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 α ρ 2 T α , where p, T and α are the density, temperature and a free parameter, respectively. Given a, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows: p(x = 0, t) oc (t c - t) -η/12-α) and P(x = 0, t) α (t c - t) 1-η)/1-α) , where t c is the epoch at which the central density becomes infinite. For η ∼ 0 the solution describes the isochoric mode, whereas for η ∼ 1 the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for 0 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 (H i clouds and molecular clouds) by thermal instability.