6 Summary

Whether there exist correlations in the orientations of galaxies or galaxy clusters has been discussed for a long time. Binggeli (1982) reported a significant alignment of the observed galaxy clusters out to 50 h^-1 Mpc. Struble & Peebles (1985, 1986) claimed that this effect is small and prone to systematics and Ulmer et al. (1989) find no indication in their investigation. Subsequently, several authors found, sometimes only weak, signs of alignments in the galaxy and galaxy cluster distribution (see e.g. Djorgovski 1986; Lambas et al. 1988; Fuller et al. 1999; Heavens et al. 2000). As a novel statistical method we have used the mark correlation functions (MCFs) to quantify the alignment of cluster sized halos, extracted from a large scale simulation based on a $\Lambda$CDM cosmology. Our sample with 3000 cluster sized halos is bigger than the currently available samples of galaxy clusters. The unambiguous signal we obtain benefits from the large statistics in our simulation.

Using two different weighting functions in the construction of the MCFs we investigate the direct alignment and the filamentary alignment. First we use the major axis of the mass ellipsoid as our direction marker. The clear signal from the direct alignment ${\cal A}(r)$extends out $\sim$30 h^-1 Mpc. For the filamentary alignment ${\cal F}(r)$ we find deviations from isotropy up to $\sim$100 h^-1 Mpc. Considering the projected mass distribution, the signal from the direct alignment ${\cal A}(r)$ already vanishes at a scale of $\sim$10 h^-1 Mpc. However, we find a filamentary alignment ${\cal F}(r)$ out to scales of $\sim$100 h^-1 Mpc, even for the projected data. This scale is very similar to the size of the large scale filaments seen in our simulation. We think that the function ${\cal F}(r)$ is a powerful tool for exploring large scale alignment effects also in observational data.

Franx et al. (1991) showed that the angular momentum of an ellipsoidal system tends to align with the minor axis of this system. We confirm this behavior in our simulation. With the angular momentum as vector mark, ${\cal F}(r)$ shows the expected filamentary correlations: the angular momentum tends to be perpendicular to the connecting line, i.e. the filament, up to separations of $\sim$40 h^-1 Mpc. However, we obtain no signal for the direct alignment ${\cal A}(r)$. This is in concordance with the perception that the angular momenta are randomly oriented in the planes perpendicular to the filaments.

With the scalar MCFs $k_{\rm m}(r)$ and ${\rm cov}(r)$ we have investigated the correlations in the absolute value of the angular momentum. Close pairs of clusters tend to have similar and also higher absolute values of the angular momentum compared to the global average. A clear signal can be detected up to $\sim$50 h^-1 Mpc. A further analysis of the mass and spin parameter distribution of the clusters with the MCFs has shown that this enhancement of the absolute value of the angular momentum is caused by an enhanced mass of close pairs of clusters as well as by the stronger rotational support of them. This behavior should be caused by the combined action of large-scale tidal fields and the hierarchical merging of progenitor structures and mass inflow onto the cluster. Since this mass growth follows the large scale filaments, tidal interactions and merger events are tightly connected. The mark correlation function with scalar and vector marks deliver quantitative measures of these effects.

Acknowledgements

M.K. was supported by the Sonderforschungsbereich 375 für Astro-Teilchenphysik der Deutschen Forschungsgemeinschaft.