The Effect of Radiative Cooling on the Sunyaev-Zel'dovich Cluster Counts and Angular Power Spectrum: Analytic Treatment

Recently, the entropy excess detected in the central cores of groups and clusters has been successfully interpreted as being due to radiative cooling of the hot intragroup/intracluster gas. In such a scenario, the entropy floors $S_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}}$ in groups/clusters at any given redshift are completely determined by the conservation of energy. In combination with the equation of hydrostatic equilibrium and the universal density profile for dark matter, this allows us to derive the remaining gas distribution of groups and clusters after the cooled material is removed. Together with the Press-Schechter mass function we are able to evaluate effectively how radiative cooling can modify the predictions of SZ cluster counts and power spectrum. It appears that our analytic results are in good agreement with those found by hydrodynamical simulations. Namely, cooling leads to a moderate decrease of the predicted SZ cluster counts and power spectrum as compared with standard scenario. However, without taking into account energy feedback from star formation which may greatly suppress cooling efficiency, it is still premature to claim that this modification is significant for the cosmological applications of cluster SZ effect.