4. The global kinematics of ELG and non-ELG
In this section we analyze the global kinematics of ELG and non-ELG. Before we enter into the details of this discussion we want to emphasize the following important point. All the results that we will obtain in this section, either on differences between ELG and non-ELG in average velocity or in velocity dispersion, are based on the implicit assumption that both types of galaxies consist of single systems. In other words: we have calculated a single average velocity (or velocity dispersion) for both ELG and non-ELG. If this assumption is incorrect (e.g. because the ELG do not have a smooth spatial distribution, but instead are in several compact groups within a cluster) the interpretation of the results obviously becomes more complicated. We will return to this question in Sect. 6.
4.1. Average velocities
Zabludoff & Franx (1993) noted that the average velocity of late-type galaxies was different from that of early-type galaxies in 3 of the 6 clusters they examined. They interpreted this as evidence for anisotropic infall of groups of spirals into the cluster. However, since their analysis is limited to 6 clusters, one cannot draw general conclusions from this result.
Here, we address the same issue on the basis of our sample of 57 clusters in which at least 5 ELG were found (sample 1). For these systems, we determined the average velocities of both ELG and non-ELG, as well as the associated 1 errors, which were calculated with the jack-knife technique (see, e.g., Beers et al. 1990). For the 12 clusters in which the velocity difference between ELG and non-ELG exceeds , we give details in Table 4. The distribution of the differences v - v in the 57 systems is shown in Fig. 4.
Table 4. The average velocity differences between ELG and non-ELG in those clusters where the difference is larger than
We thus find a much lower fraction of clusters with significant differences in the average velocities of ELG and non-ELG than did Zabludoff & Franx. One might think that the two results could be consistent, if in many of our clusters there would be a real difference which has been masked by the effects of limited statistics. However, in Sect. 4.2 we will show, from the distributions of velocity difference between galaxy pairs, that this is unlikely to be the case. In addition, the same low fraction of significant velocity offsets is found among the 20 systems that contain at least 10 ELG.
For each of the 18 systems with at least 10 ELG (sample 2), we show in Fig. 5 the velocity distributions of ELG and non-ELG separately. Note that this figure does not include every system listed in Table 4, because quite a few of those have less than 10 ELG. For the 4 systems in the figure that also appear in Table 4 (A548E, A3094, A3562 and A3764) the histograms clearly give a visual confirmation of the existence of a velocity difference. There are several systems with intrigueingly uneven velocity distributions for, in particular the ELG, but with the present statistics it is impossible to say if those are indeed clusters with real velocity differences between ELG and non-ELG.
4.2. Velocity dispersions
For the systems with significant velocity differences between ELG and non-ELG that are shown in Fig. 5, the numerical evidence is supported visually by the figure. However, it is impossible to say from that figure if there exist significant differences between the velocity dispersions of ELG and non-ELG. It turns out, however, that among the 18 systems with at least 10 ELG, 3 have a difference between ELG and non-ELG that is significant at a level of more than 2 . The values of and ( - ) for these systems and their jack-knife errors are given in cols.(2) and (3) of Table 5. It is interesting that all 3 differences are positive, i.e. that in all 3 cases the of the ELG is larger than that of the non-ELG.
Table 5. Significant velocity-dispersion differences between ELG and non-ELG
We have followed up this conclusion by considering all 75 systems of sample 3 with . For 57 of these, it is not possible to derive a meaningful estimate for the ELG separately. However, for 71 of the 75 systems (4 of which do not have an ELG), one can compare the values derived for the total galaxy population with those for the non-ELG only (i.e. excluding the ELG). As non-ELG are the dominant population, we expect that the change in on excluding the ELG will be quite small, but combining the results for all 71 systems may nevertheless give a significant result.
In Fig. 6 we show the two cumulative -distributions for all the galaxies (ELG non-ELG) and for non-ELG only, in the 75 clusters with at least 20 members (i.e. the 4 clusters without ELG are included in the Figure). The removal of the ELG from the cluster samples in general lowers the value of ; a Wilcoxon test (see e.g. Press et al. 1986) indicates that the ELG non-ELG distribution is different from that of the non-ELG at the conf.level, and that of ELG non-ELG is, on average, larger than of the non-ELG.
4.3. Velocity distributions
In order to examine the kinematical properties of ELG and non-ELG further, we have put together all galaxies in the 75 clusters in sample 3 in a single, 'synthetic', cluster. We define a "normalized velocity difference", , with respect to the average velocity of the system to which the galaxy belongs, which is normalized with respect to the velocity dispersion of the parent system, viz. .
For this discussion we could have included the systems with , but we have not done so, because later on we will include positional information which requires the centre to be known with sufficient accuracy. When comparing the -distributions of ELG and non-ELG, we do not want to be strongly affected by the tails of these distributions. As our interloper rejection method was only applied to clusters with more than 50 galaxies (see Sect. 2.2), it is possible that a few outliers are still present in the systems with less than 50 galaxies. For the preceding analysis, in which we used robust estimators, such outliers were not very important. However, combining data for many systems for which the average velocity is not known exactly will produce longer tails in the velocity distribution. As for some of the following analyses we cannot use robust estimators we have to get rid of possible outliers. To that end we have applied a 3 -clipping criterion (Yahil & Vidal 1977). This removes 30 galaxies in total (among which are 9 ELG) and yields a 'synthetic' cluster with 3699 galaxies, among which are 549 ELG.
