An Analytic Model of Gravitational Collapse Induced by Radiative Cooling: Instability Scale, Infall Velocity, and Accretion Rate

TL;DR

This paper develops an analytic model for gravitational collapse in radiatively cooling gas clouds, identifying the instability scale, infall velocity, and accretion rate, and validating results against hydrodynamical simulations.

Contribution

It introduces a novel analytic approach that links microphysical cooling processes to gravitational instability and collapse dynamics in gas clouds.

Findings

The model accurately predicts the instability mass scale across different cooling scenarios.

It clarifies the distinction between core contraction and envelope instability.

Results agree well with full hydrodynamical simulations.

Abstract

We present an analytic description of the spherically symmetric gravitational collapse of radiatively cooling gas clouds, which illustrates the mechanism by which radiative cooling induces gravitational instability at a characteristic mass scale determined by the microphysics of the gas. The approach is based on developing the "one-zone" density-temperature relationship of the gas into a full dynamical model. We convert this density-temperature relationship into a barotropic equation of state, which we use to calculate the density and velocity profiles of the gas. From these quantities, we calculate the time-dependent mass accretion rate onto the center of the cloud. The approach clarifies the mechanism by which radiative cooling induces gravitational instability. In particular, we distinguish the rapid, quasi-equilibrium contraction of a cooling gas core to high central densities from the legitimate instability this contraction establishes in the envelope. We develop a refined criterion for the mass scale of this instability, based only on the chemical-thermal evolution in the core. We explicate our model in the context of a primordial mini-halo cooled by molecular hydrogen, and then provide two further examples, a delayed collapse with hydrogen deuteride cooling and the collapse of an atomic cooling halo. In all three cases, we show that our results agree well with full hydrodynamical treatments.