Calibration of the Optical Mass Proxy for Clusters of Galaxies and an Update of the WHL12 Cluster Catalog

Accurately determining the mass of galaxy clusters is fundamental for many studies of cosmology and galaxy evolution. We collect and rescale the cluster masses of 1191 clusters of 0.05\lt z\lt 0.75 estimated by X-ray or Sunyaev-Zeldovich measurements and use them to calibrate the optical mass proxy. The total r-band luminosity (in units of {L}^*) of these clusters is obtained by using spectroscopic and photometric data of the Sloan Digital Sky Survey (SDSS). We find that the correlation between the cluster mass {M}₅₀₀ and total r-band luminosity {L}₅₀₀ significantly evolves with redshift. After correcting for the evolution, we define a new cluster richness {R}_L*,500={L}₅₀₀ E{(z)}^1.40 as the optical mass proxy. By using this newly defined richness and the recently released SDSS DR12 spectroscopic data, we update the WHL12 cluster catalog and identify 25,419 new rich clusters at high redshift. In the SDSS spectroscopic survey region, about 89% of galaxy clusters have spectroscopic redshifts. The mass can be estimated with a scatter of 0.17 dex for the clusters in the updated catalog.