The Lx-T relation and temperature function for nearby clusters revisited

The X-ray luminosity-temperature relation for nearby T similar or equal to 3.5-10 keV clusters is rederived using new ASCA temperatures and ROSAT luminosities. Both quantities are derived by directly excluding the cooling how regions. This correction results in a greatly reduced scatter in the L-X-T relation; cooling how clusters are similar to others outside the small cooling how regions. For a fit of the form L-bol infinity 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 and L-X-T relation together with a newly selected cluster sample are used to update the temperature function at z similar to 0.05. The resulting function is generally higher and flatter than, although within the errors of, the previous estimates by Edge and coworkers and Henry and Arnaud (as rederived by Eke and coworkers). For a qualitative estimate of constraints that the new data place on the density fluctuation spectrum, we apply the Press-Schechter formalism for Omega(0) = 1 and 0.3. For Omega(0) = 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(0) is different from the earlier results because of our treatment of the slope of the fluctuation spectrum, n, as a free parameter. For the considered values of Omega(0), n = -(2.0-2.3)+/- 0.3, somewhat steeper than that derived from the earlier temperature function data, in agreement with the local slope of the galaxy fluctuation spectrum from the Automatic Plate Measuring Facility (APM) survey, and significantly steeper than the standard cold dark matter prediction.