The Lx-T Relation and Temperature Function for Nearby Clusters Revisited

The X-ray luminosity-temperature relation for nearby T=3.5-10 keV clusters is rederived using new ASCA temperatures and ROSAT luminosities. Both quantities are derived by directly excluding the cooling flow regions. This correction results in a greatly reduced scatter in the Lx-T relation; cooling flow clusters are similar to others outside the small cooling flow regions. For a fit of the form L_bol ~ T^alpha, we obtain alpha=2.64+-0.27 (90%) and a residual rms scatter in log L_bol of 0.10. The derived relation can be directly compared to theoretical predictions that do not include radiative cooling. It also provides an accurate reference point for future evolution searches and comparison to cooler clusters. The new temperatures together with a newly selected cluster sample are used to update the temperature function at z~0.05. The resulting function is generally higher and flatter than the previous estimates by Edge et al (1990) and Henry & Arnaud (1991, corrected). For a qualitative estimate of constraints that the new data place on the density fluctuation spectrum, we apply the Press-Schechter formalism for Omega=1 and 0.3. For Omega=1, assuming cluster isothermality, the temperature function implies sigma_8=0.55+-0.03, while taking into account the observed cluster temperature profiles, sigma_8=0.51+-0.03, consistent with the previously derived range. The dependence of sigma_8 on Omega differs from earlier findings, because of our treatment of n as a free parameter. We find n=-(2.0-2.3)+-0.3, somewhat steeper than derived from the earlier temperature function data, in agreement with the local slope of the galaxy fluctuation spectrum from the APM survey, and significantly steeper than the standard CDM prediction.