On the Jeans criterion for hydrostatic and infalling gas

TL;DR

The work addresses local gravitational instability of non-rotating astrophysical fluids in the presence of an external potential, comparing hydrostatic and infalling configurations. It uses a self-consistent linear perturbation framework that accounts for background pressure and density gradients and derives the dispersion relations for both cases. The main result is that the classical Jeans criterion is not modified by the external field: hydrostatic backgrounds are locally stable, while infalling gas can become unstable if perturbations satisfy $k<k_{\rm J}$, even with non-gravitational forces like winds. This implies a regulatory role for Jeans fragmentation in galactic streams and molecular-cloud environments, while acknowledging limitations such as magnetic fields, turbulence, radiative cooling, and geometry that are not included in the analysis.

Abstract

We study the local gravitational instability of non-rotating astrophysical fluids allowing for the presence of an external gravitational potential in addition to the fluid self-gravity. We present a self-consistent linear-perturbation analysis taking into account pressure and density gradients in the background medium. We explore two different steady-state configurations for the unperturbed gas: hydrostatic equilibrium and infall into a gravitational potential well. We show that in both cases the instability criterion is the classical Jeans criterion, which, contrary to previous claims, is not modified by the presence of the external gravitational field. While in the case of hydrostatic equilibrium linear local perturbations are always gravitationally stable, the conditions for gravitational instability can be met in the case of infalling gas, also in the presence of additional non-gravitational forces such as that due to a wind. We conclude that the Jeans criterion can have a role in regulating the formation of clumps and star clusters in streams or shells of gas infalling into galactic gravitational potential wells, as well as, on smaller scales, the fragmentation of gas in collapsing molecular clouds.

Figures (1)

• Figure 1: Scheme of the Cartesian $x$-$z$ coordinate system adopted to describe locally a parcel of gas immersed in a gravitational potential. ${\boldsymbol g}$ is the gravitational field produced by the unperturbed total gravitational potential at the position of the parcel of gas.