CMB Comptonization in Clusters: Spectral and Angular Power from Evolving Polytropic Gas

The angular power spectrum of the Sunyaev-Zeldovich (SZ) effect is calculated in the $\Lambda$CDM cosmological model with the aim of investigating its detailed dependence on the cluster population, gas morphology, and gas evolution. We calculate the power spectrum for three different mass functions, compute it within the framework of isothermal and polytropic gas distributions, and explore the effect of gas evolution on the magnitude and shape of the power spectrum. We show that it is indeed possible to explain the `excess' power measured by the CBI experiment on small angular scales as originating from the SZ effect without (arbitrary) rescaling the value of $\sigma_8$, the mass variance parameter. The need for a self-consistent choice of the basic parameters characterizing the cluster population is emphasized. In particular, we stress the need for a consistent choice of the value of $\sigma_8$ extracted from fitting theoretical models for the mass function to the observed cluster X-ray temperature function, such that it agrees with the mass-temperature relation used to evaluate the cluster Comptonization parameter. Our treatment includes the explicit spectral dependence of the thermal component of the effect, which we calculate at various frequencies. We find appreciable differences between the non-relativistic and relativistic predictions for the power spectrum even for this superposed contribution from clusters at the full range of gas temperatures.