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 \sim 2 , if the model is required to reproduce the observed entropy and X-ray luminosity - temperature relationships of groups and clusters .
Inclusion of the cosmic variation of metallicity and the self-absorption of the cooled gas as a result of radiative cooling in groups and clusters , or exclusion of the contribution of nearby , massive clusters to the XRB does not significantly alter the situation .
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 .