Thermal Instability in the CGM of $L_{\star}$ Galaxies: Testing
  "Precipitation" Models with the FIRE Simulations
  We examine the thermodynamic state and cooling of the low-$z$ Circum-Galactic
Medium (CGM) in five FIRE-2 galaxy formation simulations of Milky Way-mass
galaxies. We find that the CGM in these simulations is generally multiphase and
dynamic, with a wide spectrum of largely nonlinear density perturbations
sourced by the accretion of gas from the Inter-Galactic Medium (IGM) and
outflows from both the central and satellite galaxies. We investigate the
origin of the multiphase structure of the CGM with a particle tracking analysis
and find that most of the low entropy gas has cooled from the hot halo as a
result of thermal instability triggered by these perturbations. The ratio of
cooling to free-fall timescales $t_{\rm cool}/t_{\rm ff}$ in the hot component
of the CGM spans a wide range $\sim 1-100$ at a given radius, but exhibits
approximately constant median values $\sim 5-20$ at all radii $0.1 R_{\rm vir}
< r < R_{\rm vir}$. These are similar to the $\approx 10-20$ value typically
adopted as the thermal instability threshold in ``precipitation'' models of the
ICM. Consequently, a one-dimensional model based on the assumption of a
constant $t_{\rm cool}/t_{\rm ff}$ and hydrostatic equilibrium approximately
reproduces the number density and entropy profiles of each simulation, but only
if it assumes the metallicity profile and temperature boundary condition taken
directly from the simulation. We explicitly show that the $t_{\rm cool}/t_{\rm
ff}$ value of a gas parcel in the hot component of the CGM does not predict its
probability of subsequently accreting onto the central galaxy. This suggests
that the value of $t_{\rm cool}/t_{\rm ff}$ is a poor predictor of thermal
stability in gaseous halos in which large-amplitude density perturbations are
prevalent.
