Statistical exploration of halo anisotropic clustering and intrinsic alignments with the mass-Peak Patch algorithm

The anisotropy or triaxiality of massive dark matter haloes largely defines the structure of the cosmic web, in particular the filaments that join the haloes together. Here we investigate such oriented correlations in mass-Peak Patch halo catalogues by using the initial strain tensor of spherical proto-halo regions to orient the haloes. To go beyond the spherically averaged two-point correlation function of haloes we use oriented stacks to compute oriented two-point correlations: we explicitly break isotropy by imposing a local frame set by the strain tensor of the reference halo before stacking neighbouring haloes. Beyond the exclusion zone of the reference halo, clustering is found to be strongly enhanced along the major direction of the strain tensor as expected. This anisotropic clustering of haloes along filaments is further quantified by using a spherical harmonics decomposition. Furthermore, we compute the evolution of cluster-scale halo principal directions relative to those of their neighbours and show that there are strong correlations extending up to very large scales. In order to provide calculations more suitable to observational confrontations, we also utilize 2D projected versions of some equivalent correlation functions. Finally, we show that the multipole structure of the mass-peak patch halo's anisotropic clustering can be qualitatively captured in an analytic treatment based on peak theory. Though highly informative, analytic evaluation involves extensive use of Monte Carlo methods, which is also what the simulated catalogue uses, taking into account as they do the adaptive nature of the mass-peak patch mass hierarchy and all non-local complexities associated with the exclusion of smaller haloes overlapping with larger ones: there is no substitute for the mass-Peak Patch simulation-based determination of oriented and anisotropic correlations.