  Using a simple analytic approach we address the question of whether radiative
cooling, nongravitational heating and cooling plus heating models can
simultaneously explain the observed global X-ray properties (entropy and X-ray
luminosity distributions) of groups and clusters and the residual soft X-ray
background (XRB) after discrete sources are removed. Within the framework of
typical cold dark matter structure formation characterized by an amplitude of
matter power spectrum sigma_8=0.9, it is argued that while radiative cooling
alone is able to marginally reproduce the entropy floor detected in the central
regions of groups and clusters, it is insufficient to account for the
steepening of the X-ray luminosity - temperature relation for groups and the
unresolved soft XRB. A phenomenological preheating model, in which either an
extra specific energy budget or an entropy floor is added to the hot gas in
groups and clusters, fails in the recovery of at least one of the X-ray
observed features. Finally, the soft XRB predicted by our combined model of
cooling plus heating exceeds the observational upper limits by a factor of ~2,
if the model is required to reproduce the observed entropy and X-ray luminosity
- temperature relationships of groups and clusters. If the discrepancy is not a
result of the oversimplification of our analytic models, this implies that
either our current understanding of the physical processes of the hot gas is
still incomplete, or the normalization of the present power spectrum has been
systematically overestimated. For the latter, both the X-ray properties of
groups and clusters and the XRB predicted by preheating model and cooling plus
heating model can be reconciled with the X-ray observations if a lower value of
the normalization parameter sigma_8 \approx 0.7 is assumed.

Astrophysics