On the streaming model for redshift-space distortions

TL;DR

This paper refines the streaming model for redshift-space distortions by deriving new equations, testing velocity PDF assumptions, and introducing a Gaussian mixture model that improves the accuracy of clustering predictions across scales.

Contribution

It provides a new derivation for the streaming model equations, tests the Gaussian assumption, and introduces a Gaussian mixture model for better accuracy in redshift-space clustering analysis.

Findings

Gaussian ansatz has limitations for pairwise velocity PDFs

Mixture of Gaussians fits velocity PDFs accurately

Enhanced modeling improves analysis of galaxy clustering

Abstract

The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory approach, we derive the fundamental equations of the streaming model for ordered and unordered pairs. In the first case, we recover the classic equation while we demonstrate that modifications are necessary for unordered pairs. We then discuss several statistical properties of the pairwise velocities for DM particles and haloes by using a suite of high-resolution $N$-body simulations. We test the often used Gaussian ansatz for the PDF of pairwise velocities and discuss its limitations. Finally, we introduce a mixture of Gaussians which is known in statistics as the generalised hyperbolic distribution and show that it provides an accurate fit to the PDF. Once inserted in the streaming equation, the fit yields an excellent description of redshift-space correlations at all scales that vastly outperforms the Gaussian and exponential approximations. Using a principal-component analysis, we reduce the complexity of our model for large redshift-space separations. Our results increase the robustness of studies of anisotropic galaxy clustering and are useful for extending them towards smaller scales in order to test theories of gravity and interacting dark-energy models.