5 Simulated CG samples

Figure 7: Distribution of the median $\sigma _{v}$ in 300 pseudo CG samples (Ts, solid histogram and Ms hatched) identified in simulated UZC catalogues in which radial velocity have been randomly reassigned. The median value of the real T and M samples are indicated by the symbols T and M. The real sample, which is 3-4 times as large as the simulated ones, appear to include many more low $\sigma _{v}$ structures than reproducible by chance projection.

In order to probe physical reliability of kinematical differences between Ts and Ms, pseudo-CG samples must be produced by running the search algorithm on a large set of randomized UZC catalogues. This allows us to correctly evaluate how much of the kinematical differences between Ts and Ms might be attributed to random properties of the UZC galaxy distribution. Yet, randomly generated catalogues (i.e. random assignment of RA, Dec and cz within the catalogue limits) would completely destroy large-scale structures in the nearby universe and hence would not constitute fair comparison samples. Random reassignment of UZC galaxy coordinates (including redshift) leads to more realistic representations.

In particular, to account for selection effects contaminating the velocity dispersion of T and M samples we have run the algorithm on 300 simulated UZC samples in which only the radial velocity of the galaxies has been reassigned. This leads to samples of $\approx$90 CGs ( $\rm median=95$, 87 and 101 first and last quartile) and allows to reproduce separately structures on the (projected) sky and in redshift space. Median values of the velocity dispersion distribution in the 300 pseudo-CGs samples are displayed in Fig. 7, together with the median of samples of the real Ts (T) and Ms (M). It is evident that pseudo-CGs generally display $\sigma _{v}$ larger than observed in the real sample and that they are unable to reproduce the severe segregation observed between Ts and Ms. Accordingly, random properties do not account for the much lower $\sigma _{v}$ associated with Ts. Specifically, simulations indicate that for CGs between 2500 and 7500 km s^-1, $\sigma _{v}$ increases as $n^{\rm0.2}$. Subtracting this contribution from the observed slope yields the true increase in $\sigma _{v}$ with multiplicity, which turns out to be $\sigma_{v}\propto n^{1.2}$. Accounting for field interlopers, which should bias the velocity dispersion of Ts towards the low end, only slightly reduces the steep slope in $\sigma _{v}$. Indeed, rejection of systems with $\sigma_{v}<100$ km s^-1 yields (after correcting for random contributions) $\sigma_{v}\propto n^{0.9}$.

Simulations which keep the projected position of galaxies are unable to fairly account for random properties affecting the average dimension of CGs. Therefore additional simulations have been run, in which RA and Dec of UZC galaxies have been separately reassigned. In this kind of simulated catalogues an average of 15 CGs are retrieved. The increase of CGs average dimension with multiplicity turns out to be rather modest ($\propto$n^0.2). Subtraction of this contribution from the observed one gives the correct increase of $r_{\rm ave}$ with n ($\propto$n^0.4). The space-number density of CGs thus appears to slightly decrease ( $\rho\propto n^{-0.2}$) from Ts to Ms, a trend which is not consistent with the relation expected in constant space-number density structures. Conversely, a small increase in surface number density ( $\Sigma\propto n^{0.2}$) holds, which might be induced by our request for a common projected scale for CGs of different multiplicity.