Fast Estimators for Redshift-Space Clustering

TL;DR

This paper introduces fast, FFT-based estimators for redshift-space galaxy clustering statistics, enabling efficient computation of power spectrum and bispectrum multipoles crucial for cosmological analyses.

Contribution

The authors develop and validate computationally efficient estimators for power spectrum and bispectrum multipoles in redshift space using FFTs, improving analysis speed for large surveys.

Findings

Estimators are computationally efficient, taking minutes for large datasets.

The method accurately measures power spectrum and bispectrum multipoles.

Enables covariance matrix computation from many mock realizations.

Abstract

Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only Fast Fourier Transforms (FFTs) of the overdensity field multipoles for a given survey geometry, compute the power spectrum monopole, quadrupole and hexadecapole, and generalize such estimators to the bispectrum. Using realistic mock catalogs we compare the signal to noise of two estimators for the power spectrum hexadecapole that require different number of FFTs and measure the bispectrum monopole, quadrupole and hexadecapole. The resulting algorithm is very efficient, e.g. for the BOSS survey requires about three minutes for $\ell=0,2,4$ power spectra for scales up to $k=0.3~h/$Mpc and about fifteen additional minutes for $\ell=0,2,4$ bispectra for all scales and triangle shapes up to $k=0.2~h/$Mpc on a single core. The speed of these estimators is essential as it makes possible to compute covariance matrices from large number of realizations of mock catalogs with realistic survey characteristics, and paves the way for improved constrains of gravity on cosmological scales, inflation and galaxy bias.