Measurements of galaxy cluster abundances, clustering properties, and mass-to-light ratios in current and future surveys can provide important cosmological constraints. Digital wide-field imaging surveys, the recently demonstrated fidelity of red-sequence cluster detection techniques, and a new generation of realistic mock galaxy surveys provide the means for construction of large, cosmologically interesting cluster samples, whose selection and properties can be understood in unprecedented depth. Here we present the details of the "maxBCG" algorithm, a cluster detection technique tailored to multiband CCD imaging data. MaxBCG primarily relies on an observational cornerstone of massive galaxy clusters: they are marked by an overdensity of bright, uniformly red galaxies. This detection scheme also exploits classical brightest cluster galaxies (BCGs), which are often found at the centers of these same massive clusters. We study the algorithm through its performance on large, realistic, mock galaxy catalogs, which reveal that it is over 90% pure for clusters at 0.1 < z < 0.3 with 10 or more red galaxies, and over 90% complete for halos at 0.1 < z < 0.3 with masses above 2 x 10~(14) h~(-1) solar mass. MaxBCG is able to approximately recover the underlying halo abundance function and assign cluster richnesses strongly coupled to the underlying halo properties. The same tests indicate that maxBCG rarely fragments halos, occasionally overmerges line-of-sight neighboring (approx= 10 h~(-1) Mpc) halos, and overestimates the intrinsic halo red-sequence galaxy population by no more than 20%. The study concludes with a discussion of considerations for cosmological measurements with such catalogs, including modeling the selection function, the role of photometric errors, the possible cosmological dependence of richness measurements, and fair cluster selection across broad redshift ranges employing multiple bandpasses.
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