Substructure Density Relation

Clusters in dense supercluster environments are expected to have a higher probability to interact with neighbouring clusters or filamentary structures connecting the cluster centers. If this hypothesis is correct, then larger fractions of clusters with distorted X-ray surface brightness distributions and thus with subclusters are expected in dense environments. To detect this effect, mean significances of/3, LEE, and FEL are computed for different local cluster number densities.

As a measure of the local_ cluster number density around each cluster one can use d~3, where d is the mean of its five nearest neighbour distances. For flux-limited samples, however, this approach introduces redshift-dependent effects. Therefore the number densities are normalized by the average density obtained with the same density estimator using all clusters in a thin redshift shell centered on the cluster's 2 value. The normalization has the additional effect of compensating also for edge effects which are known to distort next neighbour statistics (e.g., Cressie 1993).

Figure 5.13 shows the average substructure significances as a function of the normalized cluster number density of REFLEX+BCS clusters ex-eluding the very extreme densities where sample sizes are small and the results quite noisy. It is seen that the average significances of /? and LEE decrease with density, indicating that the fraction of substructured clusters increases with local density. The effect is supported by subsamples of nearby clusters with comparatively large numbers of X-ray photons. Even stronger dependencies of the average significances on density are found when the aperture radius used for substructure detection is increased from 1 Mpc to 3 Mpc. For the latter case, however, it cannot be ruled out that neighbouring clusters, not necessarily in the process of merging with the programme cluster, might artificially increase SOR.

Contrary to the results obtained with and LEE, the elongation significances, Sfel, are found to be almost insensitive to local cluster number density. It should be mentioned that a strong density-dependence is still present for FEL when 3 Mpc aperture radii are used for substructure analyses.

This substructure density relation of clusters appears to be analogous to the morphology density relation of galaxies. A related effect, namely that dynamically young optical APM clusters are more clustered than

Figure 5.13. Average significances and standard deviations for the three statistical tests as a function of the local cluster number density, normalized to the average density obtained with the 238 REFLEX+BCS clusters with at least 150 X-ray photons.

Figure 5.13. Average significances and standard deviations for the three statistical tests as a function of the local cluster number density, normalized to the average density obtained with the 238 REFLEX+BCS clusters with at least 150 X-ray photons.

the overall cluster population, was recently found by Plionis (2001) thus supporting the present findings.

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