Lagrangian approach to super-sample effects on biased tracers at field level: galaxy density fields and intrinsic alignments

TL;DR

This paper develops a Lagrangian perturbation theory-based formalism to analyze how super-sample modes influence biased tracers like galaxy density and intrinsic alignments, affecting cosmological measurements.

Contribution

It introduces a new formalism to compute the response of biased tracers to super-sample modes at the field level, extending previous power spectrum response methods.

Findings

Reproduces known power spectrum responses to super-sample modes.

Derives the field response of galaxy/halo shape bias to super-sample modes.

Discusses impacts on covariance of intrinsic alignment power spectra.

Abstract

It has been recognized that the observables of large-scale structure (LSS) is susceptible to long-wavelength density and tidal fluctuations whose wavelengths exceed the accessible scale of a finite-volume observation, referred to as the super-sample modes. The super-sample modes modulate the growth and expansion rate of local structures, thus affecting the cosmological information encoded in the statistics of galaxy clustering data. In this paper, based on the Lagrangian perturbation theory, we develop a new formalism to systematically compute the response of a biased tracer of LSS, which is expressed perturbatively in terms of the matter density field of sub-survey modes, to the super-sample modes at the field level. The formalism presented here reproduces the power spectrum responses that have been previously derived, and provides an alternative way to compute statistical quantities with super-sample modes. As an application, we consider the statistics of the intrinsic alignments of galaxies and halos, and derive the field response of the galaxy/halo shape bias to the super-sample modes. Possible impacts of the long-mode contributions on the covariance of the three-dimensional power spectra of the intrinsic alignment are also discussed, and the signal-to-noise ratios are estimated.