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 1044.5 ergs s-1 ≲ Lbol 1046.5 ergs s-1 and the redshift range z ≲ 0.5, Lbol ∝ T2.80+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, Lbol ∝ T2.65+0.23-0.20(1+z)(0.42-1.2q0)+0.75-0.83 for the same luminosity and redshift ranges