The X-Ray Luminosity--Mass Relation for Local Clusters of Galaxies

We investigate the relationship between soft \xray luminosity and mass for low redshift clusters of galaxies by comparing observed number counts to expectations of $\Lambda$CDM cosmologies. We use a three-parameter model for the conditional probability of luminosity given mass and epoch, described as a log-normal distribution of fixed width centered on a power-law scaling relation, $L \spropto M^p\rhoc^s(z)$. We use an ensemble of simulated clusters to argue that the observed, intrinsic variance in the temperature--luminosity relation is directly indicative of mass--luminosity variance, and derive $\sigm \se 0.43 \pm 0.06$ from HIFLUGCS data. Adding this to the likelihood analysis results in best-fit estimates $p \se 1.59 \pm 0.05$, $\lnlf \se 1.34 \pm 0.09$, and $\sigm \se 0.37 \pm 0.05$ for self-similar redshift evolution in a concordance ($\Omega_m \se 0.3$, $\Omega_\Lambda \se 0.7$, $\sigma_8 \se0.9$) universe. We show that the present-epoch intercept is very sensitive to power spectrum normalization, $\lnlf \spropto \sigate^{-4}$, and the slope is weakly sensitive to the matter density, $p \spropto \Omega_m^{1/2}$. The intercept derived here is dimmer by a factor 2, and slope slightly steeper, than the L-M relation published using hydrostatic mass estimates of the HIFLUGCS sample. We show that this discrepancy is largely due to Malmquist bias of the \xray\ flux-limited sample. In light of new WMAP constraints, we discuss the interplay between parameters and sources of systematic error, and offer a compromise model with $\Omega_m \se 0.24$, $\sigma_8 \se 0.85$, and somewhat lower scatter $\sigm \se 0.25$, in which hydrostatic mass estimates remain accurate to $\ssim 15$. We stress the need for independent calibration of the L-M relation via weak gravitational lensing.