A simple and accurate approximation for the Q stability parameter in multi-component and realistically thick discs

In this paper, we propose a Q stability parameter that is more realistic than those commonly used, and is easy to evaluate [see Eq. (19)]. Using our Q_N parameter, you can take into account several stellar and/or gaseous components as well as the stabilizing effect of disc thickness, you can predict which component dominates the local stability level, and you can do all that simply and accurately. To illustrate the strength of Q_N, we analyse the stability of a large sample of spirals from The HI Nearby Galaxy Survey (THINGS), treating stars, HI and H_2 as three distinct components. Our analysis shows that H_2 plays a significant role in disc (in)stability even at distances as large as half the optical radius. This is an important aspect of the problem, which was missed by previous (two-component) analyses of THINGS spirals. We also show that HI plays a negligible role up to the edge of the optical disc; and that the stability level of THINGS spirals is, on average, remarkably flat and well above unity.