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 _ { \circ } , 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 \sim 50 keV cm ^ { 2 } to \sim 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 } \sim 0.8 in agreement with WMAP measurements ( for h = 0.7 and \Omega _ { m } = 0.3 ) ; in particular the scatter in the mass–luminosity 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 _ { \circ } = 200 keV cm ^ { 2 } .
When observations are extended to group scales ( kT \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { % $ \scriptstyle \sim$ } } } 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 .