  We provide an analytic framework for interpreting observations of multiphase
circumgalactic gas that is heavily informed by recent numerical simulations of
thermal instability and precipitation in cool-core galaxy clusters. We start by
considering the local conditions required for the formation of multiphase gas
via two different modes: (1) uplift of ambient gas by galactic outflows, and
(2) condensation in a stratified stationary medium in which thermal balance is
explicitly maintained. Analytic exploration of these two modes provides
insights into the relationships between the local ratio of the cooling and
freefall time scales (i.e., t_cool / t_ff), the large-scale gradient of
specific entropy, and development of precipitation and multiphase media in
circumgalactic gas. We then use these analytic findings to interpret recent
simulations of circumgalactic gas in which global thermal balance is
maintained. We show that long-lasting configurations of gas with 5 < t_cool /
t_ff < 20 and radial entropy profiles similar to observations of local
cool-core galaxy cluster cores are a natural outcome of precipitation-regulated
feedback. We conclude with some observational predictions that follow from
these models. This work focuses primarily on precipitation and AGN feedback in
galaxy cluster cores, because that is where the observations of multiphase gas
around galaxies are most complete. However, many of the physical principles
that govern condensation in those environments apply to circumgalactic gas
around galaxies of all masses.
