On the nature of the radial orbit instability in spherically symmetric collisionless stellar systems

TL;DR

This paper investigates the radial orbit instability in spherically symmetric stellar systems, revealing different modes of instability depending on orbital configurations and challenging existing interpretations of the phenomenon.

Contribution

It provides a detailed analysis of the modes of radial orbit instability, showing that both slow and fast modes exist and questioning the sole orbital interpretation of the instability.

Findings

Slow modes occur when eccentric orbits are near the center.

Fast modes involve oscillatory unstable modes with frequencies comparable to dynamical frequencies.

Both even and odd spherical harmonics can be unstable, depending on orbital distribution.

Abstract

We consider a two-parametric family of radially anisotropic models with non-singular density distribution in the centre. If highly eccentric orbits are locked near the centre, the characteristic growth rate of the instability is much less than the Jeans and dynamic frequencies of the stars (slow modes). The instability occurs only for even spherical harmonics and the perturbations are purely growing (aperiodic). On the contrary, if all orbits nearly reach the outer radius of the sphere, both even and odd harmonics are unstable. Unstable odd modes oscillate having characteristic frequencies of the order of the dynamical frequencies (fast modes). Unstable even harmonics contain a single aperiodic mode and several oscillatory modes, the aperiodic mode being the most unstable. The question of the nature of the radial orbit instability (ROI) is revisited. Two main interpretations of ROI were suggested in the literature. The first one refers to the classical Jeans instability associated with the lack of velocity dispersion of stars in the transverse direction. The second one refers to Lynden-Bell's orbital approach to bar formation in disc galaxies, which implies slowness and bi-symmetry of the perturbation. Oscillatory modes, odd spherical harmonics modes, and non-slow modes found in one of the models show that the orbital interpretation is not the only possible.