Decomposition of Spectra from Redshift Distortion Maps

TL;DR

This paper presents a new method to extract density and velocity spectra from redshift space maps, improving measurement accuracy up to certain scales and confirming error predictions with Fisher matrix analysis.

Contribution

The authors introduce an optimized technique for decomposing observed spectra into density and velocity components using angular dependence in Fourier space.

Findings

Velocity spectra measured up to k=0.07 h/Mpc

Measured variances align with Fisher matrix predictions

Detectability extends to k~0.1 h/Mpc with conservative bounds

Abstract

We develop an optimized technique to extract density--density and velocity--velocity spectra out of observed spectra in redshift space. The measured spectra of the distribution of halos from redshift distorted mock map are binned into 2--dimensional coordinates in Fourier space so as to be decomposed into both spectra using angular projection dependence. With the threshold limit introduced to minimize nonlinear suppression, the decomposed velocity--velocity spectra are reasonably well measured up to scale k=0.07 h/Mpc, and the measured variances using our method are consistent with errors predicted from a Fisher matrix analysis. The detectability is extendable to k\sim 0.1 h/Mpc with more conservative bounds at the cost of weakened constraint.