Pixelization effects in cosmic shear angular power spectra

TL;DR

This paper investigates how pixelization affects cosmic shear power spectrum measurements, identifying biases, modeling their sources, and proposing methods to mitigate these effects for more accurate cosmological analyses.

Contribution

The study provides detailed models of pixelization biases, introduces improved estimators, and proposes mitigation techniques like interlacing and tailored window functions for cosmic shear surveys.

Findings

Residual biases can be reduced to percent level on small scales.

Interlacing scheme mitigates aliasing effects.

Custom pixel window functions effectively eliminate biases for band-limited spectra.

Abstract

We conduct a comprehensive study into the impact of pixelization on cosmic shear, uncovering several sources of bias in standard pseudo-$C_\ell$ estimators based on discrete catalogues. We derive models that can bring residual biases to the percent level on small scales. We elucidate the impact of aliasing and the varying shape of HEALPix pixels on power spectra and show how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose several improvements to the standard estimator and its modelling, based on the principle that source positions and weights are to be considered fixed. We show how empty pixels can be accounted for either by modifying the mixing matrices or applying correction factors that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and show that it can mitigate the effects of aliasing. We introduce bespoke pixel window functions adapted to the survey footprint and show that, for band-limited spectra, biases from using an isotropic window function can be effectively reduced to zero. This work partly intends to serve as a useful reference for pixel-related effects in angular power spectra, which are of relevance for ongoing and forthcoming lensing and clustering surveys.