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 proportional to T-X(3/2). 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, and Navarro. X-ray mass estimates that employ spatially resolved temperature profiles also follow a T-X(3/2) scaling although with a normalization about 40% lower than that of the fit to the virial masses. However, the isothermal beta-model and X-ray surface brightness deprojection masses follow a steeper proportional to T-X(1.8-2.0) scaling. The steepness of the isothermal estimates is due to their implicitly assumed dark matter density profile of rho(r) proportional to r(-2) at large radii, whereas observations and simulations suggest that clusters follow steeper profiles [e.g., rho(r) proportional to r(-2.4)].