Testing KiDS cross-correlation redshifts with simulations

¹ Ruhr-University Bochum, Astronomical Institute, German Centre for Cosmological Lensing, Universitätsstr. 150, 44801 Bochum, Germany
e-mail: jlvdb@astro.rub.de
² Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
³ Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA
⁴ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia
⁵ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁷ Leiden Observatory, Leiden University, PO Box 9513, 2300RA Leiden, The Netherlands

Received: 3 July 2020
Accepted: 17 August 2020

Abstract

Measuring cosmic shear in wide-field imaging surveys requires accurate knowledge of the redshift distribution of all sources. The clustering-redshift technique exploits the angular cross-correlation of a target galaxy sample with unknown redshifts and a reference sample with known redshifts. It represents an attractive alternative to colour-based methods of redshift calibration. Here we test the performance of such clustering redshift measurements using mock catalogues that resemble the Kilo-Degree Survey (KiDS). These mocks are created from the MICE simulation and closely mimic the properties of the KiDS source sample and the overlapping spectroscopic reference samples. We quantify the performance of the clustering redshifts by comparing the cross-correlation results with the true redshift distributions in each of the five KiDS photometric redshift bins. Such a comparison to an informative model is necessary due to the incompleteness of the reference samples at high redshifts. Clustering mean redshifts are unbiased at |Δz|< 0.006 under these conditions. The redshift evolution of the galaxy bias of the reference and target samples represents one of the most important systematic errors when estimating clustering redshifts. It can be reliably mitigated at this level of precision using auto-correlation measurements and self-consistency relations, and will not become a dominant source of systematic error until the arrival of Stage-IV cosmic shear surveys. Using redshift distributions from a direct colour-based estimate instead of the true redshift distributions as a model for comparison with the clustering redshifts increases the biases in the mean to up to |Δz|∼0.04. This indicates that the interpretation of clustering redshifts in real-world applications will require more sophisticated (parameterised) models of the redshift distribution in the future. If such better models are available, the clustering-redshift technique promises to be a highly complementary alternative to other methods of redshift calibration.