A new measurement of the X-ray temperature function of clusters of galaxies

We present a newly measured X-ray temperature function of galaxy clusters using a complete flux-limited sample of 61 clusters. The sample is constructed with the total survey area of 8.14 steradians and the flux limit of $1.99\times 10^{-11}$ ergs s -1 cm -2 in the 0.1–2.4 keV band. X-ray temperatures and fluxes of the sample clusters were accurately measured with ASCA and ROSAT data. The derived temperature function covers an unprecedentedly wide temperature range of 1.4–11 keV. By fitting these data with theoretically predicted temperature functions given by the Press-Schechter formalism together with a recent formation approximation and the CDM power spectrum, we obtained tight and individual constraints on $\Omega_{\rm m,0}$ and $\sigma_8$. We also employed the Formation-Epoch model in which the distribution in the formation epoch of clusters as well as the temperature evolution are taken into account, showing significantly different results. Systematics caused by the uncertainty in the mass-temperature relation are studied and found to be as large as the statistical errors.