2dFLenS and KiDS: Determining source redshift distributions with cross-correlations

TL;DR

This paper introduces a quadratic estimator method to determine galaxy redshift distributions from cross-correlations, improving accuracy in photometric surveys by combining spectroscopic data and Gaussian process modeling.

Contribution

It develops a novel quadratic estimator for redshift distributions that extends previous methods and demonstrates its robustness with simulations and real data.

Findings

Successfully constrained redshift distributions in KiDS survey

Validated the estimator with mock catalogues from N-body simulations

Compared results with other redshift inference techniques

Abstract

We develop a statistical estimator to infer the redshift probability distribution of a photometric sample of galaxies from its angular cross-correlation in redshift bins with an overlapping spectroscopic sample. This estimator is a minimum variance weighted quadratic function of the data: a quadratic estimator. This extends and modifies the methodology presented by McQuinn & White (2013). The derived source redshift distribution is degenerate with the source galaxy bias, which must be constrained via additional assumptions. We apply this estimator to constrain source galaxy redshift distributions in the Kilo-Degree imaging survey through cross-correlation with the spectroscopic 2-degree Field Lensing Survey, presenting results first as a binned step-wise distribution in the range z < 0.8, and then building a continuous distribution using a Gaussian process model. We demonstrate the robustness of our methodology using mock catalogues constructed from N-body simulations, and comparisons with other techniques for inferring the redshift distribution.