Galaxy groups in the SDSS DR4. I. The catalog and basic properties

We use a modified version of the halo-based group finder developed by Yang et al. to select galaxy groups from the Sloan Digital Sky Survey (SDSS DR4). In the first step, a combination of two methods is used to identify the centers of potential groups and to estimate their characteristic luminosity. Using an iterative approach, the adaptive group finder then uses the average mass-to-light ratios of groups, obtained from the previous iteration, to assign a tentative mass to each group. This mass is then used to estimate the size and velocity dispersion of the underlying halo that hosts the group, which in turn is used to determine group membership in redshift space. Finally, each individual group is assigned two different halo masses: one based on its characteristic luminosity and the other based on its characteristic stellar mass. Applying the group finder to the SDSS DR4, we obtain 301,237 groups in a broad dynamic range, including systems of isolated galaxies. We use detailed mock galaxy catalogs constructed for the SDSS DR4 to test the performance of our group finder in terms of completeness of true members, contamination by interlopers, and accuracy of the assigned masses. This paper is the first in a series and focuses on the selection procedure, tests of the reliability of the group finder, and the basic properties of the group catalog (e. g., the mass-to-light ratios, the halo mass-to-stellar mass ratios). The group catalogs including the membership of the groups are available on request.