Exploring the Energetics of Intracluster Gas with a Simple and Accurate
  Model
  The state of the hot gas in clusters of galaxies is investigated with a set
of model clusters, created by assuming a polytropic equation of state
(Gamma=1.2) and hydrostatic equilibrium inside gravitational potential wells
drawn from a dark matter simulation. Star formation, energy input, and
nonthermal pressure support are included. To match the gas fractions seen in
non-radiative hydrodynamical simulations, roughly 5% of the binding energy of
the dark matter must be transferred to the gas during cluster formation; the
presence of nonthermal pressure support increases this value. In order to match
X-ray observations, scale-free behavior must be broken. This can be due to
either variation of the efficiency of star formation with cluster mass M_500,
or the input of additional energy proportional to the formed stellar mass M_F.
These two processes have similar effects on X-ray scalings. If 9% of the gas is
converted into stars, independent of cluster mass, then feedback energy input
of 1.2e-5*M_Fc^2 (or ~1.0 keV per particle) is required to match observed
clusters. Alternatively, if the stellar mass fraction varies as M_500^-0.26
then a lower feedback of 4e-6*M_Fc^2 is needed, and if the stellar fraction
varies as steeply as M_500^-0.49 then no additional feedback is necessary. The
model clusters reproduce the observed trends of gas temperature and gas mass
fraction with cluster mass, as well as observed entropy and pressure profiles;
thus they provide a calibrated basis with which to interpret upcoming SZ
surveys. One consequence of the increased gas energy is that the baryon
fraction inside the virial radius is less than roughly 90% of the cosmic mean,
even for the most massive clusters.
