The formation of hot gaseous haloes around galaxies
  We use a suite of hydrodynamical cosmological simulations from the Evolution
and Assembly of GaLaxies and their Environments (EAGLE) project to investigate
the formation of hot hydrostatic haloes and their dependence on feedback
mechanisms. We find that the appearance of a strong bimodality in the
probability density function (PDF) of the ratio of the radiative cooling and
dynamical times for halo gas provides a clear signature of the formation of a
hot corona. Haloes of total mass $10^{11.5}-10^{12}{\rm{M}}_{\odot}$ develop a
hot corona independent of redshift, at least in the interval $z=0-4$ where the
simulation has sufficiently good statistics. We analyse the build up of the hot
gas mass in the halo, $M_{\rm{hot}}$, as a function of halo mass and redshift
and find that while more energetic galactic winds powered by SNe increases
$M_{\rm{hot}}$, AGN feedback reduces it by ejecting gas from the halo. We also
study the thermal properties of gas accreting onto haloes and measure the
fraction of shock-heated gas as a function of redshift and halo mass. We
develop analytic and semianalytic approaches to estimate a `critical halo
mass', $M_{\rm{crit}}$, for hot halo formation. We find that the mass for which
the heating rate produced by accretion shocks equals the radiative cooling
rate, reproduces the mass above which haloes develop a significant hot
atmosphere. This yields a mass estimate of $M_{\rm{crit}} \approx
10^{11.7}{\rm{M}}_{\odot}$ at $z=0$, which agrees with the simulation results.
The value of $M_{\rm{crit}}$ depends more strongly on the cooling rate than on
any of the feedback parameters.
