Unstable Disk Galaxies. II. the Origin of Growing and Stationary Modes

TL;DR

This paper analyzes the physical mechanisms behind instabilities in stellar disks, focusing on resonances and their role in the growth or suppression of bar and spiral modes, providing new insights into disk stability.

Contribution

It introduces a detailed Fourier decomposition of unstable modes, explores resonance effects on stability, and derives criteria for stability against non-axisymmetric perturbations.

Findings

Resonance capture of stars triggers mode growth.

Mode saturation occurs due to resonance overlapping.

Disks with diverse orbits can be stable against certain perturbations.

Abstract

I decompose the unstable growing modes of stellar disks to their Fourier components and present the physical mechanism of instabilities in the context of resonances. When the equilibrium distribution function is a non-uniform function of the orbital angular momentum, the capture of stars into the corotation resonance imbalances the disk angular momentum and triggers growing bar and spiral modes. The stellar disk can then recover its angular momentum balance through the response of non-resonant stars. I carry out a complete analysis of orbital structure corresponding to each Fourier component in the radial angle, and present a mathematical condition for the occurrence of van Kampen modes, which constitute a continuous family. I discuss on the discreteness and allowable pattern speeds of unstable modes and argue that the mode growth is saturated due to the resonance overlapping mechanism. An individually growing mode can also be suppressed if the corotation and inner Lindblad resonances coexist and compete to capture a group of stars. Based on this mechanism, I show that self-consistent scale-free disks with a sufficient distribution of non-circular orbits should be stable under perturbations of angular wavenumber $m>1$. I also derive a criterion for the stability of stellar disks against non-axisymmetric excitations.