5 Conclusion

  This paper had one key aim: to build several large group samples ($N_{\rm G} \approx 200$ groups) in the Southern Galactic Hemisphere from the PPS galaxy survey, never previously analyzed in this way. Such galaxy sample is considerably larger and/or deeper and/or wider than those used in most similar previous studies, so that our group catalog is one of the largest presently available.

Particular care was used in order to define group catalogs as homogeneous as possible to those previously published - in particular, the large group catalogs based on the CfA2 galaxy survey in the Northern Galactic Hemisphere (RGH89; RPG97). Such samples have the same depth as our sample PPS2, and comparable angular width, but different galaxy LF.

Group catalogs are customarily labelled by the redshift link V₀ and the effective density contrast threshold $\delta n/n$ used to select the groups (or, equivalently, the mean inter particle separation $\bar n^{-1/3}$). However, to specify spatial separations, the parameter actually used by the FOF algorithm is not $\delta n/n$, but rather the spatial link D₀ itself. The relations among these two parameters depends on the adopted galaxy LF and sample depth, so it differs from sample to sample. This leads to some ambiguity, and to several possibilities, which we discuss, about how to match our grouping algorithm to those used for the other samples. On one hand, and consistently with Maia et al. (1989) and RPG97, we find strong, approximately linear correlations (i) between the redshift link V₀ and the (median values of) the velocity dispersion $\sigma_{\rm v}$, and (ii) between the spatial link D₀ and the (median values of) the mean harmonic radius $R_{\rm h}$ and mean pairwise member separation $R_{\rm p}$.Even for individual groups, the redshift dependence of $R_{\rm h}$ and $\sigma_{\rm v}$ seems to be closely related to $D_{\rm L}$ and $V_{\rm L}$, respectively. On the other hand, and consistently with RPG97, group velocity dispersions (spatial sizes) are rather insensitive to the spatial link $D_{\rm L}$ (velocity link $V_{\rm L}$). All this suggests to regard D₀ and V₀ as the basic FOF parameters, and interpret $\delta n/n$ only as an estimate of the density contrast threshold.

We adopt the normalizations $D_0=0.231 \ h^{-1}~{\rm Mpc}$ and $V_0=350 \ {\rm km \ s}^{-1}$, as in RPG97. The galaxy LF for PPS2 has Schechter parameter (STY fit) $\alpha = -1.15 \pm 0.15$ and $M_* = -19.3 \pm 0.1$, in good agreement with similar estimates. The STY technique does not allow to estimate the LF normalizations $\phi_*$.We then adopt the value $\phi_*=0.02 \pm 0.1 \ h^3 \ {\rm Mpc}^{-3}$as determined by MHG94 for the CfA2 South sample, which is very similar to PPS2. The adopted normalizations and LF yield then $\delta n/n = 173$.We test for the effect of galaxy LF on group properties. The main effect is connected to the relation between D₀, $\delta n/n$, and $\phi_*$,and the uncertainty on the latter. By replacing the $\delta n/n$ parametrization with the D₀ parametrization, this problem is avoided. In fact, for given V₀ and D₀, the residual net effect on group properties due to $\alpha$ and M_* is generally small: $\delta X/X \lower.5ex\hbox{$\;\buildrel < \over \sim \;$}5-10 \%$ for all considered internal properties X, and similarly for group positions (TB96) and group clustering (TBIB97). We also test for the effect of different redshift corrections. Again, the effect is small, as expected for magnitude-limited samples.

Our main conclusions are as follows:

1. The spatial distribution of FOF-identified loose groups in PPS2 largely reproduce the LSS features in the parent galaxy catalog. Thus, galaxy loose groups can be usefully used as tracer of LSS. Analysis of group clustering in PPS2 has been presented elsewhere (TBIB96).

2. Properties of FOF-identified loose groups selected from directly comparable (in depth, selection criteria, sky coverage, etc.) parent samples are generally in good agreement, provided group are selected in a similar way.

3. However, there seems to be a complex interplay among the LSS features in the galaxy sample, the sample depth, the FOF grouping procedure, and the group properties. A more detailed assessment of this and the previous point will be presented elsewhere (Trasarti-Battistoni 1998, in preparation).

The large extent of the group catalog presented here is due to the depth, sky coverage, and high sampling density of the parent galaxy sample PPS. The deep, high-density, and wide-angle surveys CfA2 and SSRS2 have been completed already some years ago, and they should be made available in the future (Ramella, private communication). These samples are directly comparable to PPS2, and we hope that they will be suitably combined with it for future analysis. The group catalog presented here was built with this purpose in mind.

Much larger samples will be required for further, substantial improvement. In fact, the deeper surveys nowadays available are usually not well-suited to group analysis. Infrared-selected surveys (e.g., Fisher et al. 1995) contain preferentially late-type galaxies, thus biased against high density regions, and their infrared LF yields a SF rapidly decreasing with cz, in this way exhacerbating the scaling problem. Very deep surveys, sparse samples (e.g., Loveday et al. 1992) or narrow angle surveys (e.g., Vettolani et al. 1993), add extra difficulties to this kind of study, as group identification require a sampling ratio as high as possible, and it is more difficult to identify groups near the survey edges. Future surveys such as 2dF (Colles & Boyle 1998), 6dF (see Mamon 1996b), and SDSS (Gunn & Weinberg 1995), will provide homogeneous galaxy samples (250 000 in 2 slices by 1999; 90 000, near-IR selected, over the southern sky by 2002; 1 000 000 over half the northern hemisphere by 2004, respectively) that should provide considerably larger homogeneous catalogs of loose groups.

Acknowledgements

I am glad to thank R. Giovanelli & M.P. Haynes, who kindly supplied a computer version of their data and carefully commented an early version of this work. The LUMFUN package (Bardelli et al. 1990) was kindly provided by E. Zucca. I am grateful to the referee G. Mamon, for his continous suggestions who considerely helped me to improve the presentation of this work. Very helpful suggestion came also from M. Ramella, to whom I am also grateful. Special thanks are due to R. Nolthenius, for his precise and precious criticisms on an early version of this work. I also received useful suggestions from B. Bertotti, S.A. Bonometto, M.J. Geller, J.R. Primack, and the "P + GM²/R'' group at SISSA. Finally, my personal thanks go to A. Diaferio, S. Ettori, A. Gardini, S. Ghizzardi, G. Giudice, F. Governato, G. Invernizzi, and R. Mignani. This research was supported by the Italian MURST.