# Environmental dependence of ellipticity correlation functions of intrinsic alignments

## TL;DR

This study models how intrinsic galaxy shape correlations depend on cosmic environment, revealing that elliptical galaxies align more strongly in elongated structures, which can aid in separating lensing signals from intrinsic alignments.

## Contribution

It introduces a novel environment-dependent model for intrinsic ellipticity correlations using Gaussian random fields and tensor eigenvalues, enhancing understanding of galaxy alignments in different cosmic structures.

## Key findings

- Elliptical galaxies align strongest in sheets and filaments.
- Spiral galaxies show uniform alignment across environments.
- Environmental information can help distinguish lensing from intrinsic alignments.

## Abstract

In this work we investigate the environmental dependence of the intrinsic ellipticity correlations in cosmic shear surveys. We use the quadratic and linear alignment model to describe the contributions by spiral and elliptical galaxies, respectively. The density field is in both cases described by a Gaussian random field and ellipticity correlation functions that are conditional on the environment of the galaxies are constructed by sampling random values for the tidal tensor and inertial tensor. The covariance of the Gaussian random process from which the tensor entries are drawn is decomposed by means of a spherical Fourier-Bessel transformation of the density field. The dependence on environment is modelled by the number of positive eigenvalues of the tidal tensor, which allows a differentiation between voids, sheets, filaments and superclusters. We find that elliptical galaxies align strongest in elongated structures such as sheets and filaments with an amplitude almost an order of magnitude higher compared to the alignment in clusters or voids. In contrast to this, spiral galaxies align equally strong in all environments. Cross-alignments between different environments are smaller than the respective auto-correlations subject to the Cauchy-Schwarz inequality which is an effective bound on their amplitude. Furthermore, we find misalignment between inertial and tidal tensor to be stronger in anisotropic regions compared to clusters or voids. While the imprint of weak lensing on galaxy ellipticities is agnostic about the environment, using environment information can help to distinguish between lensing and the intrinsic alignment signal.