A Role for Turbulence in Circumgalactic Precipitation
  Abundant observational evidence indicates that the cooling time t_cool of the
hot ambient medium pervading a massive galaxy does not drop much below 10 times
the freefall time t_ff at any radius. Theoretical models have accounted for
this finding by hypothesizing that cold clouds start to condense out of the
ambient medium when t_cool/t_ff < 10 and fuel a strong black-hole feedback
response that reheats the ambient gas, but those models have not yet been able
to provide a simple explanation for the origin of the critical t_cool/t_ff
ratio. This paper explores a heuristic model for condensation that links the
critical ratio to turbulent driving of gravity-wave oscillations. In the linear
regime, internal gravity waves are thermally unstable in a thermally balanced
medium. Buoyancy oscillations in a balanced medium with t_cool/t_ff therefore
grow until they saturate without condensing at an amplitude that depends on
t_cool/t_ff. However, in a medium with 10 < t_cool/t_ff < 20, turbulence with a
velocity dispersion roughly half the galaxy's stellar velocity dispersion can
drive those oscillations into condensation. Intriguingly, this is indeed the
gas-phase velocity dispersion observed among galaxy-cluster cores that contain
multiphase gas. It is therefore possible that both the critical t_cool/t_ff
ratio for condensation of ambient gas and the level of turbulence in that gas
are determined by coupling between condensation, feedback, and turbulence. Such
a system can converge to a well-regulated equilibrium state, as long as the
fraction of feedback energy that goes into turbulence is significantly less
than the fraction that goes more directly into heat.
