The specific star formation rates of galaxies are influenced both by their mass and by their environment. Moreover, the mass function of groups and clusters serves as a powerful cosmological tool. It is thus important to quantify the accuracy to which group properties are extracted from redshift surveys. We test here the Friends-of-Friends (FoF) grouping algorithm, which depends on two linking lengths (LLs), plane-of-sky and line-of-sight (LOS), normalized to the mean nearest neighbor separation of field galaxies. We argue, on theoretical grounds that LLs should be b ⊥ 0.11, and b ≈ 1.3 to recover 95% of all galaxies with projected radii within the virial radius r 200 and 95% of the galaxies along the LOS. We then predict that 80 to 90% of the galaxies in FoF groups should lie within their parent real-space groups (RSGs), defined within their virial spheres. We test the FoF extraction for 16×16 pairs of LLs, using subsamples of galaxies, doubly complete in distance and luminosity, of a flux-limited mock SDSS galaxy catalog. We find that massive RSGs are more prone to fragmentation, while the fragments typically have low estimated mass, with typically 30% of groups of low and intermediate estimated mass being fragments. Group merging rises drastically with estimated mass. For groups of 3 or more galaxies, galaxy completeness and reliability are both typically better than 80% (after discarding the fragments). Estimated masses of extracted groups are biased low, by up to a factor 4 at low richness, while the inefficiency of mass estimation improves from 0.85 dex to 0.2 dex when moving from low to high multiplicity groups. The optimal LLs depend on the scientific goal for the group catalog. We propose b ⊥ 0.07, with b1.1 for studies of environmental effects, b 2.5 for cosmographic studies and b 5 for followups of individual groups.
Combining our knowledge of halo structure and internal kinematics from cosmological dark matter simulations and the distribution of halo interlopers in projected phase space measured in cosmological galaxy simulations, we develop MAGGIE, a prior-and halo-based, probabilistic, abundance matching (AM) grouping algorithm for doubly complete subsamples (in distance and luminosity) of flux-limited samples. We test MAGGIE-L and MAGGIE-M (in which group masses are derived from AM applied to the group luminosities and stellar masses, respectively) on groups of at least three galaxies extracted from a mock Sloan Digital Sky Survey Legacy redshift survey, incorporating realistic observational errors on galaxy luminosities and stellar masses. In comparison with the optimal Friends-of-Friends (FoF) group finder, groups extracted with MAGGIE are much less likely to be secondary fragments of true groups; in primary fragments, its galaxy memberships (relative to the virial sphere of the realspace group) are much more complete and usually more reliable, and its masses are much less biased and usually with less scatter, as are its group luminosities and stellar masses (computed in MAGGIE using the membership probabilities as weights). FoF outperforms MAGGIE only for high-mass clusters: for the reliability of the galaxy population and the dispersion of its total mass. In comparison with our implementation of the Yang et al. group finder, MAG-GIE reaches much higher completeness and slightly lower group fragmentation and dispersion on group total masses, luminosities and stellar masses, but slightly greater bias in the latter two and lower reliabilities. MAGGIE should therefore lead to sharper trends of environmental effects on galaxies and more accurate mass/orbit modelling.
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