A Bayesian Inference Analysis of the X-ray Cluster Luminosity-Temperature Relation

We present a Bayesian inference analysis of the Markevitch (1998) and Allen & Fabian (1998) cooling flow corrected X-ray cluster temperature catalogs that constrains the slope and the evolution of the empirical X-ray cluster luminosity-temperature (L-T ) relation. We find that for the luminosity range 1044.5 erg s−1 ∼< Lbol ∼< 10 46.5 erg s−1 and the redshift range z ∼< 0.5, Lbol ∝ T 2.80 −0.15(1 + z)0 +0.54 −1.22 . We also determine the L-T relation that one should use when fitting the Press-Schechter mass function to X-ray cluster luminosity catalogs such as the Einstein Medium Sensitivity Survey (EMSS) and the Southern Serendipitous High-Redshift Archival ROSAT Catalog (Southern SHARC), for which cooling flow corrected luminosities are not determined and a universal X-ray cluster temperature of T = 6 keV is assumed. In this case, Lbol ∝ T 2.65 −0.20(1 + z)0 +0.75 −0.83 for the same luminosity and redshift ranges. Subject headings: cosmology: observations — cosmology: theory — galaxies: clusters: general — galaxies: luminosity function, mass function — X-rays: galaxies