Wide-angle effects on galaxy ellipticity correlations

TL;DR

This paper introduces a new method to accurately compute wide-angle galaxy correlation functions in three-dimensional space, revealing significant deviations from traditional small-angle approximations crucial for cosmological analyses.

Contribution

The authors develop a spin-dependent tripolar spherical harmonic basis to decompose angular dependences, enabling the first computation of wide-angle intrinsic alignment correlations beyond the plane-parallel limit.

Findings

More than 10% deviation from PP-limit for angles >30°-50°

Curved-sky effects produce non-zero correlations even when PP-limit is zero

Highlights importance of beyond-PP analysis for precise cosmology

Abstract

We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the wide-angle auto and cross correlations between intrinsic ellipticities, number densities and velocities of galaxies, and compare them with the PP-limit results. For the ellipticity-ellipticity and density-ellipticity correlations, we find more than $10\%$ deviation from the PP-limit results if the opening angle between two LOS directions exceeds $30^\circ - 50^\circ$. It is also shown that even if the PP-limit result is strictly zero, the non-vanishing correlation is obtained over the various scales, arising purely from the curved-sky effects. Our results indicate the importance of the data analysis not relying on the PP approximation in order to determine the cosmological parameters more precisely and/or find new physics via ongoing and forthcoming wide-angle galaxy surveys.