Anisotropies of galaxy ellipticity correlations in real and redshift space: angular dependence in linear tidal alignment model

TL;DR

This paper derives formulas for galaxy intrinsic alignment statistics, including their angular dependence, to analyze anisotropies and extract cosmological information from galaxy shape correlations in real and redshift space.

Contribution

It provides explicit formulas for IA statistics with angular dependence, enabling analysis of anisotropies and cosmological parameter extraction from galaxy shape correlations.

Findings

Formulas for intrinsic ellipticity--ellipticity correlation functions.

Formulas for gravitational shear--intrinsic ellipticity correlations.

Formulas for velocity-intrinsic ellipticity correlations.

Abstract

Investigating intrinsic alignments (IAs) of galaxy shapes is important not only to constrain cosmological parameters unbiasedly from gravitational lensing but also to extract cosmological information complimentary to galaxy clustering analysis. We derive simple and useful formulas for the various IA statistics, including the intrinsic ellipticity--ellipticity correlation, the gravitational shear--intrinsic ellipticity correlation, and the velocity-intrinsic ellipticity correlation functions. The angular dependence of each statistic is explicitly given, namely the angle between the line-of-sight direction and the separation vector of two points. It thus allows us to analyze anisotropies of baryon acoustic oscillations encoded in the IA statistics, and we can extract the maximum cosmological information using the Alcock-Pacyznski and redshift-space distortion effects. We also provide these formulas for the intrinsic ellipticities decomposed into E and B modes.