  We compare the mass cooling rates and cumulative cooled-down masses predicted
by several semi-analytical (SA) cooling models with cosmological hydrodynamical
simulations performed using the AREPO code (ignoring processes such as feedback
and chemical enrichment). The SA cooling models are the new GALFORM cooling
model introduced in Hou et al. (2017), along with two earlier GALFORM cooling
models and the L-GALAXIES and MORGANA cooling models. We find that the
predictions of the new GALFORM cooling model are generally in best agreement
with the simulations. For halos with $M_{\rm halo}\lesssim 3\times
10^{11}\,{\rm M}_{\odot}$, the SA models predict that the timescale for
radiative cooling is shorter than or comparable to the gravitational infall
timescale. Even though SA models assume that gas falls onto galaxies from a
spherical gas halo, while the simulations show that the cold gas is accreted
through filaments, both methods predict similar mass cooling rates, because in
both cases the gas accretion occurs on similar timescales. For halos with
$M_{\rm halo}\gtrsim 10^{12}\,{\rm M}_{\odot}$, gas in the simulations
typically cools from a roughly spherical hot gas halo, as assumed in the SA
models, but the halo gas gradually contracts during cooling, leading to
compressional heating. SA models ignore this heating, and so overestimate mass
cooling rates by factors of a few. At low redshifts halo major mergers or a
sequence of successive smaller mergers are seen in the simulations to strongly
heat the halo gas and suppress cooling, while mergers at high redshifts do not
suppress cooling, because the gas filaments are difficult to heat up. The new
SA cooling model best captures these effects.
