X-RAY-CLUSTERS IN OPEN UNIVERSES

We examine the constraints that can be set on galaxy formation theory from the temperature distribution function of X-ray clusters in universes with arbitrary density. Present observations severely constrain the power spectrum. In agreement with previous works in the case OMEGA-0 = 1, we find that only n approximately -2 is consistent with present observations. This conclusion is reinforced by the recent discovery of a 13.6 keV cluster (Arnaud et al. 1992). Both open and critical density models fit present data. However, redshift evolution is very different; high temperature clusters should exist at large redshift in low density universes. We show that ROSAT observations may provide strong constraints on OMEGA-0.