The 2dF Galaxy Redshift Survey:: correlation with the ROSAT-ESO flux-limited X-ray galaxy cluster survey

The ROSAT-European Southern Observatory (ESO) flux-limited X-ray (REFLEX) galaxy cluster survey and the Two-degree Field Galaxy Redshift Survey (2dFGRS), respectively, comprise the largest, homogeneous X-ray selected cluster catalogue and completed galaxy redshift survey. In this work, we combine these two outstanding data sets in order to study the effect of the large-scale cluster environment, as traced by X-ray luminosity, on the properties of the cluster member galaxies. We measure the L(X)-sigma(r) relation from the correlated data set and find it to be consistent with recent results found in the literature. Using a sample of 19 clusters with L(X) >= 0.36 x 10(44) erg s(-1) in the 0.1-2.4 keV band, and 49 clusters with lower X-ray luminosity, we find that the fraction of early spectral type (eta <= -1.4), passively evolving galaxies is significantly higher in the high-L(X) sample within R(200). We extend the investigation to include composite b(J) cluster luminosity functions, and find that the characteristic magnitude of the Schechter-function fit to the early-type luminosity function is fainter for the high-L(X) sample compared to the low-L(X) sample (Delta M* = 0.58 +/- 0.14). This seems to be driven by a deficit of such galaxies with Mb(J) similar to -21. In contrast, we find no significant differences between the luminosity functions of star-forming, late-type galaxies. We believe these results are consistent with a scenario in which the high-L(X) clusters are more dynamically evolved systems than the low-L(X) clusters.