Self-calibration and robust propagation of photometric redshift distribution uncertainties in weak gravitational lensing

TL;DR

This paper introduces a method to accurately propagate uncertainties in photometric redshift distributions into weak lensing cosmological inferences, enabling self-calibration and improved robustness of results.

Contribution

The authors develop a flexible Gaussian mixture model for redshift distributions and implement an analytic marginalisation, allowing self-calibration directly from cosmic shear data.

Findings

Constraints agree with previous KV450 analysis

Redshift distribution medians shift by up to 0.02

Intrinsic alignment amplitude decreases by about 10%

Abstract

We present a method that accurately propagates residual uncertainties in photometric redshift distributions into the cosmological inference from weak lensing measurements. The redshift distributions of tomographic redshift bins are parameterised using a flexible modified Gaussian mixture model. We fit this model to pre-calibrated redshift distributions and implement an analytic marginalisation over the potentially several hundred redshift nuisance parameters in the weak lensing likelihood, which is demonstrated to accurately recover the cosmological posterior. By iteratively fitting cosmological and nuisance parameters arising from the redshift distribution model, we perform a self-calibration of the redshift distributions via the tomographic cosmic shear measurements. Our method is applied to the third data release of the Kilo-Degree Survey combined with the VISTA Kilo-Degree Infrared Galaxy Survey (KV450). We find constraints on cosmological parameters that are in very good agreement with the fiducial KV450 cosmic shear analysis and investigate the effects of the more flexible model on the self-calibrated redshift distributions. We observe posterior shifts of the medians of the five tomographic redshift distributions of up to $\Delta z \approx 0.02$, which are however degenerate with an observed decrease of the amplitude of intrinsic galaxy alignments by about $10\%$.