ON THE EVOLUTION OF THE TEMPERATURE-VIRIAL MASS RELATION FOR CLUSTERSOF GALAXIES

X-ray temperature measurements of clusters of galaxies are now reachin g to redshifts high enough to constrain Ohm(0). A redshift-dependent r elation that maps these X-ray temperatures to the virial masses of clu sters is an essential ingredient when one is trying to determine cosmo logical parameters from cluster evolution. Most such relations assume that clusters form from top-hat perturbations that virialized just bef ore the time at which we are observing them. The smaller Ohm(0) is, th e less accurate these relations become. Here we derive a relation betw een virial mass and cluster temperature that allows for the fact that clusters form gradually and cease forming when the density of the univ erse drops well below the critical value. We show how sensitively the expected redshift distribution of clusters depends on the mass-tempera ture relation used and argue that one needs to use a relation that yie lds no evolution in the low-Ohm(0) limit.