6. Properties of groups
In this section we discuss properties of ESP groups that can be used to characterize the LSS and that set useful constraints to the predictions of cosmological N-body models.
6.1. Abundances of groups and members
The first "global" property of groups we consider is the ratio, , of their number to the number of non-member galaxies within the survey. For ESP we have = 0.13 0.01, for CfA2N RPG find = 0.13 0.01, for SSRS2 Ramella et al. 1998 find = 0.12 0.01. Clearly the proportion of groups among galaxies is the same in all three independent volumes of the universe surveyed with ESP, CfA2N and SSRS2. Because CfA2N and SSRS2 mostly sample only one large structure while ESP intercepts several large structures, our result means that the clustering of galaxies in groups within the large scale structure is homogeneous on scales smaller than those of the structures themselves.
We point out that, on the basis of our simple simulation, we do not expect the OPTOPUS mask to affect the determination of .
We now consider the ratio of member to non-member galaxies, . Within ESP we have = 0.68 0.02; within CfAN and SSRS2, the values of the ratio are = 0.81 0.02 and = 0.67 0.02 respectively. Quoted uncertainties are one poissonian standard deviation. According to the poissonian uncertainties, and are undistinguishable. The value of is significantly different from the other two ratios. However, the real uncertainty in the ratio of members to non-members is higher than the poissonian estimate because the fluctuations in the number of members is dominated by the fluctuations in the smaller number of groups. Moreover, the total number of members is strongly influenced by few very rich systems. In fact, it is sufficient to eliminate two clusters, Virgo and Coma, from CfA2N in order to reduce the value of to = 0.70 0.02, in close agreement with the ratio observed within ESP and SSRS2.
In conclusion, groups are a remarkably stable property of the large-scale distribution of galaxies. Once the richest clusters are excluded, the abundances of groups and of members relative to that of non-member or"field" galaxies are constant over several large and independent regions of the universe.
6.2. Distribution of groups in redshift-space
We plot in the top panel of Fig. 4 the cone diagram ( vs cz) for the 3085 ESP galaxies within 5000 60000 km s-1 . In the bottom panel of Fig. 4 we plot the cone diagram of the 231 ESP groups. Figs. 4 shows that groups trace very well the galaxy distribution, as they do in shallower surveys ( 12000 km s-1 ). Note that in Fig. 4 we project adjacent beams, not a strip of constant thickness.
The topology of the galaxy distribution in redshift space has already been described by Vettolani et al. (1997) and will be the subject of a forthcoming paper. The most striking features are the voids of sizes 50 Mpc and the two density peaks at 18000 km s-1 and 30000 km s-1 . These features are also the main features of the group distribution.
In Fig. 5 we plot the redshift distributions of groups (thick histogram) and galaxies (thin galaxies), divided by the total number of groups and by the total number of galaxies, respectively. In Fig. 6 we plot number densities of galaxies in redshift bins. Number densities are computed using the estimator of Davis & Huchra (1982): all the details about the density estimates are given in Zucca et al. 1997. We vary the size of the redshift bins in order to keep constant the number of galaxies expected in each bin based on the selection function. The top panel is for member galaxies, the middle panel is for isolated and binary galaxies, and the bottom panel is for all ESP galaxies. The dashed lines represent the one sigma corridor around the mean galaxy density.
It is clear from Fig. 5 that the redshift distributions of groups and galaxies are undistinguishable (98% confidence level). Not surprisingly, the number density in redshift bins of members and all galaxies are highly correlated (Fig. 6a and 6c). More interestingly, the number density distribution of non-member galaxies is also correlated with the number density distribution of all galaxies (Fig. 6b and 6c). In particular, the two density peaks at 18000 km s-1 and 30000 km s-1 of the number density distribution of all galaxies are also identifiable in the number density distribution of non-member galaxies, even if with a lower contrast.
We know from the previous section that groups are a very stable global property of the galaxy distribution within the volume of the ESP and within other shallower surveys. Here we show that a tight relation between non-member galaxies and groups exists even on smaller scales.
Our result is particularly interesting in view of the depth of the ESP survey and of the number of large structures intercepted along the line-of-sight.
6.3. The distribution of velocity dispersions
We now discuss the velocity dispersions of ESP groups. According to our simulation in Sect. 2, the effect on the velocity dispersions of the OPTOPUS mask is statistically negligible.
The median velocity dispersion of all groups is = 194 (106,339) km s-1 . The numbers in parenthesis are the 1st and 3rd quartiles of the distribution. Poor groups with 5 have a median velocity dispersion =145 (65,254) km s-1 , richer groups have =272 (178,399) km s-1 . For comparison, the median velocity dispersions of CfA2N and SSRS2 are =198 (88,368) km s-1 and = 171 (90,289) km s-1 . We take the values of the velocity dispersions for the CfA2 and SSRS2 groups from Ramella et al. (1997,1998). In order to compare these velocity dispersions with ours, we correct them for a fixed error of 50 km s-1 (corresponding to an RVSAO error of 35 km s-1 ) and multiply them by . We note that, because of the OPTOPUS mask, the comparison of the velocity dispersions of "rich" and "poor" groups within ESP with those of similar systems within CfA2N and SSRS2 is not meaningful. A fraction of ESP "poor" groups may actually be part of "rich" groups.
In Fig. 7 we plot (thick histogram) the distribution of the velocity dispersions, , normalized to the total number of groups. Errorbars are one sigma poissonian errors. We also plot the normalized distributions of CfA2N and SSRS2. According to the KS test, differences between and the other two distributions are not significant = 0.3 and 0.2 for the comparison between ESP and CfA2N and SSRS2 respectively).
It is interesting to point out that and do differ significantly (97% level), being richer of high velocity dispersion systems (Marzke et al. , 1995). Groups with dispersion velocities 700 km s-1 are rare and the fluctuations from survey to survey correspondingly high. The abundance of these high systems is the same within both ESP and SSRS2 (2%) but it is higher within CfA2N (5%). If we disregard these few high velocity dispersion systems, the difference between and ceases to be significant. From this result we conclude that each survey contains a fair representation of groups.
The distribution of velocity dispersions is an important characteristic of groups because it is linked to the group mass. Therefore constitutes an important constraint for cosmological models. Furthermore, is a much better parameter for the classification of systems than the number of members (even more so in the case of the present catalog where the OPTOPUS mask affects the number of members much more than velocity dispersions)
The ESP survey provides a new determination of the shape of in a much deeper volume than those of existing shallower surveys. We find that, within the errors, is very similar to both and .
© European Southern Observatory (ESO) 1999
Online publication: December 22, 1998