SZE Signals in Cluster Models
  The upcoming generation of SZE surveys will shed fresh light onto the study of clusters. What will this new observational window reveal about cluster properties? What can we learn from combining X-ray, SZE, and optical observations? How do variations in the gas entropy profile, dark matter concentration, accretion pressure, and intracluster medium (ICM) mass fraction affect SZE observables? We investigate the signature of these important cluster parameters with an analytic model of the ICM. Given the current uncertainties in ICM physics, our approach is to span the range of plausible models motivated by observations and a small set of assumptions. We find a tight relation between the central Compton parameter and the X-ray luminosity outside the cluster core, suggesting that these observables carry the same information about the ICM. The total SZE luminosity is proportional to the thermal energy of the gas, and is a surprisingly robust indicator of cluster mass: $L_{SZ} \propto f_{ICM} M^{5/3}$. We show that a combination of $L_{SZ}$ and the half-luminosity radius $r_{SZ}$ provides a measure of the potential energy of the cluster gas, and thus we can deduce the total energy content of the ICM. We caution that any systematic variation of the ICM mass fraction will distort the expected $L_{SZ} - M$ calibration to be used to study the evolution of cluster number density, and propose a technique using kSZ to constrain $f_{ICM}(M,z)$. 
Beth A. Reid and David N. Spergel