Thermal Instability in Gravitationally-Stratified Plasmas: Implications for Multi-Phase Structure in Clusters and Galaxy Halos

We study the interplay among cooling, heating, conduction, and magnetic fields in gravitationally-stratified plasmas using simplified, plane-parallel numerical simulations. Since the physical heating mechanism remains uncertain in massive halos such as groups or clusters, we adopt a simple, phenomenological prescription which enforces global thermal equilibrium and prevents a cooling-flow. The plasma remains susceptible to local thermal instability, however, and cooling drives an inward flow of material. For physically plausible heating mechanisms in clusters, the thermal stability of the plasma is independent of its convective stability. We find that the ratio of the cooling timescale to the dynamical timescale tcool/tff controls the non-linear evolution and saturation of the thermal instability: when tcool/tff. 1, the plasma develops extended multi-phase structure, whereas when tcool/tff & 1 it does not. (In a companion paper, we show that the criterion for thermal instability in a more realistic, spherical potential is somewhat less stringent, tcool/tff. 10.) When thermal conduction is anisotropic with respect to the magnetic field, the criterion for multi-phase gas is essentially independent of th