4 The main properties of CGs

One essential question is whether Ts constitute a fair subsample of CGs, especially since Ts are much more numerous than Ms in all subsamples. With this aim, we compare here the magnitude of member galaxies and the CG kinematical-dynamical properties. The spectral properties and large scale environment are examined in Sects. 6 and 7. As the KS test shows that, except for subsample I, Ms are more luminous than Ts (at 99.5% c.l.) we first check whether a similar difference is also retrieved between the luminosity of Ts and Ms member galaxies. It is found that within each of the 4 distance classes Ms and Ts member galaxies display similar absolute magnitude distributions. Hence the larger luminosity associated with Ms simply arises from the fact that Ms include more members than Ts and does not indicate that higher multiplicity CGs are typically associated with brighter galaxies.

Figure 3: Distribution of Ts and Ms (hatched) as a function of $\sigma _{v}$, tracing the extension of the CG in redshift space.

As far as kinematical properties are concerned, Fig. 2 shows the distribution of the average extension ( $r_{\rm ave}$) for Ts (solid histogram) and Ms (hatched) in the four subsamples. Ts appear more compact than Ms in all but the first subsample. However, according to the KS test, differences in $r_{\rm ave}$ between Ts and Ms are not significant (59%, 56% and 77% c.l. respectively). This is not unexpected, given our selection criteria, and actually confirms that we sample Ts and Ms on a common scale. When $r_{\rm max}$ rather than $r_{\rm ave}$ is examined differences get significant (above 90% c.l.) in subsamples II and III. While $\approx$40% of the Ms include a member which is at a distance larger than 150 h^-1 kpc from the center, this is the case for less than 7% of Ts. The excess of Ms with members close to the limiting distance, together with the high fraction of Ms among rejected non symmetric CGs, possibly indicates that we are sampling subclumps embedded in larger structures eventhough the external limit of 200  $h^{\rm -1}$ kpc imposed by the algorithm prevents from drawing definite conclusions concerning any typical dimensions for Ms. In the cz range between 2500 and 7500 km s^-1, including 60% of Ms, the average dimension of CGs increases with multiplicity following the relation $r_{\rm ave}\propto n^{\rm0.6}$. This relation has been derived for the median number of galaxies in multiplets which is 4.5. The velocity dispersion of galaxies in a bound system provides an estimate of the potential well, although in CGs errors caused by random orientation of the system along the line of sight might dominate the result. In any case values obtained on a large sample of CGs are less affected by this bias, and thus yield more reliable results. In Fig. 3 the distributions of Ts and Ms relative to the parameter $\sigma _{v}$ are shown. Distributions are different at 61%, 99.6%, 97% and 98% c.l. respectively. Comparison of $\sigma_{\rm max}$ yields obviously more significant differences (98%, 99.99%, 99.9% and 99.8% c.l.). Considering again CGs within the range 2500-7500 km s^-1, we find $\sigma _{v}$ to increase with multiplicity as $n^{\rm 1.4}$.

Next, before estimating the mass associated with CGs, we check whether and how many CGs in the sample satisfy the necessary (but not sufficient) criterion for a galaxy system to be virialized. In Fig. 4 $r_{\rm ave}/R_{\rm vir}$ as a function of $\sigma _{v}$ for Ts and Ms is plotted. $R_{\rm vir}$ is computed according to prescriptions in $\Lambda$CDM ( $\Omega_{\rm M}=0.3$, $\Omega_{\rm\Lambda}=0.7$) cosmologies, requiring a virialized system to display an overdensity greater than 333 with respect to the mean density of the universe. Figure 4 shows that most CGs (95%) in the sample satisfy the virialization condition and might therefore be physical bound systems. Had we compared $R_{\rm vir}$ with the harmonic radius, the fraction of virialized systems would be slightly lower (90%).

Figure 4: Ratio of average dimension $r_{\rm ave}$ over virialization radius $R_{\rm vir}$, as a function of the parameter $\sigma _{v}$ for Ts (empty triangles) and Ms (filled squares).

Concerning the real nature of CGs it must also be stressed that the median velocity dispersion associated with galaxies in Ts (Table 3) is comparable to the mean galaxy-galaxy velocity difference associated with field galaxies (Somerville et al. 1996; Fisher et al. 1994). Accordingly one could speculate that the Ts sample suffers from serious contamination by pseudo-structures of unrelated field galaxies (filaments viewed nearly edge on), in which redshift tracing the Hubble flow is used to compute a velocity dispersion. If this is the case the contamination by interlopers is expected to bias the velocity dispersion of Ts towards the low end. However the exclusion of suspiciously low-$\sigma$ systems would also cause any genuine bound CG representing a system in its final state of coalescence to be excluded from the sample. In our sample the fraction of low $\sigma _{v}$ CGs (i.e. $\sigma_{ v}\leq 100$ km s^-1) turns out to be 32% and 16% among Ts and Ms. The first value is slightly lower than the 40% unbound Triplets claimed by Diaferio (2000). Figures are roughly consistent given that Diaferio selects systems with a FoF algorithm, which, when applied to small systems, tends to return an excess of elongated structures displaying enhanced contamination by outliers. Concerning Ms, the bias induced by interlopers might well push the velocity dispersion higher so that it is not obvious how to separate structures contaminated by interlopers from bound structures.

The substantial difference in the kinematical characteristics of Ts and Ms might affect also parameters directly derived from $\sigma _{v}$ and $r_{\rm ave}$ such as estimated mass ( $M \propto \sigma^2_{v}$ $\times r_{\rm ave}$) and dynamical time ( $H_{\rm0}t_{\rm d}\propto H_{\rm0}r_{\rm ave}/\sigma_{v}$). To compute these quantities we use $r_{\rm ave}$ instead of the harmonic radius $r_{\rm h}$, because we select groups according to their maximal extension rather than constraining their maximum galaxy-galaxy separation. In Figs. 5 and 6 distributions of estimated M/L and $H_{\rm0}t_{\rm d}$ are shown. It appears that Ms possibly display higher M/L and shorter $H_{\rm0}t_{\rm d}$ than Ts, even though differences concerning these quantities are only marginally significant. The use of the harmonic radius (or of the median galaxy-galaxy separation) to compute these quantities would confirm the possible difference, with significance similar to that obtained with $r_{\rm ave}$. The higher mean M/L associated with Ms could indicate either a higher mean $(M/L)_{\rm gal}$ or a higher fraction of mass between galaxies. Concerning $H_{\rm0}t_{\rm d}$, the longer values associated with Ts might indicate that these are systems closer to turnaround, which are therefore less likely to be virialized. Alternatively the smaller M/L and higher $H_{\rm0}t_{\rm d}$ associated with Ts might well be claimed to arise because of contamination by interlopers, and hence to be non-physical.

Figure 5: M/L distribution of Ts and Ms (hatched). Ms display larger M/L than Ts at 46%, 98%, 87% and 94% c.l. in the four classes.

Figure 6: Distribution of Ts and Ms (hatched) as a function of the dynamical time $H_{\rm0}t_{\rm d}$ in Hubble time units. Ms display shorter $H_{\rm0}t_{\rm d}$ than Ts at 42%, 86%, 90% and 98% c.l. in the four classes.

In summary, the observed kinematical differences between Ts and Ms suggest that globally Ts do not constitute a fair subsample of Ms. Interestingly, differences are not significant between Ts and Ms in sample I, including mainly faint galaxies.