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

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 proportional to rho T-2(alpha) rho, T and alpha are the 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) proportional to (t(c)-t)(-eta/(2-alpha)) P(x=0,t) proportional to (t(c)-t)((1-eta)/(1-alpha)), where t(c) is the epoch at which the central density becomes infinite. For eta similar to 0 the solution describes the isochoric mode, whereas for eta similar to 1 the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for 0 < 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 clouds and molecular clouds) by thermal instability.