Observational Tests of the Mass-Temperature Relation for Galaxy Clusters

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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 ~ 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, & Navarro (1996). X-ray mass estimates which employ spatially resolved temperature profiles also follow 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 show steeper power law indices ( ~ 1.8-2.0). The steepness of the isothermal estimates is due to their implied dark matter density profile of rho (r) ~ r(-2) at large radii while observations and simulations suggest that clusters follow steeper profiles (e.g. rho (r) ~ r(-2.4) ). The gas distribution is also seen to be a function of T_x, consistent with a history of non-gravitational energy input.

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