Bisymmetric normal modes in soft-centred and realistic galactic discs

TL;DR

This paper compares three numerical methods for identifying unstable modes in stellar galactic discs, demonstrating their effectiveness and limitations across different galaxy models with varying central mass concentrations.

Contribution

It evaluates the reliability and applicability of a point collocation scheme, a basis expansion method, and a finite element approach for analyzing galactic disc stability.

Findings

The collocation scheme reliably detects spectra in both low and high mass concentration models.

The basis expansion method was unsuitable for high mass concentration models.

The finite element method is sensitive to resonant orbits depending on interpolation choices.

Abstract

We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method. Using models of galaxies with low and high mass concentration to the center, the existence of two different kinds of spectra of unstable modes is demonstrated. Characteristic features of methods and obtained spectra are discussed. Despite ignoring any constraint on the continuity or differentiability of the perturbed DF, the collocation scheme is reliable for obtaining spectra and patterns in both kinds of models. The method based on the expansion of the perturbed potential and surface density over a biorthogonal basis was not applicable to a model with high mass concentration. The finite element method successfully used in various fields of science and engineering is currently sensitive to the presence of resonant orbits due to the choice of interpolation functions for the distribution function.