An empirical method for mitigating an excess up-scattering mass bias on the weak lensing mass estimates for shear-selected cluster samples

TL;DR

This paper presents an empirical Bayesian method to correct for the excess up-scattering mass bias in weak lensing cluster mass estimates, improving the accuracy of mass measurements in shear-selected cluster samples.

Contribution

The authors develop and validate a novel empirical correction technique using Bayesian statistics to mitigate the excess up-scattering bias in weak lensing mass estimates.

Findings

The correction method reduces mass bias to within 10% of true values.

Standard $$ analysis provides correct confidence intervals but biased mass estimates.

Application to real cluster data yields bias-corrected mass estimates.

Abstract

An excess up-scattering mass bias on a weak lensing cluster mass estimate is a statistical bias that an observed weak lensing mass ($M_{\rm obs}$) of a cluster of galaxies is, in a statistical sense, larger than its true mass ($M_{\rm true}$) because of a higher chance of up-scattering than that of down-scattering due to random noises in a weak lensing cluster shear profile. This non-symmetric scattering probability is caused by a monotonically decreasing cluster mass function with increasing mass. We examine this bias (defined by $b=M_{\rm obs}/M_{\rm true}$) in weak lensing shear-selected clusters, and present an empirical method for mitigating it. In so doing, we perform the standard weak lensing mass estimate of realistic mock clusters, and find that the weak lensing mass estimate based on the standard $\chi^2$ analysis gives a statistically correct confidence intervals, but resulting best-fitting masses are biased high on average. Our correction method uses the framework of the standard Bayesian statistics with the prior of the probability distribution of the cluster mass and concentration parameter from recent empirical models. We test our correction method using mock weak lensing clusters, and find that the method works well with resulting corrected $M_{\rm obs}$-bin averaged mass biases being close to unity within $\sim 10$ percent. We applied the correction method to weak lensing shear-selected cluster sample of Hamana et al. (2020), and present bias-corrected weak lensing cluster masses.