Unbiased contaminant removal for 3D galaxy power spectrum measurements - Kalus, B.; Percival, W. J.; Bacon, D. J.; Samushia, Lado (My University, 2016)
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 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.
Citation: Kalus, B., Percival, W. J., Bacon, D. J., & Samushia, L. (2016). Unbiased contaminant removal for 3D galaxy power spectrum measurements. Monthly Notices of the Royal Astronomical Society, 463(1), 467-476. doi:10.1093/mnras/stw2008
Keywords: Methods: Statistical; Large-Scale Structure Of Universe; Redshift Surveys; Systematics; Astronomy & Astrophysics