The mass-Peak Patch algorithm for fast generation of deep all-sky dark matter halo catalogues and its N-body validation

We present a detailed description and validation of our massively parallel update to the mass-Peak Patch method, a fully predictive initial-space algorithm to quickly generate dark matter halo catalogues in very large cosmological volumes. We perform an extensive systematic comparison to a suite of N-body simulations covering a broad range of redshifts and simulation resolutions, and find that, without any parameter fitting, our method is able to generally reproduce N-body results while typically using over 3 orders of magnitude less CPU time, and a fraction of the memory cost. Instead of calculating the full non-linear gravitational collapse determined by an N-body simulation, the mass-Peak Patch method finds an overcomplete set of just-collapsed structures around a hierarchy of density-peak points by coarse-grained (homogeneous) ellipsoidal dynamics. A complete set of mass peaks, or haloes, is then determined by exclusion of overlapping patches, and second-order Lagrangian displacements are used to move the haloes to their final positions and to give their flow velocities. Our results show that the mass-Peak Patch method is well suited for creating large ensembles of halo catalogues to mock cosmological surveys, and to aid in complex statistical interpretations of cosmological models.