Nonlinear Redshift-Space Distortions in the Harmonic-space Galaxy Power Spectrum

TL;DR

This paper develops a formalism to accurately model nonlinear redshift-space distortions in the harmonic-space galaxy power spectrum, accounting for wide-angle effects and fingers-of-God, crucial for future high-resolution galaxy surveys.

Contribution

It introduces a general projection method for higher-order RSD terms into spherical harmonic space, including nonlinear effects like FoG, improving modeling accuracy for upcoming surveys.

Findings

Nonlinear RSD effects can be modeled as modifications to the radial window function.

Linear RSD enhances the harmonic-space power spectrum, but the effect diminishes on small scales.

FoG suppresses the power spectrum across all transverse scales for small radial bins.

Abstract

Future high spectroscopic resolution galaxy surveys will observe galaxies with nearly full-sky footprints. Modeling the galaxy clustering for these surveys, therefore, must include the wide-angle effect with narrow redshift binning. In particular, when the redshift-bin size is comparable to the typical peculiar velocity field, the nonlinear redshift-space distortion (RSD) effect becomes important. A naive projection of the Fourier-space RSD model to spherical harmonic space leads to diverging expressions. In this paper we present a general formalism of projecting the higher-order RSD terms into spherical harmonic space. We show that the nonlinear RSD effect, including the fingers-of-God (FoG), can be entirely attributed to a modification of the radial window function. We find that while linear RSD enhances the harmonic-space power spectrum, unlike the three-dimensional case, the enhancement decreases on small angular-scales. The fingers-of-God suppress the angular power spectrum on all transverse scales if the bin size is smaller than $\Delta r \lesssim \pi \sigma_u$; for example, the radial bin sizes corresponding to a spectral resolution $R=\lambda/\Delta \lambda$ of a few hundred satisfy the condition. We also provide the flat-sky approximation which reproduces the full calculation to sub-percent accuracy.