Spiral instabilities: Linear and nonlinear effects

TL;DR

This paper investigates how co-orbiting perturbations in a stable disc galaxy induce spiral responses, revealing linear and nonlinear effects, resonance scattering, and the superposition of modes leading to transient spiral patterns.

Contribution

It demonstrates the linear and nonlinear responses of galactic discs to perturbations and explains the origin of shearing transient spirals as superpositions of normal modes.

Findings

Response amplitudes are proportional to perturbation masses.

Low-mass rings' responses disperse when removed, matching linear theory.

High-mass rings induce nonlinear resonance scattering and instabilities.

Abstract

We present a study of the spiral responses in a stable disc galaxy model to co-orbiting perturbing masses that are evenly spaced around rings. The amplitudes of the responses, or wakes, are proportional to the masses of the perturbations, and we find that the response to a low-mass ring disperses when it is removed -- behaviour that is predicted by linear theory. Higher mass rings cause nonlinear changes through scattering at the major resonances, provoking instabilities that were absent before the scattering took place. The separate wake patterns from two rings orbiting at differing frequencies, produce a net response that is an apparently shearing spiral. When the rings have low mass, the evolution of the simulation is both qualitatively and quantitatively reproduced by linear superposition of the two separate responses. We argue that apparently shearing transient spirals in simulations result from the superposition of two or more steadily rotating patterns, each of which is best accounted for as a normal mode of the non-smooth disc.