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 size-temperature (ST) distri bution predicted in a flat Gaussian cluster-abundance-normalized Omega (0)= 0.3 model agrees well with the fairly tight ST relation observed. A larger power-spectrum amplitude sigma (8) would give rise to a larger scatter abou t the ST relation as would a larger value of Omega (0) and/or long non-Gaus sian high-density tails in the probability density function. For Gaussian i nitial conditions, the ST distribution suggests a constraint sigma (8)Omega (0.26)(0)similar or equal to0.76. The ST relation is expected to get tight er at high redshifts. In the process, we derive a simple formula for the ha lo formation-redshift 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 cluste rs form over a wider range of redshifts. An Appendix derives an equation fo r the formation-redshift distribution of haloes.