Nonlinear redshift space distortion in halo ellipticity correlations: Analytical model and N-body simulations

TL;DR

This paper develops an analytical model for nonlinear redshift space distortions in halo ellipticity correlations, incorporating the Finger-of-God effect, and validates it with N-body simulations, improving predictions over linear models.

Contribution

The paper introduces a new nonlinear model for galaxy/halo ellipticity correlations in redshift space, accounting for the Finger-of-God effect, and derives analytic formulas for multipole moments.

Findings

The nonlinear model better predicts alignment signals than linear models.

Analytic formulas for multipole moments are derived and validated.

The model has been applied to cosmological constraints using SDSS data.

Abstract

We present an analytic model of nonlinear correlators of galaxy/halo ellipticities in redshift space. The three-dimensional ellipticity field is not affected by the redshift-space distortion (RSD) at linear order, but by the nonlinear one, known as the Finger-of-God effect, caused by the coordinate transformation from real to redshift space. Adopting a simple Gaussian damping function to describe the nonlinear RSD effect and the nonlinear alignment model for the relation between the observed ellipticity and underlying tidal fields, we derive analytic formulas for the multipole moments of the power spectra of the ellipticity field in redshift space expanded in not only the associated Legendre basis, a natural basis for the projected galaxy shape field, but also the standard Legendre basis, conventionally used in literature. The multipoles of the corresponding correlation functions of the galaxy shape field are shown to be expressed by a simple Hankel transform, as is the case for those of the conventional galaxy density correlations. We measure these multipoles of the power spectra and correlation functions of the halo ellipticity field using large-volume N-body simulations. We then show that the measured alignment signals can be better predicted by our nonlinear model than the existing linear alignment model. The formulas derived here have already been used to place cosmological constraints using from the redshift-space correlation functions of the galaxy shape field measured from the Sloan Digital Sky Survey (Okumura and Taruya, 2023).