Galaxy shape statistics in the effective field theory

TL;DR

This paper develops a formalism using spherical tensors within the effective field theory framework to analyze galaxy shape statistics, including two- and three-point functions, relevant for upcoming large-scale surveys.

Contribution

It introduces a new formalism for projecting galaxy shapes onto the sky and computes higher-order correlation functions within the EFT framework.

Findings

Nonlinear intrinsic alignment effects become significant at angular scales with l > 100.

The formalism is optimized for efficient numerical implementation.

Results are relevant for Stage IV galaxy surveys.

Abstract

Intrinsic galaxy alignments yield an important contribution to the observed statistics of galaxy shapes. The general bias expansion for galaxy sizes and shapes in three dimensions has been recently described by Vlah, Chisari \& Schmidt using the general perturbative effective field theory (EFT) framework, in analogy to the clustering of galaxies. In this work, we present a formalism that uses the properties of spherical tensors to project galaxy shapes onto the observed sky in the flat-sky approximation and compute the two-point functions at next-to-leading order as well as the leading-order three-point functions of galaxy shapes and number counts. The resulting expressions are given in forms that are convenient for efficient numerical implementation. For a source redshift distribution typical of Stage IV surveys, we find that that nonlinear intrinsic alignment contributions to galaxy shape correlations become relevant at angular wavenumbers $l \gtrsim 100$.