Group analysis in the SSRS2 catalog

We present an automated method to detect populations of groups in galaxy redshift catalogs. This method uses both analysis of the redshift distribution along lines of sight in fixed cells to detect elementary structures and a friend-of-friend algorithm to merge these elementary structures into physical structures. We apply this method to the SSRS2 galaxy redshift catalog. The groups detected with our method are similar to group catalogs detected with pure friend-of-friend algorithms. They have similar mass distribution, similar abundance versus redshift, a similar 2-point correlation function (modeled by a power law: $ (r/r_0)^\gamma $ with $r_0=7~h^{-1}~{\rm Mpc}$ and $\gamma =-1.79$) and the same redshift completeness limit, close to 5000 km s-1. If instead of SSRS2, we use catalogs of the new generation (deep redshift surveys obtained with 10 m class telescopes), it would lead to a completeness limit of $z\sim0.7$. We model the luminosity function for nearby galaxy groups by a Schechter function with parameters $M_{\rm SSRS2}^{*}=(-19.99\pm 0.36)+5~{\rm log}h$ and $\alpha =-1.46\pm 0.17$ to compute the mass to light ratio. The median value of the mass to light ratio is 360 $hM_{\odot }$/$L_{\odot }$ (in the SSRS2 band, close to a B band magnitude) and we deduce a relation between mass to light ratio and velocity dispersion $\sigma $ ($ M/L=(3.79\pm 0.64)\sigma -(294\pm 570)$). The more massive the group, the higher the mass to light ratio, and therefore, the larger the amount of dark matter inside the group. Another explanation is a significant stripping of the gas of the galaxies in massive groups as opposed to low mass groups. This extends to groups of galaxies the mild tendency already detected for rich clusters of galaxies. Finally, we detect a barely significant fundamental plane for these groups ($L\propto R_{\rm Vir}^{2.26\pm 1.39}\times \sigma ^{2.93\pm 1.64}$ for groups with more than 8 galaxies) but it is much less narrow than for clusters of galaxies