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.
