The RASS-SDSS Galaxy Cluster Survey. III. Scaling relations of galaxy clusters

We use the RASS-SDSS galaxy cluster sample to compare the quality of optical and X-ray luminosities as predictors of other cluster properties such as their masses, temperatures, and velocity dispersions. We use the SDSS spectroscopic data to estimate the velocity dispersions and the virial masses of a subsample of 69 clusters within r_{500} and r_{200}. The ASCA temperature of the intra-cluster medium, T_X, is retrieved from the literature for a subsample of 49 clusters. For this subsample we estimate the cluster masses also by using the mass-temperature relation. We show that the optical luminosity, L_{op}, correlates with the cluster mass much better than the X-ray luminosity, L_X. L_{op} can be used to estimate the cluster mass with an accuracy of 40% while L_X can predict the mass only with a 55% accuracy. We show that correcting $L_X$ for the effect of a cool core at the center of a cluster, lowers the scatter of the $L_X-M$ relation only by 3%. We find that the scatter observed in the L_{op}-L_X relation is determined by the scatter of the L_X-M relation. The mass-to-light ratio in the SDSS i band clearly increases with the cluster mass with a slope 0.2\pm0.08. The optical and X-ray luminosities correlate in excellent way with both T_X and \sigma_V with an orthogonal scatter of 20% in both relations. Moreover, L_{op} and L_X can predict with the same accuracy both variables. We conclude that the cluster optical luminosity is a key cluster parameter since it can give important information about fundamental cluster properties such as the mass, the velocity dispersion, and the temperature of the intra-cluster medium.