3. Velocity distribution and dynamics in Abell 521
3.1. Global mean velocity and velocity dispersion of the cluster
From a visual inspection of the cone diagram displayed in Fig. 2, we selected a reasonable range of velocities (70000 to 80000 km s-1) which brackets candidate members of the cluster. One galaxy (number 2) is identified as a clear foreground object. Three background objects are found at a redshift ; others are at redshifts of 0.289, 0.310 0.331 and 0.360.
We have employed the ROSTAT package (Beers et al. 1990, hereafter BFG) to analyze the velocity distribution of the 41 remaining galaxies in the selected velocity range. In order to quantify the central location and scale of the velocity distribution for Abell 521, we have used the resistant and robust biweight estimators ( and , respectively) recommended by BFG. For the complete sample of velocities, we obtain km s-1 and km s-1. Estimates of these quantities obtained with alternative estimators show similar values. The one-sigma errors in these quantities are calculated in ROSTAT by bootstrap re-sampling of 1000 subsamples of the velocity data.
In Fig. 3 (top) we show a stripe density plot of the velocity distribution for Abell 521. The velocity histogram, calculated with a binning of 1000 km s-1, is shown in Fig. 3 (bottom), along with a superposed Gaussian of standard deviation 1386 km s-1, shifted to the velocity of the cluster. The radial velocity of the brightest cluster galaxy (hereafter, BCG) is shown with an arrow.
The apparent velocity dispersion of Abell 521, km s-1, is among the largest values observed in galaxy clusters, as compared, for example, to the velocity dispersion distribution of the recent ENACS survey (Mazure et al. 1996). The dispersion is well above the median value of 744 km s-1 estimated by Zabludoff et al. (1990) for a sample of 65 clusters. However, the velocity dispersion of Abell 521 is significantly larger than the value ( km s-1) we would predict from X-ray observations, using our measurement of the gas temperature, and assuming equipartition between kinetic and potential energy (Arnaud et al. 2000).
We endeavor to determine how reliable this estimate of the velocity dispersion is, and whether or not it is affected by various problems such as subclustering or contamination by outliers. A fair assessment of the impact of potential interlopers is essential for derivation of an unbiased measurement of the velocity dispersion (see for instance Mazure et al. 1996). Given that the spatial coverage of our velocity sample is far from complete, and strongly favors the high-density regions of the cluster, and the limitations imposed by the relatively small number of measured velocities, we cannot proceed to a sophisticated analysis of subclustering. For the present we limit ourselves to classical tests which examine whether our velocity measurements are drawn from a single parent population, or are drawn from a mix of slightly-offset velocity distributions which, taken as a single kinematic entity, would mimic this large velocity dispersion.
3.2. Simple statistical tests of the velocity distribution
We have performed a number of statistical tests of the velocity data for Abell 521. All twelve of the simple tests implemented in ROSTAT are consistent with the hypothesis that the velocities are drawn from a Gaussian parent population. We also searched for the existence of statistically significant gaps in the velocity distribution, which can indicate the possible presence of subclustering, especially when located in the center of a distribution - none were found. Bird & Beers (1993) discuss alternative measures of the classical coefficients of skewness and kurtosis, the asymmetry index (AI) and the tail index (TI), which are useful for detecting subtle deviations from normality in distributions. For the complete velocity set, we obtain and , respectively. Neither of these values allow rejection of a Gaussian parent population according to the tables supplied by Bird and Beers (1993).
While we cannot exclude some contamination from outliers or groups along the line-of-sight to Abell 521, these results do exclude the presence of significant projection effects in velocity space.
3.3. Testing for substructure in the projected spatial and redshift distribution
To search for the presence of substructure in the projected spatial distribution of galaxies in Abell 521 we have fit the observed galaxy positions to a number of Gaussian mixture models, following the procedures described in Kriessler & Beers (1997). In this analysis we have only used the galaxies brighter than , to limit contamination from background galaxies projected on the face of the cluster. Fig. 4 shows an adaptive-kernel contour map of the region centered on Abell 521.
