Jeans instability criterion modified by external tidal field

TL;DR

This paper generalizes the classical Jeans instability criterion by incorporating external tidal fields, revealing how such fields can either stabilize or destabilize astrophysical systems depending on their nature.

Contribution

It introduces a linear perturbation analysis that accounts for external tidal fields, deriving a modified dispersion relation and instability criterion applicable to realistic astrophysical environments.

Findings

Disruptive tidal fields increase the Jeans wavelength and stability.

Compressible tidal fields lower the instability threshold.

The modified criterion is analytically simple and broadly applicable.

Abstract

The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the influence of an external field such as the tidal field due to a neighbour. Here we do a linear perturbation analysis for a system in an external field, and obtain a generalized dispersion relation that depends on the wavenumber, the sound speed, and also the magnitude of the tidal field. A typical, disruptive tidal field is shown to make the system more stable against perturbations, and results in a higher effective Jeans wavelength. The minimum mass that can become unstable is then higher (super-Jeans) than the usual Jeans mass. Conversely, in a compressive tidal field, perturbations can grow even when the mass is lower (sub-Jeans). This approach involving the inclusion of tidal field opens up a new way of looking at instabilities in gravitating systems. The treatment is general and the simple analytical form of the modified Jeans criterion obtained makes it easily accessible.