The X-ray luminosity-mass relation for local clusters of galaxies

We investigate the relationship between soft X-ray luminosity and mass for low-redshift clusters of galaxies by comparing observed number counts and scaling laws to halo-based expectations of Lambda CDM cosmologies. We model the conditional likelihood of halo luminosity as a lognormal distribution of fixed width, centered on a scaling relation, L proportional to M-p rho(s)(c) (z), and consider two values for s, appropriate for self-similar evolution or no evolution. Convolving with the halo mass function, we compute expected counts in redshift and flux that, after appropriate survey effects are included, we compare to REFLEX survey data. Counts alone provide only an upper limit on the scatter in mass at fixed luminosity, sigma(ln M) < 0.4. We argue that the observed, intrinsic variance in the temperature-luminosity relation is directly indicative of mass-luminosity variance and derive sigma(ln M) = 0.43 +/- 0.06 from HIFLUGCS data. When added to the likelihood analysis, we derive values p = 1.59 +/- 0.05, ln L-15,L-0 1.34 +/- 0.09, and sigma(ln M) = 0.37 +/- 0.05 for self-similar redshift evolution in a concordance (Omega(m) = 0.3, Omega(Lambda) = 0.7, sigma(8) = 0.9) universe. The present-epoch intercept is sensitive to power spectrum normalization, L-15,L-0 proportional to sigma(-4)(8), and the slope is weakly sensitive to the matter density, p proportional to Omega(1/2)(m). We find a substantially ( factor 2) dimmer intercept and slightly steeper slope than the values published using hydrostatic mass estimates of the HIFLUGCS sample and show that a Malmquist bias of the X-ray flux-limited sample accounts for this effect. 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) = 0.24, sigma(8) = 0.85, and somewhat lower scatter sigma(ln M) =0.25, in which hydrostatic mass estimates remain accurate to similar to 15%. We stress the need for independent calibration of the L-M relation via weak gravitational lensing.