Self-similar solutions for the dynamical condensation of a radiative gas layer

Abstract

A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time $\propto {\rho }^2{T}^{\alpha }$, where $\rho$, $T$ and $\alpha$ are density, temperature and a free parameter, respectively. Given $\alpha$, a family of self-similar solutions with one parameter $\eta$ is found in which the central density and pressure evolve as follows: $\rho (x=0,t)\propto (t_{\mathrm{c}}-t{)}^{-\eta /(2-\alpha )}$ and $P(x=0,t)\propto (t_{\mathrm{c}}-t{)}^{(1-\eta )/(1-\alpha )}$, where $t_{\mathrm{c}}$ is an epoch when the central density becomes infinite. For $\eta \sim 0$, the solution describes the isochoric mode, whereas for $\eta \sim 1$, the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for $0<\eta <1$. No self-similar solution is found for $\alpha >1$. We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (HI cloud and molecular cloud) by thermal instability.

Accepted for Monthly Notices of the Royal Astronomical Society: 9 pages, 7 figures

References in corpus (3)

• Molecular Cloud Evolution II. From cloud formation to the early stages of star formation in decaying conditions
• The Birth of Molecular Clouds: Formation of Atomic Precursors in Colliding Flows
• Formation and evolution of density singularities in hydrodynamics of inelastic gases