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) distribution 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 about the ST relation as would a larger value of Omega_0 and/or long non-Gaussian high-density tails in the probability density function. For Gaussian initial conditions, the ST distribution suggests a constraint sigma_8 Omega_0^{0.26} \simeq 0.76. The ST relation is expected to get tighter at high redshifts. In the process, we derive a simple formula for the halo 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 due, 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 formation-redshift distribution of halos.