Reconstruction in Fourier space

TL;DR

This paper introduces a fast FFT-based iterative reconstruction algorithm for non-parallel redshift-space distortions, demonstrating improved convergence and accuracy over traditional methods using simulations and mock galaxy data.

Contribution

The authors develop a novel FFT-based iterative reconstruction method that effectively handles non-parallel RSD and outperforms configuration space approaches in estimating real-space displacements.

Findings

Converges in two iterations with RSD approximation for BOSS-like samples.

Outperforms configuration space methods in estimating displacement fields.

Lognormal transform benefits dense samples but less so for sparse galaxy distributions.

Abstract

We present a fast iterative FFT-based reconstruction algorithm that allows for non- parallel redshift-space distortions (RSD). We test our algorithm on both N-body dark matter simulations and mock distributions of galaxies designed to replicate galaxy survey conditions. We compare solenoidal and irrotational components of the redshift distortion and show that an approximation of this distortion leads to a better estimate of the real-space potential (and therefore faster convergence) than ignoring the RSD when estimating the displacement field. Our iterative reconstruction scheme converges in two iterations for the mock samples corresponding to BOSS CMASS DR11 when we start with an approximation of the RSD. The scheme takes six iterations when the initial estimate, measured from the redshift-space overdensity, has no RSD correction. Slower convergence would be expected for surveys covering a larger angle on the sky. We show that this FFT based method provides a better estimate of the real space displacement field than a configuration space method that uses finite difference routines to compute the potential for the same grid resolution. Finally we show that a lognormal transform of the overdensity, used as a proxy for the linear overdensity, is beneficial in estimating the full displacement field from a dense sample of tracers. However the lognormal transform of the overdensity does not perform well when estimating the displacements from sparser simulations with a more realistic galaxy density.