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We identify galaxy groups and clusters in volume-limited samples of the SDSSredshift survey, using a redshift-space friends-of-friends algorithm. Weoptimize the friends-of-friends linking lengths to recover galaxy systems thatoccupy the same dark matter halos, using a set of mock catalogs created bypopulating halos of N-body simulations with galaxies. Extensive tests withthese mock catalogs show that no combination of perpendicular and line-of-sightlinking lengths is able to yield groups and clusters that simultaneouslyrecover the true halo multiplicity function, projected size distribution, andvelocity dispersion. We adopt a linking length combination that yields, forgalaxy groups with ten or more members: a group multiplicity function that isunbiased with respect to the true halo multiplicity function; an unbiasedmedian relation between the multiplicities of groups and their associatedhalos; a spurious group fraction of less than ~1%; a halo completeness of morethan ~97%; the correct projected size distribution as a function ofmultiplicity; and a velocity dispersion distribution that is ~20% too low atall multiplicities. These results hold over a range of mock catalogs that usedifferent input recipes of populating halos with galaxies. We apply ourgroup-finding algorithm to the SDSS data and obtain three group and clustercatalogs for three volume-limited samples that cover 3495.1 square degrees onthe sky. We correct for incompleteness caused by fiber collisions and surveyedges, and obtain measurements of the group multiplicity function, with errorscalculated from realistic mock catalogs. These multiplicity functionmeasurements provide a key constraint on the relation between galaxypopulations and dark matter halos.Comment: 26 emulateapj pages including 19 figures. Replaced with final ApJ  versio

Percolation Galaxy Groups and Clusters in the SDSS Redshift Survey: Identification, Catalogs, and the Multiplicity Function