Wide Angle Effects in Future Galaxy Surveys

TL;DR

This paper investigates the significance of wide-angle effects in large-scale galaxy clustering measurements, demonstrating their negligible impact on correlation functions but potential importance in power spectrum analyses for future surveys.

Contribution

It provides a comprehensive analysis of wide-angle effects using the full formula, clarifies misconceptions, and assesses their impact on different statistical measures in galaxy surveys.

Findings

Wide-angle effects are negligible in correlation functions when properly averaged.

Corrections to the wide-angle formula are identified and clarified.

Significant deviations can occur in power spectrum analysis due to non-uniform galaxy pair distribution.

Abstract

Current and future galaxy surveys cover a large fraction of the entire sky with a significant redshift range, and the recent theoretical development shows that general relativistic effects are present in galaxy clustering on very large scales. This trend has renewed interest in the wide angle effect in galaxy clustering measurements, in which the distant-observer approximation is often adopted. Using the full wide-angle formula for computing the redshift-space correlation function, we show that compared to the sample variance, the deviation in the redshift-space correlation function from the simple Kaiser formula with the distant-observer approximation is negligible in galaxy surveys such as the SDSS, Euclid and the BigBOSS, if the theoretical prediction from the Kaiser formula is properly averaged over the survey volume. We also find corrections to the wide-angle formula and clarify the confusion in literature between the wide angle effect and the velocity contribution in galaxy clustering. However, when the FKP method is applied, substantial deviations can be present in the power spectrum analysis in future surveys, due to the non-uniform distribution of galaxy pairs.