Fundamental plane of Sunyaev-Zel'dovich clusters

Sunyaev-Zel'dovich (SZ) cluster surveys are considered among the most promising methods for probing dark energy up to large redshifts. However, their premise is hinged on an accurate mass-observable relationship, which could be affected by the (rather poorly understood) physics of the intracluster gas. In this paper, using a semianalytic model of the intracluster gas that accommodates various theoretical uncertainties, I develop a fundamental plane relationship between the observed size, thermal energy, and mass of galaxy clusters. In particular, I find that M proportional to (Y-SZ/R-SZ,R-2)(3/4), where M is the mass, Y-SZ is the total SZ flux or thermal energy, and R-SZ,R-2 is the SZ half-light radius of the cluster. I first show that, within this model, using the fundamental plane relationship reduces the (systematic+random) errors in mass estimates to 14%, from 22% for a simple mass-flux relationship. Since measurement of the cluster sizes is an inevitable part of observing the SZ clusters, the fundamental plane relationship can be used to reduce the error of the cluster mass estimates by similar to 34%, improving the accuracy of the resulting cosmological constraints without any extra cost. I then argue why our fundamental plane is distinctly different from the virial relationship that one may naively expect between the cluster parameters. Finally, I argue that while including more details of the observed SZ profile cannot significantly improve the accuracy of mass estimates, a better understanding of the impact of nongravitational heating/cooling processes on the outskirts of the intracluster medium (apart from external calibrations) might be the best way to reduce these errors.