Global effects of thermal conduction on two-phase media

Abstract

Astrophysical gases are often constrained to exist in two or more phases, which have approximately the same pressure but different temperatures and densities. Such systems are often modeled as consisting of cold clouds or filaments embedded in a hot intercloud medium. However, thermal conduction or hydrodynamic mixing processes tend to homogenize a multiphase system, so it is unlikely that such systems are in a stationary state. This paper examines the evolution of two-phase systems which exchange mass between the phases. The general time-dependent theory of two-phase media with mass exchange due to thermal conduction is developed. Heating and cooling processes in the hot intercloud medium dominate thermal conduction over distances exceeding a critical value, which we term the "Field length." In this paper we focus on the case in which the size of the medium is greater than the Field length, so that thermal conduction from the boundary is negligible; our work is thus complementary to that of Balbus. Furthermore, the volume filling factor of the clouds is taken to be small, and classical thermal conduction is assumed. The criterion for thermal instability in a cloudy medium is derived. In the isochoric case, the mean density of the system is held fixed, and we determine how the pressure and density of the intercloud medium evolve under the combined effects of heating and radiative cooling of the intercloud gas on the one hand and evaporation and condensation of the clouds on the other. For the case in which the pressure is held fixed (the "isobaric" case), we determine the equilibrium density to which the system evolves. The theory is illustrated by a detailed discussion of the case in which the intercloud gas is heated by Compton scattering in a hard radiation field and cooled by brems-strahlung and inverse Compton scattering. The theory is applied briefly to the broad-line regions of active galactic nuclei and the interstellar medium. An appendix presents the simpler theory of two-phase media in the absence of mass exchange.