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 10 ^ { 44.5 } erg s ^ { -1 } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < % $ } } } L _ { bol } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } % \hbox { $ < $ } } } 10 ^ { 46.5 } erg s ^ { -1 } and the redshift range z \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 0.5 , L _ { bol } \propto T ^ { 2.80 ^ { +0.15 } _ { -0.15 } } ( 1 + z ) ^ { ( 0.91 - 1.12 q _ { 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 , L _ { bol } \propto T ^ { 2.65 ^ { +0.23 } _ { -0.20 } } ( 1 + z ) ^ { ( 0.42 - 1.26 q _ { 0 } ) ^ { +0.75 } _ { -0.83 } } for the same luminosity and redshift ranges .