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 tocooling, self-gravity and thermal conduction is carried out for the case whenthe unperturbed state is subject to global cooling and expansion. A general,recursive WKB solution for the perturbation problem is obtained which can beapplied to a large variety of situations in which there is a separation oftime-scales for the different physical processes. Solutions are explicitlygiven and discussed for the case when sound propagation and/or self-gravity arethe fastest processes, with cooling, expansion and thermal conduction operatingon slower time-scales. A brief discussion is also added for the solutions inthe cases in which cooling or conduction operate on the fastest time-scale. Thegeneral WKB solution obtained in this paper permits solving the problem of theeffect of thermal conduction and self-gravity on the thermal stability of aglobally cooling and expanding medium. As a result of the analysis, thecritical wavelength (often called Field length) above which cooling makes theperturbations unstable against the action of thermal conduction is generalizedto the case of an unperturbed background with net cooling. As an astrophysicalapplication, the generalized Field length is calculated for a hot (10^4 - 10^8K), optically thin medium (as pertains, for instance, for the hot interstellarmedium of SNRs or superbubbles) using a realistic cooling function andincluding a weak magnetic field. The stability domains are compared with thepredictions made on the basis of models for which the background is in thermalequilibrium. The instability domain of the sound waves, in particular, is seento be much larger in the case with net global cooling.Comment: 36 pages, 6 figures, accepted by ApJ, probable publication date: April 20, 200