Photometric redshift calibration with self-organising maps

Abstract

Accurate photometric redshift calibration is central to the robustness of all cosmology constraints from cosmic shear surveys. Analyses of the Kilo-Degree Survey (KiDS) re-weighted training samples from all overlapping spectroscopic surveys to provide a direct redshift calibration. Using self-organising maps we demonstrate that this spectroscopic compilation is sufficiently complete for KiDS, representing 99% of the effective 2D cosmic shear sample. We used the SOM to define a 100% represented “gold” cosmic shear sample, per tomographic bin. Using mock simulations of KiDS and the spectroscopic training set, we estimated the uncertainty on the SOM redshift calibration, and we find that photometric noise, sample variance, and spectroscopic selection effects (including redshift and magnitude incompleteness) induce a combined maximal scatter on the bias of the redshift distribution reconstruction (Δ⟨z⟩ = ⟨z⟩est − ⟨z⟩true) of σΔ⟨z⟩ ≤ 0.006 in all tomographic bins. Photometric noise and spectroscopic selection effects contribute equally to the observed scatter. We show that the SOM calibration is unbiased in the cases of noiseless photometry and perfectly representative spectroscopic datasets, as expected from theory. The inclusion of both photometric noise and spectroscopic selection effects in our mock data introduces a maximal bias of Δ⟨z⟩ = 0.013 ± 0.006, or Δ⟨z⟩ ≤ 0.025 at 97.% confidence, once quality flags have been applied to the SOM. The method presented here represents a significant improvement over the previously adopted direct redshift calibration implementation for KiDS, owing to its diagnostic and quality assurance capabilities. The implementation of this method in future cosmic shear studies will allow better diagnosis, examination, and mitigation of systematic biases in photometric redshift calibration.