RASS - SDSS Galaxy Clusters 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 r500 and r200. The ASCA temperature of the intracluster medium, TX , 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, Lop, correlates with the cluster mass much better than the X-ray luminosity, LX . Lop can be used to estimate the cluster mass with an accuracy of 40% while LX can predict the mass only with a 55% accuracy. We show that correcting LX for the effect of a cool core at the center of a cluster, lowers the scatter of the LX −M relation only by 3%. We find that the scatter observed in the Lop−LX relation is determined by the scatter of the LX −M relation. The mass-to-light ratio in the SDSS i band clearly increases with the cluster mass with a slope 0.2± 0.08. The optical and X-ray luminosities correlate in excellent way with both TX and σV with an orthogonal scatter of 20% in both relations. Moreover, Lop and LX 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.