Intracluster entropy from joint X-ray and Sunyaev-Zel'dovich observations

The temperature and density of the hot diffuse medium pervading galaxy groups and clusters combine into one significant quantity, the entropy. Here we express the entropy levels and profiles in model-independent forms by joining two observables: the X-ray luminosity and the change in the cosmic microwave background (CMB) intensity due to the Sunyaev-Zel'dovich (SZ) effect. Thus we present both global scaling relations for the entropy levels from clusters and groups, and a simple expression yielding the entropy profiles in individual clusters from resolved X-ray surface brightness and SZ spatial distributions. We propose that our approach provides two useful tools for comparing large data samples with models, in order to probe the processes that govern the thermal state of the hot intracluster medium. The feasibility of using such a diagnostic for the entropy is quantitatively assessed, based on current X-ray and upcoming SZ measurements.