The best-fit KMM partition of the projected galaxy positions, evaluated using a maximum-likelihood ratio test and a bootstrap procedure, is a three-group partition which is significant at the 99% level (parameters of the partition are specified in Table 2). Column (1) of this table lists the identification number of the group (indicated in Fig. 4). Column (2) lists the number of galaxies assigned to each group. Columns (3) and (4) list the fraction of the total number of galaxies present in each group, and the fraction of total luminosity in each group, respectively. The x and y positions of the groups, along with their one-sigma errors, are listed in columns (5) and (6). The median magnitude of the galaxies within each group is listed in column (7); column (8) lists the mean magnitude of the 10th to 20th brightest galaxies in each group. Fig. 5 shows the reconstructed contour maps of the three Gaussians corresponding to the best-fit partition obtained with the KMM algorithm.
Table 2. Mixture Model Parameters for Abell 521
From application of a K-S test to the magnitude distributions of the various groups, we find that group 3 is marginally fainter than the others. This, along with the fainter value of (see Jones & Mazure 1996), suggests that group 3 may contain a large fraction of background galaxies.
We next obtain a split of the velocity sample, assigning each galaxy to a group associated to the nearest projected group center obtained from the KMM analysis. This results in 9 galaxies associated with KMM1, 19 with KMM2, and 2 galaxies with KMM3. Galaxies located farther than 1.5 arcmin from any of the group centers are set aside.
We then obtain a further split of the KMM2 group into two components: KMM2 North (14 galaxies) and KMM2 South (5 galaxies) in order to isolate the Southern extension of KMM2 seen in the adaptive kernel map shown in Fig. 4. There are only two galaxies with measured velocities assigned to the KMM3 region (numbers 40 and 42), both of which have slightly higher velocities than the adopted central location velocity for the cluster as a whole. More measured velocities are required to reliably determine the mean velocity of KMM3.
We are thus left with three subsamples of the velocity catalog on which we have run the ROSTAT package, corresponding to regions KMM1, KMM2 North, and KMM2 South. The results of this analysis are summarized in Table 3. Although the small number of velocities in each subsample do not allow us to derive precise measurements of the velocity dispersions, two qualitative conclusions can be drawn. First, there are no significant velocity offsets between the individual partitions with respect to one another, at least to within the bootstrapped errors on the velocity locations. Second, the KMM2 North partition has a significantly higher value of the velocity dispersion than the other two partitions, or as compared to the cluster as a whole. This result is also strikingly clear on the stripe density plots of these three partitions displayed in Fig. 6. The KMM2 North group, which includes the so-called "ridge" structure described by Arnaud et al. (1999), is probably kinematically complex, and may well be comprised of several subclusters.
Table 3. ROSTAT analysis of velocity samples in Abell 521
We have also examined the location of the three galaxies with (objects 4, 40, and 46) to check if they are spatially clustered, as would be expected for a background group. These galaxies are all located in the Eastern part of the cluster. Taking into account the velocity measurement in Table 1, galaxies 4 and 46 are separated from one another by Mpc, and lie at the Eastern part of the KMM2 structure. Galaxy 40 lies Mpc from galaxy 4, and Mpc from galaxy 46 in the Southern direction. It is thus not excluded that these three galaxies are members of a background loose group, but a much more complete redshift survey of Abell 521 is required to resolve this question.
3.4. Analysis of the velocity distribution with the color index
Several analyses have shown that the velocity distribution of galaxies in clusters can be very different for individual morphological types (e.g., see the analysis by Binggeli et al. 1987 on the Virgo Cluster, Beers et al. 1992 on A400, Bird et al. 1995 on Abell 151, and of Girardi et al. 1996 on a larger sample of clusters). A higher value of velocity dispersion is generally found for late-type galaxies, as compared to early types, which is expected if the latter have fallen into the cluster potential following the initial collapse (Tully & Shaya 1984). The spatial resolution of our imaging data for Abell 521 is unfortunately not sufficient to assign a morphological type to all the objects with measured velocities, in particular at the faintest magnitudes. As an alternative, we have used the color indices of the galaxies in order to define two subsamples within our velocity catalog, with values of respectively higher and lower that the median value for the sample as a whole. In the following we refer to these as the "red " and "blue " subsamples.
