Systematics mitigation for catalogue-based angular power spectra

TL;DR

This paper introduces a formalism and methods for accurately measuring angular power spectra directly from catalogues, mitigating systematic biases and mode loss, and demonstrates its effectiveness on simulated and real data.

Contribution

It adapts the catalogue-based formalism to include template deprojection and a transfer function approach for bias mitigation, improving accuracy over existing methods.

Findings

The method effectively removes bias in simulated datasets.

It produces unbiased power spectra in various sampling scenarios.

Results are consistent with standard map-based methods on real data.

Abstract

Recent work has developed a formalism for computing angular power spectra directly from catalogues containing field values at discrete positions on the sky, thereby circumventing the need to create pixelised maps of the fields, as well as avoiding aliasing and finite-resolution effects. We adapt this formalism to incorporate template deprojection for mitigating systematic biases in the measured angular power spectra. We also introduce an alternative method of mitigating the `deprojection bias' - the loss of modes induced by deprojection - employing simple simulations to compute a transfer function. We find that this approach performs at least as well as existing methods, and is relatively insensitive to how well one can guess the true power spectrum of the observed field, except at the largest scales ($\ell \lesssim 3$). Additionally, we develop exact expressions for the bias introduced by deprojection in the shot-noise component, which further improves the accuracy of this approach. We test our formalism on simulated datasets, demonstrating its applicability both to discretely sampled fields, and to the special case of galaxy clustering, with the survey selection function defined in terms of a random catalogue or as a continuous sky map. After removing the bias in the shot noise and correcting for the remaining mode loss using a transfer function, our formalism produces unbiased measurements of the angular power spectrum in all scenarios tested here. Finally, we apply our formalism to real data and show it produces results consistent with the standard map-based pseudo-$C_\ell$ formalism. We implement our method in the public code NaMaster.