Q criterion for disc stability modified by external tidal field

TL;DR

This paper generalizes the Q stability criterion for astrophysical discs by incorporating external gravitational and tidal fields, revealing that such fields can significantly influence disc stability, with applications to galactic structures.

Contribution

It introduces a linear perturbation analysis that modifies the classical Q criterion to account for external gravitational and tidal effects on disc stability.

Findings

External fields increase the modified Q value, enhancing stability.

Galactic discs are often marginally stable without dark matter halos.

Dark matter halos play a crucial role in stabilizing galactic discs.

Abstract

The standard Q criterion (with Q > 1) describes the local stability of a disc supported by rotation and random motion. Most astrophysical discs, however, are under the influence of an external gravitational field which can affect their stability. A typical example is a galactic disc embedded in a dark matter halo. Here we do a linear perturbation analysis for a disc in an external field, and obtain a generalized dispersion relation and a modified stability criterion. An external field has two effects on the disc dynamics: first, it contributes to the unperturbed rotational field, and second, it adds a tidal field term in the stability parameter. A typical disruptive tidal field results in a higher modified Q value and hence leads to a more stable disc. We apply these results to the Milky Way, and to a low surface brightness galaxy UGC 7321. We find that in each case the stellar disc by itself is barely stable and it is the dark matter halo that stabilizes the disc against local, axisymmetric gravitational instabilities. This result has been largely missed so far because in practice the value for Q for a galactic disc is obtained in a hybrid fashion using the observed rotational field that is set by both the disc and the halo, and hence is higher than for a pure disc.