Adiabatic collapse of non-homogeneous self-gravitating gas cloud

Abstract

In this letter, we find the critical mass of a self-gravitating, spherically symmetric gas cloud, above which the fluid, within the bubble, collapses. Our analysis departs from a non-homogeneous equilibrium density, satisfying the Boltzmann relation. A time scale is defined in terms of the adiabatic index of the gas. Subsequently, a sinusoidal perturbation around equilibrium is regarded, thereby leading to a dispersion relation of frequency with wavelength, which does not depend on geometrical curvature effects. Such a formulation clearly justifies that the collapse occurs much faster than predicted by the well-known Jeans approach. The equilibrium profiles of the density, gravitational field, and potential are obtained as functions of the spherical radius coordinate at marginal instability. Since our theory captures the essential physics of gravitational collapse, it can be used as the starting point for several advancements in galactic dynamics.