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

We present a Bayesian inference analysis of the Markevitch and Allen & Fabian 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 10^44.5 ergs s^-1<~L_bol<~10^46.5 ergs s^-1 and the redshift range z<~0.5, L_bol~T^{2.80+0.15_-0.15}(1-z)^{(0.91-1.12q₀)+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, L_bol~T^{2.65+0.23_-0.20}(1+z)^{(0.42-1.26q₀)+0.75_-0.83} for the same luminosity and redshift ranges.