  Studies of the X-ray surface brightness profiles of clusters, coupled with
theoretical considerations, suggest that the breaking of self-similarity in the
hot gas results from an `entropy floor', established by some heating process,
which affects the structure of the intracluster gas strongly in lower mass
systems. Fitting analytical models for the radial variation in gas density and
temperature to X-ray spectral images from the ROSAT PSPC and ASCA GIS, we
derive gas entropy profiles for 20 galaxy clusters and groups. Scaling these
profiles to coincide in the self-similar case, the lowest mass systems are
found to have higher scaled entropy profiles than more massive systems. This
appears to be due to a baseline entropy of 70-140 h50^-1/3 keV cm^2, depending
on the extent to which shocks have been suppressed in low mass systems. The
extra entropy may be present in all systems, but is detectable only in poor
clusters, compared to the entropy generated by gravitational collapse. This
excess entropy appears to be distributed uniformly with radius outside the
central cooling regions. We determine the energy associated with this entropy
floor, by studying the net reduction in binding energy of the gas in low mass
systems, and find that it corresponds to a preheating temperature of ~0.3 keV.
Since the relationship between entropy and energy injection depends upon gas
density, we can combine the excesses of 70-140 keV cm^2 and 0.3 keV to derive
the typical electron density of the gas into which the energy was injected. The
resulting value of 1-3x10^-4 h50^1/2 cm-3, implies that the heating must have
happened prior to cluster collapse but after a redshift z~7-10. The energy
requirement is well matched to the energy from supernova explosions responsible
for the metals which now pollute the intracluster gas.
