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,
observationally-motivated prescription which enforces global thermal
equilibrium when averaged over large scales. The plasma remains susceptible to
local thermal instability, however, and cooling drives an inward flow of
material. In contrast to previous results, we argue that 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 t_cool/t_ff controls
the saturation of the thermal instability: when t_cool/t_ff < 1, the plasma
develops extended multi-phase structure, whereas when t_cool / t_ff > 1 it does
not. (In a companion paper, we show that the criterion for thermal instability
in a spherical potential is somewhat less stringent, t_cool / t_ff < 10.) When
thermal conduction is anisotropic with respect to the magnetic field, the
criterion for multi-phase structure is essentially independent of the thermal
conductivity of the plasma. Our criterion for local thermal instability to
produce multi-phase structure is an extension of the cold vs. hot accretion
modes in galaxy formation that applies at all radii in hot halos, not just to
the virial shock. We show that this criterion is consistent with data on
multi-phase gas in the ACCEPT sample of clusters; in addition, when t_cool /
t_ff > 1, the net cooling rate to low temperatures and the mass flux to small
radii are suppressed enough relative to models without heating to be
qualitatively consistent with star formation rates and x-ray line emission in
groups and clusters.
