Redshift-space distortions with wide angular separations

TL;DR

This paper develops a formalism to accurately model redshift-space distortions considering wide angular separations, moving beyond the traditional plane-parallel approximation for large sky surveys.

Contribution

It derives an operational formula for matter correlators that accounts for wide angles in both configuration and Fourier spaces, including first-order corrections to the plane-parallel limit.

Findings

Derived a formula for matter correlators with wide angles

Recovered the plane-parallel limit in both spaces

Identified first-order corrections for large surveys

Abstract

Redshift-space distortions are generally considered in the plane parallel limit, where the angular separation between the two sources can be neglected. Given that galaxy catalogues now cover large fractions of the sky, it becomes necessary to consider them in a formalism which takes into account the wide angle separations. In this article we derive an operational formula for the matter correlators in the Newtonian limit to be used in actual data sets, both in configuration and in Fourier spaces without relying on a plane-parallel approximation. We then recover the plane-parallel limit not only in configuration space where the geometry is simpler, but also in Fourier space, and we exhibit the first corrections that should be included in large surveys as a perturbative expansion over the plane-parallel results. We finally compare our results to existing literature, and show explicitly how they are related.