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 properties of galaxy clusters .
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 logarithmic slope from the self-similar prediction of 1.5 , to that of the observed relation , \sim 2 .
Heating of the intracluster 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 in the range 0.5-0.75 keV per particle , while concentration variation is found to have only a small effect on this relation .
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 logarithmic slope of \sim 2.7 compared to recent observations in the range 2.6-2.9 , whilst the observed steepening of the relation in galaxy groups is predicted by the model when heating in the range 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 all the observed relations .
Scatter in the energy injection and concentration may account for a large proportion of the scatter in the observed relations .