.

Slow modes include parent and hybrid child modes arising from resonant interactions.

Features like clumps and spirals in debris discs may result from slow modes, not just planets.

Abstract

We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a finite-element method, we solve the linearized collisionless Boltzmann equation and Poisson's equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We find that these discs can support large-scale `slow' modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal precession. We find that slow modes are of two general types: parent modes and hybrid child modes, the latter arising from resonant interactions between parent modes and singular van Kampen modes. The most prominent slow modes have azimuthal wavenumbers $m=1$ and $m=2$. We illustrate how slow modes in debris discs are excited during a fly-by of a neighbouring star. Many of the non-axisymmetric features seen in debris discs (clumps, eccentricity, spiral waves) that are commonly attributed to planets could instead arise from slow modes; the two hypotheses can be distinguished by long-term measurements of the pattern speed of the features.