A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO

Heisenberg, Lavinia ; Schäfer, Björn Malte ; Bartelmann, Matthias

In: Monthly Notices of the Royal Astronomical Society, 2011, vol. 416, no. 4, p. 3057-3066

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    Subject of this paper is a detailed analysis of the PINpointing Orbit-Crossing Collapsed HIerarchical Object (PINOCCHIO) algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field δl is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position q and each smoothing radius R, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian perturbation theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++, recovered the mass function and optimized the construction of halo merging histories. When compared with the output of the Millennium Simulation our results suggest that the PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution