A semi-analytic model of pairwise velocity distribution between dark matter halos

TL;DR

This paper introduces a simplified semi-analytic model for the pairwise velocity distribution of dark matter halos, achieving high accuracy with fewer parameters than previous models, and demonstrating its effectiveness in predicting clustering and redshift-space distortions.

Contribution

The paper presents a new semi-analytic model with only three parameters for the pairwise velocity PDF, improving accuracy over previous models with more parameters across various masses and redshifts.

Findings

Model predicts mean and dispersion with 5% accuracy for certain halo masses and redshifts.

Accurately maps two-point clustering between real and redshift space at intermediate scales.

Explains monopole and quadrupole moments of two-point correlations with better than 5% precision.

Abstract

We study the probability distribution function (PDF) of relative velocity between two different dark matter halos (i.e. pairwise velocity) with a set of high-resolution cosmological $N$-body simulations. We investigate the pairwise velocity PDFs over a wide range of halo masses of $10^{12.5-15}\, h^{-1}M_{\odot}$ and redshifts of $0<z<1$. At a given set of masses, redshift and the separation length between two halos, our model requires three parameters to set the pairwise velocity PDF, whereas previous non-Gaussian models in the literature assume four or more free parameters. At the length scales of $r=5-40\, [h^{-1}\, \mathrm{Mpc}]$, our model predicts the mean and dispersion of the pairwise velocity for dark matter halos with their masses of $10^{12.5-13.5} \, [h^{-1}M_{\odot}]$ at $0.3 < z < 1$ with a 5%-level precision, while the model precision reaches a 20% level (mostly a 10% level) for other masses and redshifts explored in the simulations. We demonstrate that our model of the pairwise velocity PDF provides an accurate mapping of the two-point clustering of massive-galaxy-sized halos at the scales of $O(10)\, h^{-1}\mathrm{Mpc}$ between redshift and real space for a given real-space correlation function. For a mass-limited halo sample with their masses greater than $10^{13.5}\, h^{-1}M_{\odot}$ at $z=0.55$, our model can explain the monopole and quadropole moments of the redshift-space two-point correlations with a precision better than 5% at the scales of $5-40$ and $10-30\, h^{-1}\mathrm{Mpc}$, respectively. Our model of the pairwise velocity PDF will give a detailed explanation of statistics of massive galaxies at the intermediate scales in redshift surveys, including the non-linear redshift-space distortion effect in two-point correlation functions and the measurements of the kinematic Sunyaev-Zel'dovich effect.