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

James Gurian, Boyuan Liu, Donghui Jeong, Takashi Hosokawa, Shingo Hirano, Naoki Yoshida

Published 2024-08-23Version 1

We present an analytic description of the spherically symmetric gravitational collapse of radiatively cooling gas clouds. 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, our results agree well with full hydrodynamical treatments.