Properties of dark matter haloes in clusters, filaments, sheets and voids

Using a series of high-resolution N-body simulations of the concordance cosmology we investigate how the formation histories, shapes and angular momenta of dark matter haloes depend on environment. We first present a classification scheme that allows us to distinguish between haloes in clusters, filaments, sheets and voids in the large-scale distribution of matter. This method (which goes beyond a simple measure of the local density) is based on a local-stability criterion for the orbits of test particles and closely relates to the Zel'dovich approximation. Applying this scheme to our simulations we then find that: (i) mass assembly histories and formation redshifts strongly depend on environment for haloes of mass M < M* (haloes of a given mass tend to be older in clusters and younger in voids) and are independent of it for larger masses (M* here indicates the typical mass scale which is entering the non-linear regime of perturbation growth); (ii) low-mass haloes in clusters are generally less spherical and more prolate than in other regions; (iii) low-mass haloes in clusters have a higher median spin than in filaments and present a more prominent fraction of rapidly spinning objects. We identify recent major mergers as a likely source of this effect. For all these relations, we provide accurate functional fits as a function of halo mass and environment. We also look for correlations between halo-spin directions and the large-scale structures: the strongest effect is seen in sheets where halo spins tend to lie within the plane of symmetry of the mass distribution. Finally, we measure the spatial autocorrelation of spin directions and the cross-correlation between the directions of intrinsic and orbital angular momenta of neighbouring haloes. While the first quantity is always very small, we find that spin-orbit correlations are rather strong especially for low-mass haloes in clusters and high-mass haloes in filaments.