  We construct a family of simple analytical models of galaxy clusters at the
present epoch and compare its predictions with observational data. We explore
two processes that break the self-similarity of galaxy clusters: systematic
variation in the dark matter halo concentration and energy injection into the
intracluster gas, through their effects on the observed cluster properties.
Three observed relations between cluster properties and temperature are
employed to constrain the model; mass, slope of gas density profile (beta) and
luminosity. The slope of the mass-temperature relation is found to be
reproduced by our model when the observed variation in concentration is
included, raising the slope from the self-similar prediction of 1.5, to that of
the observed relation, ~ 2. Heating of the gas is observed to have little
effect on the mass-temperature relation. The mean trend in the beta-temperature
relation is reproduced by energy injection of 0.5-0.75 keV per particle, while
concentration variation has only a small effect. Excess energies calculated for
individual systems from the beta-temperature relation suggest that the lowest
mass systems may have excess energies that are biased to lower values by
selection effects. The observed properties of the luminosity-temperature
relation are reproduced by the combined effects of excess energy and a trend in
the dark matter concentration. At high masses the observed variation in dark
matter concentration results a slope of ~ 2.7 compared to recent observations
in the range 2.6-2.9, whilst the observed steepening in galaxy groups is
predicted when heating of 0.5-0.75 keV per particle is included. Hence a
combination of energy injection and dark matter concentration variation appears
able to account for the mean trends in the observed relations.
