The effects of similarity breaking on the intracluster medium
  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. 
E. J. Lloyd-Davies, R. G. Bower, T. J. Ponman