Catalog-based pseudo-$C_\ell$s

TL;DR

This paper introduces a formalism to accurately estimate the angular power spectrum from catalog data with arbitrary source positions, effectively handling shot noise and avoiding pixelization and aliasing issues, validated on cosmic shear data.

Contribution

It extends the pseudo-$C_ll$ method to catalog-based data, providing an unbiased, noise-resistant estimator implemented in the NaMaster software.

Findings

The method accurately estimates power spectra from sparse catalogs.

It effectively subtracts shot noise analytically.

Validated on cosmic shear datasets.

Abstract

We present a formalism to extract the angular power spectrum of fields sampled at a finite number of points with arbitrary positions -- a common situation for several catalog-based astrophysical probes -- through a simple extension of the standard pseudo-$C_\ell$ algorithm. A key complication in this case is the need to handle the shot noise component of the associated discrete angular mask which, for sparse catalogs, can lead to strong coupling between very different angular scales. We show that this problem can be solved easily by estimating this contribution analytically and subtracting it. The resulting estimator is immune to small-scale pixelization effects and aliasing, and, more interestingly, unbiased against the contribution from measurement noise uncorrelated between different sources. We demonstrate the validity of the method in the context of cosmic shear datasets, and showcase its usage in the case of other spin-0 and spin-1 astrophysical fields of interest. We incorporate the method in the public $\texttt{NaMaster}$ code (https://github.com/LSSTDESC/NaMaster).