Elsner, F;
Leistedt, B;
Peiris, HV;
(2017)
Unbiased pseudo-Cℓ power spectrum estimation with mode projection.
Monthly Notices Of The Royal Astronomical Society
, 465
(2)
pp. 1847-1855.
10.1093/mnras/stw2752.
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Abstract
With the steadily improving sensitivity afforded by current and future galaxy surveys, a robust extraction of two-point correlation function measurements may become increasingly hampered by the presence of astrophysical foregrounds or observational systematics. The concept of mode projection has been introduced as a means to remove contaminants for which it is possible to construct a spatial map, reflecting the expected signal contribution. Owing to its computational efficiency compared to minimum-variance methods, the sub-optimal pseudo-Cℓ (PCL) power spectrum estimator is a popular tool for the analysis of high-resolution data sets. Here, we integrate mode projection into the framework of PCL power spectrum estimation. In contrast to results obtained with optimal estimators, we show that the uncorrected projection of template maps leads to biased power spectra. Based on analytical calculations, we find exact closed-form expressions for the expectation value of the bias and demonstrate that they can be recast in a form which allows a numerically efficient evaluation, preserving the favourable O(ℓ 3 max ) O(ℓmax3) time complexity of PCL estimator algorithms. Using simulated data sets, we assess the scaling of the bias with various analysis parameters and demonstrate that it can be reliably removed. We conclude that in combination with mode projection, PCL estimators allow for a fast and robust computation of power spectra in the presence of systematic effects – properties in high demand for the analysis of ongoing and future large-scale structure surveys.
| Type: | Article |
|---|---|
| Title: | Unbiased pseudo-Cℓ power spectrum estimation with mode projection |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/mnras/stw2752 |
| Publisher version: | https://doi.org/10.1093/mnras/stw2752 |
| Language: | English |
| Additional information: | This article has been accepted for publication in Monthly Notices Of The Royal Astronomical Society, copyright © The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. |
| Keywords: | methods: data analysis, methods: numerical, methods: statistical, cosmology: observations, large-scale structure of Universe |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1546391 |
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