Unbiased contaminant removal for 3D galaxy power spectrum measurements

Benedict Kalus, Will J. Percival, David Bacon, Lado Samushia

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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 N2mode matrices (Nmode 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.
Original languageEnglish
Pages (from-to)467-476
Number of pages10
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
Early online date15 Aug 2016
Publication statusPublished - 21 Nov 2016


  • astro-ph.CO
  • methods: statistical
  • cosmology: large-scale structure of Universe
  • RCUK
  • STFC
  • ST/K0090X/1
  • ST/N00180X/1


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