Flat-Sky Pseudo-Cls Analysis for Weak Gravitational Lensing

TL;DR

This paper evaluates the accuracy of flat-sky Pseudo-Cl estimators for weak lensing power spectra, demonstrating they can recover full-sky convergence power within a few percent for surveys up to 1200 deg$^2$, but face challenges with biases in larger surveys.

Contribution

It introduces a calibration method for mask bias in flat-sky Pseudo-Cl analysis and assesses its effectiveness for different survey geometries and masks.

Findings

Unbiased power spectrum recovery within a few percent for surveys up to 1200 deg$^2$.

Small-area star masks can be accurately corrected, but checkerboard masks cause biases.

Flat-sky PCl analysis is suitable for current surveys but needs higher accuracy for Euclid-like surveys.

Abstract

We investigate the use of estimators of weak lensing power spectra based on a flat-sky implementation of the Pseudo-Cl (PCl) technique, where the masked shear field is transformed without regard for masked regions of sky. This masking mixes power, and E-convergence and B-modes. To study the accuracy of forward-modelling and full-sky power spectrum recovery we consider both large-area survey geometries, and small-scale masking due to stars and a checkerboard model for field-of-view gaps. The power spectrum for the large-area survey geometry is sparsely-sampled and highly oscillatory, which makes modelling problematic. Instead, we derive an overall calibration for large-area mask bias using simulated fields. The effects of small-area star masks can be accurately corrected for, while the checkerboard mask has oscillatory and spiky behaviour which leads to percent biases. Apodisation of the masked fields leads to increased biases and a loss of information. We find that we can construct an unbiased forward-model of the raw PCls, and recover the full-sky convergence power to within a few percent accuracy for both Gaussian and lognormal-distributed shear fields. Propagating this through to cosmological parameters using a Fisher-Matrix formalism, we find we can make unbiased estimates of parameters for surveys up to 1,200 deg$^2$ with 30 galaxies per arcmin$^2$, beyond which the percent biases become larger than the statistical accuracy. This implies a flat-sky PCl analysis is accurate for current surveys but a Euclid-like survey will require higher accuracy.