Alcock-Paczynski effects on wide-angle galaxy statistics

TL;DR

This paper develops a new method to accurately compute the Alcock-Paczynski effect on wide-angle galaxy correlations, surpassing the plane-parallel approximation, crucial for upcoming large-scale galaxy surveys in precision cosmology.

Contribution

The authors introduce a tripolar spherical harmonic basis approach to model wide-angle AP distortions without relying on the plane-parallel approximation, enabling precise analysis at large angular scales.

Findings

PP approximation errors grow with angular separation, exceeding 10% for angles over 30°.

The new method accurately captures wide-angle effects on galaxy correlation functions.

Errors are significant for density auto-correlations at large angles, emphasizing the need for beyond-PP analysis.

Abstract

The Alcock-Paczynski (AP) effect is a geometrical distortion in three-dimensional observed galaxy statistics. In anticipation of precision cosmology based on ongoing and upcoming all-sky galaxy surveys, we build an efficient method to compute the AP-distorted correlations of galaxy number density and peculiar velocity fields for any larger angular scale not relying on the conventionally used plane-parallel (PP) approximation. Here, instead of the usual Legendre polynomial basis, the correlation functions are decomposed using tripolar spherical harmonic basis; hence, characteristic angular dependence due to the wide-angle AP effect can be rigorously captured. By means of this, we demonstrate the computation of the AP-distorted correlations over the various scales. Comparing our results with the PP-limit ones, we confirm that the errors due to the PP approximation become more remarkable as the visual angle of separation between target galaxies, $\Theta$, enlarges, and especially for the density auto correlation, the error exceeds $10\%$ when $\Theta \gtrsim 30^\circ$. This highlights the importance of the analysis beyond the PP approximation.