A MaxBCG catalog of 13,823 galaxy clusters from the sloan digital sky survey

We present a catalog of galaxy clusters selected using the maxBCG red-sequence method from Sloan Digital Sky Survey photometric data. This catalog includes 13,823 clusters with velocity dispersions greater than approximate to 400 km s(-1) and is the largest galaxy cluster catalog assembled to date. They are selected in an approximately volume-limited way from a 0.5 Gpc(3) region covering 7500 deg(2) of sky between redshifts 0.1 and 0.3. Each cluster contains between 10 and 190 E/S0 ridgeline galaxies brighter than 0.4L(*) within a scaled radius R-200. The tight relation between ridgeline color and redshift provides an accurate photometric redshift estimate for every cluster. Photometric redshift errors are shown by comparison to spectroscopic redshifts to be small (Delta(z) similar or equal to 0.01), essentially independent of redshift, and well determined throughout the redshift range. Runs of maxBCG on realistic mock catalogs suggest that the sample is more than 90% pure and more than 85% complete for clusters with masses >= 1 x 10(14) M-circle dot. Spectroscopic measurements of cluster members are used to examine line-of-sight projection as a contaminant in the identification of brightest cluster galaxies and cluster member galaxies. Spectroscopic data are also used to demonstrate the correlation between optical richness and velocity dispersion. Comparison to the combined NORAS and REFLEX X-ray-selected cluster catalogs shows that X-ray-luminous clusters are found among the optically richer maxBCG clusters. This paper is the first in a series that will consider the properties of these clusters, their galaxy populations, and their implications for cosmology.