How well does the Friends-of-Friends algorithm recover group properties from galaxy catalogs limited in both distance and luminosity?

Abstract

We test 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 $b_{\perp }\simeq 0.11$, and $b_{\parallel }\simeq 1.3$ 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 16x16 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 $b_{\perp }\simeq 0.07$, with $b_{\parallel }\simeq 1.1$ for studies of environmental effects, $b_{\parallel }\simeq 2.5$ for cosmographic studies and $b_{\parallel }\simeq 5$ for followups of individual groups.

Revised version resubmitted to MNRAS. 16 pages. Smaller optimal linking lengths. Two extra figures. Comments welcome!

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