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

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 neighbour separation of field galaxies. We argue, on theoretical grounds, that LLs should be b(perpendicular to) similar or equal to 0.11, and b() approximate to 1.3 to recover 95 per cent of all galaxies with projected radii within the virial radius r(200) and 95 per cent of the galaxies along the LOS. We then predict that 80 to 90 per cent 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 x 16 pairs of LLs, using subsamples of galaxies, doubly complete in distance and luminosity, of a flux-limited mock Sloan Digital Sky Survey (SDSS) galaxy catalogue. We find that massive RSGs are more prone to fragmentation, while the fragments typically have low estimated mass, with typically 30 per cent of groups of low and intermediate estimated mass being fragments. Group merging rises drastically with estimated mass. For groups of three or more galaxies, galaxy completeness and reliability are both typically better than 80 per cent (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 catalogue. We propose b(perpendicular to) similar or equal to 0.07, with b() similar or equal to 1.1 for studies of environmental effects, b() similar or equal to 2.5 for cosmographic studies and b() similar or equal to 5 for followups of individual groups.