Local gravitational instability of two-component thick discs in three dimensions

¹ Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
² DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark

Received: 22 April 2024
Accepted: 20 May 2024

Abstract

Aims. The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study the local gravitational instability of two-component thick discs in three dimensions.

Methods. We use as a starting point a recently proposed analytic three-dimensional (3D) instability criterion for discs with non-negligible thickness that takes the form Q_3D < 1, where Q_3D is a 3D version of the classical 2D Toomre Q parameter for razor-thin discs. Here, we extend the 3D stability analysis to two-component discs, considering first the influence on Q_3D of a second unresponsive component, and then the case in which both components are responsive. We present the application to two-component discs with isothermal vertical distributions, which can represent, for instance, galactic discs with both stellar and gaseous components. Finally, we relax the assumption of vertical isothermal distribution, by studying one-component self-gravitating discs with polytropic vertical distributions for a range of values of the polytropic index corresponding to convectively stable configurations.

Results. We find that Q_3D < 1, where Q_3D can be computed from observationally inferred quantities, is a robust indicator of local gravitational instability, depending only weakly on the presence of a second component and on the vertical gradient of temperature or velocity dispersion. We derive a sufficient condition for local gravitational instability in the midplane of two-component discs, which can be employed when both components have Q_3D > 1.