The effective stability parameter for two-component galactic discs: Is 1/Q ~ 1/Q_stars + 1/Q_gas ?

TL;DR

This paper critically examines the Wang-Silk approximation for the effective stability parameter in two-component galactic discs, proposing a more accurate formula that includes disc thickness effects, with broad applications in galaxy stability analysis.

Contribution

It introduces a refined approximation for the effective Q parameter in two-component discs, improving accuracy over the Wang-Silk approximation by incorporating disc thickness effects.

Findings

The Wang-Silk approximation's accuracy depends on velocity dispersions and Toomre parameters.

A new approximation significantly improves stability predictions.

The generalized Q parameter can be applied across various galactic contexts.

Abstract

The Wang-Silk approximation, 1/Q ~ 1/Q_stars + 1/Q_gas, is frequently used for estimating the effective Q parameter in two-component discs of stars and gas. Here we analyse this approximation in detail, and show how its accuracy depends on the radial velocity dispersions and Toomre parameters of the two components. We then propose a much more accurate but still simple approximation for the effective Q parameter, which further takes into account the stabilizing effect of disc thickness. Our effective Q parameter is a natural generalization of Toomre's Q, and as such can be used in a wide variety of contexts, e.g. for predicting star formation thresholds in galaxies or for measuring the stability level of galactic discs at low and high redshifts.