Cold gas in cluster cores: Global stability analysis and non-linear
  simulations of thermal instability
  We perform global linear stability analysis and idealized numerical
simulations in global thermal balance to understand the condensation of cold
gas from hot/virial atmospheres (coronae), in particular the intracluster
medium (ICM). We pay particular attention to geometry (e.g., spherical versus
plane-parallel) and the nature of the gravitational potential. Global linear
analysis gives a similar value for the fastest growing thermal instability
modes in spherical and Cartesian geometries. Simulations and observations
suggest that cooling in halos critically depends on the ratio of the cooling
time to the free-fall time ($t_{cool}/t_{ff}$). Extended cold gas condenses out
of the ICM only if this ratio is smaller than a threshold value close to 10.
Previous works highlighted the difference between the nature of cold gas
condensation in spherical and plane-parallel atmospheres; namely, cold gas
condensation appeared easier in spherical atmospheres. This apparent difference
due to geometry arises because the previous plane-parallel simulations focussed
on {\em in situ} condensation of multiphase gas but spherical simulations
studied condensation {\em anywhere} in the box. Unlike previous claims, our
nonlinear simulations show that there are only minor differences in cold gas
condensation, either in situ or anywhere, for different geometries. The amount
of cold gas condensing depends on the shape of the gravitational potential
well; gas has more time to condense if gravitational acceleration decreases
toward the center. In our idealized simulations with heating balancing cooling
in each layer, there can be significant mass/energy/momentum transfer across
layers that can trigger condensation and drive $t_{cool}/t_{ff}$ far beyond the
critical value close to 10. Triggered condensation is very prominent in
plane-parallel simulations, in which a large amount of cold gas condenses out.
