THE IMPACT OF SIGNAL-TO-NOISE, REDSHIFT, AND ANGULAR RANGE ON THE BIAS OF WEAK LENSING 2-POINT FUNCTIONS

Abstract

Weak lensing data follow a naturally skewed distribution, implying the data vector most likely yielded from a survey will systematically fall below its mean. Although this effect is qualitatively known from CMB-analyses, correctly accounting for it in weak lensing is challenging, as a direct transfer of the CMB results is quantitatively incorrect. While a previous study (Sellentin et al. 2018) focused on the magnitude of this bias, we here focus on the frequency of this bias, its scaling with red-shift, and its impact on the signal-to-noise of a survey. Filtering weak lensing data with COSEBIs, we show that weak lensing likelihoods are skewed up until ℓ ≈ 100, whereas CMB-likelihoods Gaussianize already at ℓ ≈ 20. While COSEBI-compressed data on KiDS-and DES-like redshift-and angular ranges follow Gaussian distributions, we detect skewness at 6σ significance for half of a Euclid-or LSST-like data set, caused by the wider coverage and deeper reach of these surveys. Computing the signal-to-noise ratio per data point, we show that precisely the data points of highest signal-to-noise are the most biased. Over all redshifts, this bias affects at least 10% of a survey’s total signal-to-noise, at high redshifts up to 25%. The bias is accordingly expected to impact parameter inference. The bias can be handled by developing non-Gaussian likelihoods. Otherwise, it could be reduced by removing the data points of highest signal-to-noise.