Combining cosmic shear data with correlated photo-$z$ uncertainties: constraints from DESY1 and HSC-DR1

TL;DR

This paper presents a method to quantify and propagate correlated uncertainties in source redshift distributions for combined cosmic shear analyses, applied to DESY1 and HSC-DR1 data, improving constraints on cosmological parameters.

Contribution

The authors introduce an analytical approach to account for correlated redshift uncertainties in joint weak lensing analyses, enhancing the robustness of combined cosmological constraints.

Findings

Correlated redshift uncertainties have minimal impact on final cosmological constraints.

Combining DESY1 and HSC-DR1 improves the precision of the $S_8$ parameter by about 40%.

Residual systematic effects from photometric redshifts are negligible in Stage-IV datasets.

Abstract

An accurate calibration of the source redshift distribution $p(z)$ is a key aspect in the analysis of cosmic shear data. This, one way or another, requires the use of spectroscopic or high-quality photometric samples. However, the difficulty to obtain colour-complete spectroscopic samples matching the depth of weak lensing catalogs means that the analyses of different cosmic shear datasets often use the same samples for redshift calibration. This introduces a source of statistical and systematic uncertainty that is highly correlated across different weak lensing datasets, and which must be accurately characterised and propagated in order to obtain robust cosmological constraints from their combination. In this paper we introduce a method to quantify and propagate the uncertainties on the source redshift distribution in two different surveys sharing the same calibrating sample. The method is based on an approximate analytical marginalisation of the $p(z)$ statistical uncertainties and the correlated marginalisation of residual systematics. We apply this method to the combined analysis of cosmic shear data from the DESY1 data release and the HSC-DR1 data, using the COSMOS 30-band catalog as a common redshift calibration sample. We find that, although there is significant correlation in the uncertainties on the redshift distributions of both samples, this does not change the final constraints on cosmological parameters significantly. The same is true also for the impact of residual systematic uncertainties from the errors in the COSMOS 30-band photometric redshifts. Additionally, we show that these effects will still be negligible in Stage-IV datasets. Finally, the combination of DESY1 and HSC-DR1 allows us to constrain the ``clumpiness'' parameter to $S_8 = 0.768^{+0.021}_{-0.017}$. This corresponds to a $\sim\sqrt{2}$ improvement in uncertainties with respect to either DES or HSC alone.