From the Press-Schechter mass function and the empirical X-ray cluster luminosity-temperature ( L - T ) relation , we construct an X-ray cluster luminosity function that can be applied to the growing number of high-redshift , X-ray cluster luminosity catalogs to constrain cosmological parameters .
In this paper , we apply this luminosity function to the Einstein Medium Sensitivity Survey ( EMSS ) and the ROSAT Brightest Cluster Sample ( BCS ) luminosity function to constrain the value of \Omega _ { m } .
In the case of the EMSS , we find a factor of 4 - 5 fewer X-ray clusters at redshifts above z = 0.4 than below this redshift at luminosities above L _ { X } = 7 \times 10 ^ { 44 } erg s ^ { -1 } ( 0.3 - 3.5 keV ) , which suggests that the X-ray cluster luminosity function has evolved above L _ { \star } .
At lower luminosities , this luminosity function evolves only minimally , if at all .
Using Bayesian inference , we find that the degree of evolution at high luminosities suggests that \Omega _ { m } = 0.96 ^ { +0.36 } _ { -0.32 } , given the best-fit L - T relation of Reichart , Castander , & Nichol ( 1998 ) .
When we account for the uncertainty in how the empirical L - T relation evolves with redshift , we find that \Omega _ { m } \approx 1.0 \pm 0.4 .
However , it is unclear to what degree systematic effects may affect this and similarly obtained results .