Euclid: Photometric redshift calibration with self-organising maps

TL;DR

This paper evaluates the use of self-organising maps for calibrating photometric redshifts in the Euclid survey, demonstrating that photo-$z$ based tomography improves redshift bias control and minimally impacts cosmological parameter estimates.

Contribution

It introduces a novel application of self-organising maps for photometric redshift calibration and compares different redshift tomography methods using realistic mock samples.

Findings

Photo-$z$ based tomography meets Euclid's redshift bias requirement in most bins.

Spec-$z$ based tomography fails to meet the requirement in all bins.

Redshift bias impacts on cosmological parameters are minimal, below 0.3$\sigma$.

Abstract

The Euclid survey aims to trace the evolution of cosmic structures up to redshift $z$ $\sim$ 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-$z$s) suffer from systematic biases arising from various sources of uncertainty. To address these challenges, we utilised self-organising maps (SOMs) with mock samples resembling the Euclid Wide Survey (EWS), to validate Euclid's uncertainty requirement of $|\Delta\langle z \rangle| = \langle z_{\text{est}} \rangle - \langle z \rangle \leq 0.002 (1+z)$ per tomographic bin, assuming DR3-level data. 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-$z$s of the EWS-like sample yields superior results, with eight out of ten bins [$0 < z\leq 2.5$] 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-$z$s of individual galaxies rather than the commonly used mean spec-$z$ of SOM cells. To examine the impact on the expected biases for $\Omega_{\text{m}}$, $\sigma_{8}$, and $\Delta w_{0}$ 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 0.1$\sigma$ in the idealised scenario and below 0.3$\sigma$ in the more realistic case.