Unbiased contaminant removal for 3D galaxy power spectrum measurements

• Published in: Monthly notices of the Royal Astronomical Society Vol. 463; no. 1; pp. 467 - 476
• Main Authors: Kalus, B., Percival, W. J., Bacon, D. J., Samushia, L.
• Format: Journal Article
• Language: English
• Published: London Oxford University Press 21.11.2016; Royal Astronomical Society
• Subjects: Astronomy & Astrophysics; ASTRONOMY AND ASTROPHYSICS; Contaminants; Cosmology; Equivalence; Estimates; Estimating techniques; Estimators; Galaxies; large-scale structure of Universe; Mathematical analysis; Matrices (mathematics); Matrix; Maximum likelihood method; methods: statistical; Optimization; Spectrum analysis; Star & galaxy formation; Three dimensional imaging; methods: statistical; large-scale structure of Universe
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stw2008

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 and (iii) debiasing the resulting estimates. For (i), we show that removing the best-fitting 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 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 Feldman, Kaiser & Peacock (FKP) 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.