5. The spatial distributions of ELG and non-ELG
We have analyzed the spatial distributions of ELG and non-ELG (and possible differences between them) in several different ways. First, we have used the harmonic mean pair distances, , for which no cluster centre needs to be known. As the number of ELG per system is often not very large, the determination of for the ELG separately is mostly not very robust. We have therefore compared the cumulative distributions of all cluster galaxies (ELG non-ELG) and of non-ELG only, for the 75 systems of sample 3. According to the Wilcoxon test, the two distributions are significantly different (at the conf.level). More specifically: when ELG are excluded from the systems, smaller values are found. Although these differences are systematic, they are quite small because the average fraction of ELG is only 16 %. The average reduction of is only 3 % which implies that is larger than by %.
Another way to look at the differences in the spatial distribution of ELG and non-ELG is to study the local densities of their immediate environment. We calculated the local density, , as the surface density of galaxies within a circular area centered on the galaxy, with radius equal to the distance to its N -th neighbour, where N is the total number of galaxies in the system. In Fig. 9 we show the normalized distributions of the values of for ELG and non-ELG, for all galaxies in the 75 systems of sample 3. The distributions are significantly different (at the conf.level), and the local density around ELG is, on average, times the density around non-ELG.
Both tests show that the spatial distribution of the ELG is significantly broader than that of the non-ELG. Additional information on the differences between the spatial distributions of ELG and non-ELG can be obtained from a comparison of the density profiles of the two classes. Because the number of ELG in a cluster is rather small, a reliable density profile of the ELG can only be obtained from the combination of all systems. We then assume implicitly that different clusters have similar profiles. This is not unreasonable, since cluster density profiles have similar slopes (see, e.g., Lubin & Bahcall 1993, Girardi et al. 1995), although their core-radii have a large spread (see, e.g., Sarazin 1986; Girardi et al. 1995; note, however, that the very existence of cluster cores is doubtful, see, e.g., Beers & Tonry 1986, Merritt & Gebhardt 1995). All these possible complications are not very important at this point, because here we are only interested in the relation between the density profiles of ELG and non-ELG.
In constructing the surface density profiles we have considered only the 51 systems from sample 3 for which the data extend at least out to 1 h-1 Mpc , in order to avoid possible problems of incompleteness, and we have limited our analysis to galaxies within 1 h-1 Mpc .
The density profiles of ELG and non-ELG are shown in Fig. 10, and they have been fitted by the usual -model:
The maximum-likelihood fit to the unbinned distribution of the non-ELG yields the following values: , h-1 Mpc , with a reduced of 1.9 (8 degrees of freedom). For the ELG we obtain maximum-likelihood values , h-1 Mpc , with a reduced of 0.9 (again, 8 degrees of freedom). The simultaneously fitted model-parameters for the ELG are quite uncertain, largely due to the flatness of the ELG density profile within 1 h-1 Mpc . We have therefore made a second fit to the ELG data in which we have taken (equal to the value for the non-ELG), which gives h-1 Mpc for the ELG.
The -models with are also shown in Fig. 10. The fit for the non-ELG is not very good because of the peak in the first bin (note that a peaky profile is expected when an accurate choice of the cluster center is made; see Beers & Tonry 1986). Nevertheless, the values found for and are consistent with recent results obtained by Lubin & Bahcall (1993) and Girardi et al. (1995).
We note in passing that the AGN, which are a subset of the ELG, have a spatial distribution that cannot be distinguished from that of the ELG; however, their distribution is different from that of the non-ELG.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998