Thermal Instability in a Cooling and Expanding Medium Including Self-Gravity and Conduction

A systematic study of the linear thermal stability of a medium subject to cooling, self-gravity, and thermal conduction is carried out for the case when the unperturbed state is subject to global cooling and expansion. A general, recursive WKB solution for the perturbation problem is obtained that can be applied to a large variety of situations in which there is a separation of timescales for different physical processes. Solutions are explicitly given and discussed for the case in which sound propagation and/or self-gravity are the fastest processes, with cooling, expansion, and thermal conduction operating on slower timescales. A brief discussion is also added for the solutions in the cases in which cooling or conduction operate on the fastest timescale. The general WKB solution obtained in this paper permits solving the problem of the effect of thermal conduction and self-gravity on the thermal stability of a globally cooling and expanding medium. As a result of the analysis, the critical wavelength (often called the "Field length") above which cooling makes the perturbations unstable against the action of thermal conduction is generalized to the case of an unperturbed background with net cooling. As an astrophysical application, the "generalized Field length" is calculated for a hot (104-108 K), optically thin medium (as pertains, for instance, for the hot interstellar medium of supernova remnants or superbubbles) using a realistic cooling function and including a weak magnetic field. The stability domains are compared with the predictions made on the basis of models for which the background is in thermal equilibrium. The instability domain of the sound waves in particular is seen to be much larger in the case with net global cooling.