An analytic investigation of the scatter in the integrated X-ray proprties of galaxy groups and clusters

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, K-degrees, 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 and X-ray luminosity (M-L) relation. Instead, a range of entropy floors at a fixed halo mass, spanning approximately similar to 50-700 keV cm(2), 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, with a normalization of sigma(8)similar to 0.8 in agreement with Wilkinson Microwave Anisotropy Probe (WMAP) measurements (for h= 0.7 and Omega(m)= 0.3); in particular, the scatter in the M-L relation has an important influence on the shape of the luminosity function, and must be accounted for to provide a consistent result. 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 K-degrees= 200 keV cm(2). When observations are extended to group scales (kT less than or similar to 1 keV), this evolution will have the potential to discriminate between an entropy floor that is independent of redshift (e.g. in a preheating scenario) and one that depends on the cooling time of the halo.