Galaxy Groups in the Sdss Dr4: Ii. Halo Occupation Statistics

We investigate various galaxy occupation statistics of dark matter halos using a large galaxy group catalogue constructed from the Sloan Digital Sky Survey Data Release 4 (SDSS DR4) with an adaptive halo-based group finder. The conditional luminosity function (CLF), which describes the luminosity distribution of galaxies in halos of a given mass, is measured separately for all, red and blue galaxies, as well as in terms of central and satellite galaxies. The CLFs for central and satellite galaxies can be well modelled with a log-normal distribution and a modified Schechter form, respectively. About 85% of the central galaxies and about 80% of the satellite galaxies in halos with masses Mh & 10 hM⊙ are red galaxies. These numbers decrease to 50% and 40%, respectively, in halos with Mh ∼ 10 hM⊙. For halos of a given mass, the distribution of the luminosities of central galaxies, Lc, has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the central galaxies scales with halo mass as Lc ∝ M h (M∗,c ∝ M h ) for halos with masses M ≫ 10 hM⊙, and both relations are significantly steeper for less massive halos. We also measure the luminosity (stellar mass) gap between the first and second brightest (most massive) member galaxies, logL1 − logL2 (logM∗,1 − logM∗,2). These gap statistics, especially in halos with Mh . 10 14.0 hM⊙, indicate that the luminosities of central galaxies are clearly distinct from those of their satellites. The fraction of fossil groups, defined as those groups with logL1 − logL2 ≥ 0.8, ranges from ∼ 2.5% for groups with Mh ∼ 10 hM⊙ to 18-60% for groups with Mh ∼ 10 hM⊙. The number distribution of satellite galaxies in groups of a given mass follows a Poisson distribution, in agreement with the occupation statistics of dark matter sub-halos. This provides strong support for the standard lore that satellite galaxies reside in sub-halos. Finally, we measure the fraction of satellites, which changes from ∼ 5.0% for galaxies with Mr − 5 log h ∼ −22.0 to ∼ 40% for galaxies with Mr − 5 logh ∼ −17.0. Subject headings: dark matter large-scale structure of the universe galaxies: halos methods: statistical