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 log-normal distributon of fixed width , centered on a scaling relation , L \propto M ^ { p } \hbox { $ \rho _ { c } $ } ^ { s } ( 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 which , 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 , \hbox { $ \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 \hbox { $ \sigma _ { { \ln } M } $ } = 0.43 \pm 0.06 from HIFLUGCS data .
When added to the likelihood analysis , we derive values p = 1.59 \pm 0.05 , \hbox { $ { \ln } L _ { 15 , 0 } $ } = 1.34 \pm 0.09 , and \hbox { $ \sigma _ { { \ln } M } $ } = 0.37 \pm 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 , 0 } \propto \hbox { $ \sigma _ { 8 } $ } ^ { -4 } , and the slope is weakly sensitive to the matter density , p \propto \Omega _ { m } ^ { 1 / 2 } .
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 \hbox { $ \sigma _ { { \ln } M } $ } = 0.25 , in which hydrostatic mass estimates remain accurate to \sim 15 \% .
We stress the need for independent calibration of the L-M relation via weak gravitational lensing .