Inspection of the brightest galaxies, whose morphological type is unequivocally determined by eye, shows that typical cluster ellipticals belong to the red subsample, and spirals to the blue subsample. Galaxies of the cluster with detected emission lines (Table 1) belong to the blue subsample, as expected. Fig. 7 shows stripe density plots of the velocity distributions for the red and blue subsamples. These subsets appear rather different. ROSTAT analysis of the two subsamples yields values of km s-1 and km s-1 for the red subsample of 19 galaxies, and km s-1 and km s-1 for the blue subsample of 20 galaxies, respectively. The central locations on velocity of the high and low subsamples are consistent with one another, but the velocity scales are significantly different. We have further checked how stable these results are by testing different subsamples obtained by translating the color cut on within around the median value. The range is of course limitated, as the number of objects falls rapidly when moving off the median. The values of the dispersions which are obtained fluctuate around the previously calculated ones, but the general trend is confirmed and becomes even more accentuated when considering the most extreme regions of the color distribution. In any case, the velocity distribution of the blue subsample is quite large, while the red subsample shows a value which is typical of other galaxy clusters.
One might wonder if the colors of the galaxies are correlated with the high-density structures evidenced in the V-band density map. Based on our inspection of the color indexes, there might be a color segregation in the various structures, with a bluer NE/SW extension including KMM2 North and more compact redder clumps along the NW/SE extension. However the bluest galaxies belonging to our velocity sample are distributed across the entire field of the cluster, so the high velocity dispersion of these galaxies cannot be due solely to the contribution of the KMM2 North region.
The higher velocity dispersion of the blue subsample can be explained under the hypothesis that Abell 521 is in fact dynamically complex; one might expect this class of galaxies to include many spirals which are not yet virialized within the cluster potential. In this case the distribution of the spirals would be much more dispersed than that of the ellipticals (Girardi et al. 1996). In fact, the velocity dispersion as estimated from the red subsample, km s-1, is quite in line with the predicted cluster dispersion based on the X-ray analysis, which is at variance with the dispersion based on the entire set of galaxies with measured velocities.
3.5. Virial mass estimate
Based on our existing data, one can naiively attempt to derive a mass estimate for Abell 521. We can, for instance, calculate the virial mass estimator:
where is the line-of-sight velocity dispersion of the cluster, and the three-dimensional virial radius. The projected mean harmonic separation:
where the ij sum is done over all pairs, can be used to derive the three-dimensional virial radius from the relation: (Limber and Mathews 1960). However, a number of problems are present. We have several pieces of evidence that our cluster is currently undergoing strong dynamical evolution and is not yet virialized. It follows that if our measured velocity dispersion is over-estimated by the presence of sub-clustering, the virial estimate of the mass from our measured velocity dispersion will be a large over-estimate of the real value. Another potential problem is that our imaging field is quite small ( Mpc), and the cluster probably extends well beyond the extension of our image. The estimate of may not have reached a stable value, and our measurement of the mass will be an under-estimate of the total value. This problem can be in some cases overrided by considering the ringwise projected harmonic radius (Carlberg et al. 1996), which is less sensitive to the narrowness of the field. Unfortunately, as this method assumes symmetry about the center of the cluster, and has been shown to be biased in the case of a substantially subclustered distribution, we did not feel appropriate to use it for this highly irregular cluster. We have thus limited our analysis to an estimate of the mass within our imaging field. The virial estimate of the mass as applied to a system bounded at a finite radius will be an over-estimate (by at most 50) of the real mass contained in this radius, due to ignoring the surface term in the scalar virial theorem (Carlberg 1996). We therefore derive a virial estimate of the mass within a radius of Mpc, which should be an upper bound of the mass within the same region: .
© European Southern Observatory (ESO) 2000
Online publication: March 21, 2000