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.
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