Observational Tests of the Mass‐Temperature Relation for Galaxy Clusters

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Abstract
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, and Navarro. X-ray mass estimates that 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, whereas observations and simulations suggest that clusters follow steeper profiles [e.g., ρ(r) ∝ r-2.4].
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