Numerical calculation of linear modes in stellar disks

TL;DR

This paper introduces a coordinate-space method for calculating linear modes in stellar disks, providing a feasible alternative to action-angle approaches, and analyzes the stability of various disk models.

Contribution

It presents a novel coordinate-space Fourier expansion method for solving the collisionless Boltzmann equation in stellar disks.

Findings

The method is feasible and straightforward to implement.

Velocity dispersion, halo mass, and anisotropy influence disk stability.

Stability varies with different disk parameters.

Abstract

We present a method for solving the two-dimensional linearized collisionless Boltzmann equation using Fourier expansion along the orbits. It resembles very much solutions present in the literature, but it differs by the fact that everything is performed in coordinate space instead of using action-angle variables. We show that this approach, though less elegant, is both feasible and straightforward. This approach is then incorporated in a matrix method in order to calculate self-consistent modes, using a set of potential-density pairs which is obtained numerically. We investigated the stability of some unperturbed disks having an almost flat rotation curve, an exponential disk and a non-zero velocity dispersion. The influence of the velocity dispersion, halo mass and anisotropy on the stability is further discussed.