The X-ray Luminosity Function of Nearby Rich and Poor Clusters of Galaxies: A Cosmological Probe

In this letter, we present a new determination of the local (z<0.09) X-ray luminosity function (XLF) using a large, statistical sample of 294 Abell clusters and the ROSAT All-Sky-Survey. Given our large sample size, we have reduced errors by a factor of two for L(X)(0.5-2keV)>10^43 ergs/sec. We combine our data with previous work in order to explore possible constraints imposed by the shape of the XLF on cosmological models. A set of currently viable cosmologies is used to construct theoretical XLFs assuming Lx is proportional to M^p and a sigma_8-Omega_0 constraint (from Viana & Liddle 1996) based on the local X-ray temperature function. We fit these models to our observed XLF and verify that the simplest adiabatic, analytic scaling relation (e.g. Kaiser 1986) disagrees strongly with observations. If we assume that clusters can be described by the pre-heated, constant core-entropy models of Evrard & Henry (1991) then the observed XLF is consistent only with 0.1 < Omega_0 < 0.4 if the energy per unit mass in galaxies is roughly equal to the gas energy (ie if beta=1). (abridged)