Euclid: Photometric redshift calibration with self-organising maps

The Euclid large-scale weak-lensing survey aims to trace the evolution of cosmic structures up to redshift z ∼ 3 and beyond. Its success depends critically on obtaining highly accurate mean redshifts for ensembles of galaxies n(z) in all tomographic bins, essential for deriving robust cosmological constraints. However, photometric redshifts (photo-zs) are affected by systematic biases, arising from various sources of uncertainty and dominated by selection effects of the spectroscopic sample used for calibration. To address these challenges, we utilised self-organising maps (SOMs) with mock samples resembling the Euclid Wide Survey (EWS) from the Flagship2 simulation, to validate Euclid’s uncertainty requirement of |∆hzi| = hz_esti − hzi ≤ 0.002(1 + z) per tomographic bin, assuming DR3-level data. Consequently, we identify the most effective galaxy selection for our tomographic bins, while systematically examining the implementation of quality control cuts to reduce sources of uncertainty. In particular, we observe that defining the redshift tomography using the mean spectroscopic redshift (spec-z) per SOM cell, results in none of the ten tomographic redshift bins satisfying the requirement. In contrast, the redshift tomography on the photo-zs of the EWS-like sample yields superior results, with eight out of ten bins [0 < z ≤ 2.5] meeting the Euclid requirement. To enhance the realism of our study, we morph our calibration sample to mimic the C3R2 survey in incremental steps. In this context, a maximum of six out of ten bins meet the requirement, strongly advocating the adoption of a redshift tomography defined by the photo-zs of individual galaxies rather than the commonly used mean spec-z of SOM cells. To examine the impact on the expected biases for Ω_m, σ₈, and ∆w₀ measured by Euclid, we perform a Fisher forecast for cosmic shear only, based on our redshift uncertainties. Here, we find that even under an evaluation of the uncertainty where the impact of the redshift bias is substantial, most absolute biases remain below 0.1σ in the idealised scenario and below 0.3σ in the more realistic case.