Photometric Redshift Calibration with Self Organising Maps

Accurate photometric redshift calibration is central to the robustness of all cosmology constraints from cosmic shear surveys. Analyses of the KiDS re-weighted training samples from all overlapping spectroscopic surveys to provide a direct redshift calibration. Using self-organising maps (SOMs) we demonstrate that this spectroscopic compilation is sufficiently complete for KiDS, representing $99\%$ of the effective 2D cosmic shear sample. We use 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 estimate the uncertainty on the SOM redshift calibration, and 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 ($Δ\langle z \rangle=\langle z \rangle_{\rm est}-\langle z \rangle_{\rm true}$) of $σ_{Δ\langle z \rangle} \leq 0.006$ in all tomographic bins. 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 $Δ\langle z \rangle =0.013\pm0.006$, or $Δ\langle z \rangle \leq 0.025$ at $97.5\%$ 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.

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