  In several models of galaxy formation feedback occurs in cycles or mainly at
high redshift. At times and in regions where feedback heating is ineffective,
hot gas in the galaxy halo is expected to form a cooling flow, where the gas
advects inward on a cooling timescale. Cooling flow solutions can thus be used
as a benchmark for observations and simulations to constrain the timing and
extent of feedback heating. Using analytic calculations and idealized 3D
hydrodynamic simulations, we show that for a given halo mass and cooling
function, steady-state cooling flows form a single-parameter family of
solutions, while initially hydrostatic gaseous halos converge on one of these
solutions within a cooling time. The solution is thus fully determined once
either the mass inflow rate $\dot{M}$ or the total halo gas mass are known. In
the Milky Way (MW) halo, a cooling flow with $\dot{M}$ equal to the star
formation rate predicts a ratio of the cooling time to the free-fall time of
~10, similar to some feedback-regulated models. This solution also correctly
predicts observed OVII and OVIII absorption columns, and the gas density
profile implied by OVII and OVIII emission. These results suggest ongoing
heating by feedback may be negligible in the inner MW halo. Extending similar
solutions out to the cooling radius however underpredicts observed OVI columns
around the MW and around other low-redshift star-forming galaxies. This can be
reconciled with the successes of the cooling flow model with either a mechanism
which preferentially heats the OVI-bearing outer halo, or alternatively if OVI
traces cool photoionized gas beyond the accretion shock. We also demonstrate
that the entropy profiles of some of the most relaxed clusters are reasonably
well described by a cooling flow solution.
