Observational Tests of the Mass‐Temperature Relation for Galaxy Clusters

We examine the relationship between the mass and x-ray gas temperature of galaxy clusters using data drawn from the literature. Simple theoretical arguments suggest that the mass of a cluster is related to the x-ray temperature as M ∝ Tₓ3/2. Virial theorem mass estimates based on cluster galaxy velocity dispersions seem to be accurately described by this scaling with a normalization consistent with that predicted by the simulations of Evrard, Metzler, & Navarro (1996). X-ray mass estimates which employ spatially resolved temperature profiles also follow a Tₓ3/2 scaling although with a normalization about 40% lower than that of the fit to the virial masses. However, the isothermal β-model and x-ray surface brightness deprojection masses follow a steeper ∝ Tₓ1.8-2.0 scaling. The steepness of the isothermal estimates is due to their implicitly assumed dark matter density profile of ρ(r) ∝ r⁻² at large radii while observations and simulations suggest that clusters follow steeper profiles (e.g., ρ(r) ∝ r-2.4).