4. Group identification
We identify groups with the so-called friend-of-friend algorithm (FOFA; Huchra & Geller, 1982) as described in RPG. We implement here the cosmological corrections required by the depth of the sample (). Throughout this paper we use = 100 km s-1 Mpc-1 and .
For each galaxy in the magnitude limited ESP catalog, the FOFA identifies all other galaxies with a projected comoving separation
and a line-of-sight velocity difference
Here and are the velocities of the two galaxies in the pair. All pairs linked by a common galaxy form a "group".
The two parameters , are scaled with distance in order to take into account the decrease of the magnitude range of the luminosity function sampled at increasing distance. The scaling is
and is the absolute magnitude corresponding to at a fiducial velocity . We compute with the Mattig (1958) expression, where . Finally, is the correction "weighted" with the expected morphological mix at each redshift as in Zucca et al. (1997).
The scaling is the same for both and and it is normalized at the fiducial velocity = 5000 km s-1 , where 0. = ) and 0 = ). In particular, a given value of 0. corresponds to a minimum number overdensity threshold for groups, . The luminosity function we use is the Schechter parametrization with , , and Mpc-3 computed for ESP galaxies by Zucca et al. (1997).
We do not consider galaxies with velocities because the linear extension of the survey in the direction of the declination is smaller than the typical size of a group for 5000 km s-1 . We also limit the maximum depth of our group catalog to km s-1 . Beyond this limit the accessible part of the luminosity function becomes very small and the scaling of the FOFA linking parameters excessively large.
The main characteristics of the distribution of galaxies within the volume of the universe surveyed by ESP (Vettolani et al. 1997) are very similar to those observed within shallower, wider angle magnitude limited redshift surveys. For this reason we expect that the conclusions on the fine-tuning of FOFA reached by Ramella et al. 1989, Frederic 1995a, and RPG will hold true also for ESP. In particular, RPG show that within the CfAN2 redshift survey the choice of the FOFA parameters is not critical in a wide region of the parameter space around ( = 80, 0 = 350 km s-1 ). With our luminosity function and fiducial velocity, we obtain = 80 for 0. = 0.26 Mpc, a value comparable to the 0. value used for CfAN2. It is therefore reasonable to expect that the same results of the exploration of the parameter space will hold also for the ESP survey. In order to verify our expectation, we run FOFA with the following five pairs of values of the linking parameters selected among those used by RPG: ( = 80, ( = 80, 0 = 350 km s-1 ), ( = 80, 0 = 600 km s-1 ), ( = 60, 0 = 350 km s-1 ), ( = 100, 0 = 350 km s-1 ). Based on RPG, these pairs of values are sufficient to give an indication of the stability of the group catalogs in the parameter space ( , ). The number of groups in the five cases is = 217, 231, 253, 239, and 217 respectively.
We plot in Fig. 3 the observed distributions of the velocity dispersions of the five group catalogs. We compare the distribution obtained for ( = 80, 0 = 350 km s-1 ) -thick histogram in Fig. 3 - with the other four distributions and find that the only significant difference (99.9% level, according to the KS test) occurs with the distribution obtained using the largest velocity link, 0 = 600 km s-1 (dotted histogram). This value of the velocity-link produces an excess of high velocity dispersion systems. Frederic 1995a, Ramella et al. 1989, and RPG argue that these high velocity dispersion systems are likely to include a significant number of interlopers (galaxies with high barycentric velocity that are not physically related to the group in real space).
On the basis of the results of our tests, we choose the catalog obtained with = 80 (0. = 0.26 Mpc) and 0 = 350 km s-1 as our final ESP group catalog. This choice offers the advantage of a straightforward comparison between the properties of ESP catalog and those of the CfA2N (RPG), and SSRS2 (Ramella et al. 1998) catalogs.
© European Southern Observatory (ESO) 1999
Online publication: December 22, 1998