On galaxy cluster sizes and temperatures

We show that the distribution of the sizes and temperatures of clusters can be used to constrain cosmological models. The sizetemperature (ST) distribution predicted in a flat Gaussian cluster-abundance-normalized V 0 0X3 model agrees well with the fairly tight ST relation observed. A larger power-spectrum amplitude s 8 would give rise to a larger scatter about the ST relation as would a larger value of V 0 and/or long non-Gaussian high-density tails in the probability density function. For Gaussian initial conditions, the ST distribution suggests a constraint s 8 V 0X26 0 . 0X76X The ST relation is expected to get tighter at high redshifts. In the process, we derive a simple formula for the halo formationredshift distribution for non-Gaussian models. We also suggest that the discrepancy between the naive zero-redshift ST relation and that observed may be owing, at least in part, to the fact that lower-mass clusters form over a wider range of redshifts. An Appendix derives an equation for the formationredshift distribution of haloes.