The mass-temperature relation for clusters of galaxies

A tight mass-temperature relation, M(r)/r proportional to T-x, is expected in most cosmological models if clusters of galaxies are homologous and the intracluster gas is in global equilibrium with the dark matter. We here calibrate this relation using eight clusters with well-defined global temperatures measured with ASCA and masses inferred from weak and strong gravitational lensing. The surface lensing masses are deprojected in accordance with N-body simulations and analytic results. The data are well-fitted by the mass-temperature relation and are consistent with the empirical normalization found by Evrard et al. (1996) using gas-dynamic simulations. Thus, there is no discrepancy between lensing and X-ray-derived masses using this approach. The dispersion around the relation is 27 per cent, entirely dominated by observational errors. The next generation of X-ray telescopes combined with wide-held HST imaging could provide a sensitive test of the normalization and intrinsic scatter of the relation, resulting in a powerful and expedient way of measuring masses of clusters of galaxies. In addition, as M(r)/r las derived from lensing) is dependent on the cosmological model at high redshift, the relation represents a new tool for determination of cosmological parameters, notably the cosmological constant Lambda.