The ELG and non-ELG -distributions are shown in Fig. 7. The -distribution for ELG is broader than that for non-ELG; the KS-test gives a probability of 0.029 that the two distributions are drawn from the same parent population. The dispersion of the 's of the ELG is % larger than the dispersion of the 's of the non-ELG.
Among the 549 ELG, 37 are AGN; the KS-test indicates that the -distributions of AGN and non-ELG are significantly different (with a probability of 0.047 for the two distributions to be drawn from the same parent population), but the -distributions of AGN and the other 512 ELG are not. Therefore, AGN seem to follow the velocity distribution of the other ELG.
In principle there are two possible explanations for the wider distribution for the ELG. On the one hand, the ratio of and may be larger than unity by roughly the same amount in essentially all systems. On the other hand, the broader distribution of the of the ELG could be due to the fact that we have superposed many ELG systems. Even if, in most systems, the of the ELG were identical to the of the non-ELG, the width of the distribution could be larger for ELG than for non-ELG if the average velocities of ELG and non-ELG are substantially different in the large majority of the systems. The reason is that the 's are calculated with the overall values of and , which are determined primarily by the non-ELG.
These two possible explanations are obviously extreme cases, and it is very unlikely that one of them applies exclusively. In Sect. 4.1 we saw that in a small fraction of the clusters there is evidence for a significant offset between the average velocities of ELG and non-ELG. However, we could not tell whether such offsets occur in essentially all systems (but were not detectable in many systems due to limited statistics). Here, we will show that the main reason for the apparently larger of the ELG must be that the intrinsic of the ELG is about 20% larger than that of the non-ELG. In other words: only a small part of the larger dispersion of the ELG is due to the fact that we have combined several narrower gaussians with different means. This conclusion is based on an analysis of the pairwise velocity differences of the ELG.
In Fig. 8 we show the sum (over all systems) of the distribution, for all galaxy pairs in a given system, of the absolute value of the pairwise velocity difference (again, normalized to the velocity dispersion of the system to which the two galaxies belong), i.e. . These distributions were calculated separately for pairs of non-ELG (thin line), pairs of ELG (thick line), and for mixed pairs of an ELG and a non-ELG (dashed line). The three distributions have been normalized to the total number of pairs of each kind; clearly the uncertainties are largest for the ELG/ELG-pairs. If essentially all ratios / for the individual systems would be larger than one (and if velocity offsets between ELG and non-ELG were non-existent) one would expect three gaussian distributions in Fig. 8, with widths increasing from the non-ELG/non-ELG, via the non-ELG/ELG to the ELG/ELG pairs.
The distributions for the non-ELG/non-ELG and non-ELG/ELG pairs are indeed very close to gaussian, and the non-ELG/ELG distribution is broader than that of the non-ELG/non-ELG pairs. However, the distribution for the ELG/ELG pairs is quite different from this gaussian expectation. The ELG/ELG distribution for v smaller than has a curvature opposite to that of a gaussian. Therefore, there must be a component that produces an n() that is small for small values of and has a peak at of about 2 and then decreases again. One way to produce such a component is by having systems in which the ELG have a velocity offset of about one with regard to the non-ELG. However, at the same time, there must be a second component which produces the broadening of the ELG/ELG distribution for large values of (say, larger than about 2). In other words: we are led to a schematic model with two components in the ELG velocity distribution, one with fairly small internal and significant velocity offsets, and another with a global that is larger than the of the non-ELG but without a significant velocity offset.
We have attempted to estimate the relative importance of these two components by some simple modeling. Although there is not a single, unique solution, it appears that the distribution for the ELG/ELG pairs in Fig. 8 requires that 25% of the ELG reside in systems with an average velocity offset of about 600 km s-1 (i.e. almost equal to the value of the global ). However, the internal of these ELG systems with significant velocity offsets must be small, i.e. less than about half the value of . If the fraction of ELG in these systems is much larger or smaller than 25% and/or the values of these systems is comparable to the values of the non-ELG, the steep slope of the ELG/ELG distribution at small values (say, below 1.5) cannot be reproduced.
For the other 75% of ELG, i.e. those in the systems without large velocity offsets, the global value of must be a factor of about 1.25 larger than in order to reproduce the number of ELG/ELG pairs for values of between 2 and 4 to 5. This simple model clearly cannot give information on how the latter 75% of ELG are distributed, and how their (of, on average, 1.25 ) comes about. As mentioned earlier, they can either be essentially isolated galaxies (and distributed more or less uniformly in their parent clusters), or they may be in compact groups, or a combination of these. From Fig. 5 one gets the impression that both cases occur. We will return to this question in Sect. 6.
It is worth remembering that in Sect. 4.1 we found that for 12 out of 57 systems there is a significant difference in the average velocities of ELG and non-ELG. The observed offsets range from about 300 to 1400 km s-1 (with a median of about 600 km s-1 ). Both the fraction of systems with a significant offset and the size of the offsets that we derived here from a simple model thus agree very nicely with the observed values.
Finally, we note that the distribution of normalized velocities for the AGN subset of the ELG cannot be distinguished from that of the non-ELG or ELG, due to the limited number of AGN in the ENACS.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998