Unbiased contaminant removal for 3D galaxy power spectrum measurements

TL;DR

This paper develops and compares techniques for removing contaminants from 3D galaxy power spectrum measurements, proposing a debiasing method for FKP estimates that avoids large matrix computations and improves accuracy.

Contribution

It introduces a new debiasing method for FKP measurements that does not require large matrix manipulations, enhancing the accuracy of contaminant removal in galaxy surveys.

Findings

Mode deprojection is equivalent to best-fit contaminant subtraction.

QML provides an optimal unbiased estimate but is computationally intensive.

The proposed debiasing method improves FKP estimates without large matrix calculations.

Abstract

We assess and develop techniques to remove contaminants when calculating the 3D galaxy power spectrum. We separate the process into three separate stages: (i) removing the contaminant signal, (ii) estimating the uncontaminated cosmological power spectrum, (iii) debiasing the resulting estimates. For (i), we show that removing the best-fit contaminant mode subtraction), and setting the contaminated components of the covariance to be infinite (mode deprojection) are mathematically equivalent. For (ii), performing a Quadratic Maximum Likelihood (QML) estimate after mode deprojection gives an optimal unbiased solution, although it requires the manipulation of large $N_{\rm mode}^2$ matrices ($N_{\rm mode}$ being the total number of modes)}, which is unfeasible for recent 3D galaxy surveys. Measuring a binned average of the modes for (ii) as proposed by \citet*[FKP]{Feldman} is faster and simpler, but is sub-optimal and gives rise to a biased solution. We present a method to debias the resulting FKP measurements that does not require any large matrix calculations. We argue that the sub-optimality of the FKP estimator compared with the QML estimator, caused by contaminants is less severe than that commonly ignored due to the survey window.