Oscillations and stability of polytropic filaments

TL;DR

This paper analyzes the oscillations and stability of self-gravitating cylindrical fluid and collisionless systems, identifying conditions for stability and instability of various modes through perturbation analysis.

Contribution

It provides a detailed stability analysis of polytropic filaments, including the classification of modes and conditions for their stability or instability, extending understanding beyond spherical systems.

Findings

Radial modes become unstable if adiabatic exponent < 1

Nonradial g modes become unstable if adiabatic exponent > polytrope index

Collisionless filaments with ergodic distributions are stable to perturbations

Abstract

We study the oscillations and stability of self-gravitating cylindrically symmetric fluid systems and collisionless systems. This is done by studying small perturbations to the equilibrium system and finding the normal modes, using methods similar to those used in astroseismology. We find that there is a single sequence of purely radial modes that become unstable if the adiabatic exponent is less than 1. Nonradial modes can be divided into p modes, which are stable and pressure-driven, and g modes, which are are gravity driven. The g modes become unstable if the adiabatic exponent is greater than the polytrope index. These modes are analogous to the modes of a spherical star, but their behavior is somewhat different because a cylindrical geometry has less symmetry than a spherical geometry. This implies that perturbations are classified by a radial quantum number, an azimuthal quantum number, and wavelength in the z direction, which can become arbitrarily large. We find that decreasing this wavelength increases the frequency of stable modes and increases the growth rate of unstable modes. We use use variational arguments to demonstrate that filaments of collisionless matter with ergodic distribution functions are stable to purely radial perturbations, and that filaments with ergodic power-law distribution functions are stable to all perturbations.