ON THE EVOLUTION OF CLUSTER SCALING RELATIONS

Abstract

Understanding the evolution of scaling relations between the observable properties of clusters and their total mass is key to realizing their potential as cosmological probes. In this study, we investigate whether the evolution of cluster scaling relations is affected by the spurious evolution of mass caused by the evolving reference density with respect to which halo masses are defined (pseudo-evolution). We use the relation between mass, M, and velocity dispersion, sigma, as a test case, and show that the deviation from the M-sigma relation of cluster-sized halos caused by pseudo-evolution is smaller than 10% for a wide range of mass definitions. The reason for this small impact is a tight relation between the velocity dispersion and mass profiles, sigma(<r) = const * (GM(<r) / r)^1/2, which holds across a wide range of radii. We show that such a relation is generically expected for a variety of density profiles, as long as halos are in approximate Jeans equilibrium. Thus, as the outer "virial" radius used to define the halo mass, R, increases due to pseudo-evolution, halos approximately preserve their M-sigma relation. This result highlights the fact that tight scaling relations are the result of tight equilibrium relations between radial profiles of physical quantities. We find exceptions at very small and very large radii, where the profiles deviate from the relations they exhibit at intermediate radii. We discuss the implications of these results for other cluster scaling relations, and argue that pseudo-evolution should have a small effect on most scaling relations, except for those that involve the stellar masses of galaxies. In particular, we show that the relation between stellar-mass fraction and total mass is affected by pseudo-evolution and is largely shaped by it for halo masses of less than 10^14 solar masses.