Wide angle effects for peculiar velocities

TL;DR

This paper investigates how wide-angle effects influence the measurement of galaxy peculiar velocities and their correlation functions, providing exact expressions to improve analysis in upcoming low-redshift surveys.

Contribution

It offers a comprehensive analysis of wide-angle effects on momentum statistics, including exact formulas in various spaces, highlighting their significance for future survey data interpretation.

Findings

Deviations from the plane-parallel limit are significant at low redshift.

Even multipoles in density-momentum cross-correlation are non-zero regardless of line-of-sight choice.

Exact expressions are derived for configuration, Fourier, and spherical spaces.

Abstract

The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as `wide angle' effects in redshift space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work we study how wide-angle effects modify the predicted correlation function and power spectrum for momentum statistics, both in auto-correlation and in cross-correlation with the density field. Using both linear theory and the Zeldovich approximation, we find that deviations from the plane-parallel limit are large and could become important in data analysis for low redshift surveys. We point out that even multipoles in the cross-correlation between density and momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information that could be exploited. We discuss configuration-space, Fourier-space and spherical analyses, providing exact expressions in each case rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcoming surveys for redshift-space distortions and peculiar velocities.