The mass-temperature relation for clusters of galaxies

A tight mass-temperature relation, M(r)/r ∝ TX , 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 8 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-fit by the mass-temperature relation and are consistent with the empirical normalisation found by Evrard et al. (1996) using gasdynamic 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-field HST imaging could provide a sensitive test of the normalisation 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 (as 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 Λ.