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

TL;DR

This paper analyzes the PINOCCHIO algorithm's effectiveness in studying the relative velocity statistics of merging haloes within Lagrangian perturbation theory, demonstrating its ability to reproduce velocity distributions comparable to large-scale simulations.

Contribution

The paper presents a reimplementation and optimization of the PINOCCHIO algorithm, validating its accuracy in modeling halo merger histories and velocity statistics against the Millennium simulation.

Findings

PINOCCHIO accurately reproduces pairwise velocity distributions.

Optimized C++ implementation improves computational efficiency.

Results align well with Millennium simulation data.

Abstract

Subject of this paper is a detailed analysis of the 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 $\delta_{\rm l}$ is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position $\bmath{q}$ 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 optimised the construction of halo merging histories. Comparing our results with the output of the Millennium simulation suggests that PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution.