An analytic investigation of the scatter in the integrated X-ray   properties of galaxy groups and clusters
  (Abridged) We revisit the scaling relationships between the dark matter mass and observed X-ray luminosity and temperature of galaxy clusters and groups in the local Universe. Specifically, we compare recent observations with analytic models of the intracluster medium in which the gas entropy distribution has been shifted by a variable amount, K0, to investigate the origin of the scatter in these scaling relations, and its influence on the luminosity and temperature functions. We find that variations in halo concentration or formation epoch (which might determine the time available for low entropy gas to cool out) are insufficient to explain the amount of scatter in the mass-luminosity relation. Instead, a range of entropy floors at a fixed halo mass, spanning approximately 50 keV sq.cm to 700 keV sq.cm, is required to match the data. This range is likely related to the variance in heating and/or cooling efficiency from halo to halo. We demonstrate that these models are consistent with the observed temperature and luminosity functions of clusters, if scatter in the mass-luminosity relation is accounted for. Finally, we present predictions for the redshift evolution of these scaling relations and luminosity/temperature functions. Comparison with recent data at z<0.7 shows reasonable agreement with a model that assumes a median entropy floor of K0=200 keV sq.cm. When observations are extended to group scales (kT < 1 keV), this evolution will have the potential to discriminate between an entropy floor that is independent of redshift (for example, in a preheating scenario) and one that depends on the cooling time of the halo. 
Michael L. Balogh (1), Arif Babul (2), G. Mark Voit (3), Ian G.   McCarthy (2,4), Laurence R. Jones, Geraint F. Lewis (5), H...