Euclid: Photometric redshift calibration performance with the clustering-redshifts technique in the Flagship 2 simulation

Aims. The precision of cosmological constraints from imaging surveys hinges on an accurately estimated redshift distribution n(z) of the tomographic bins, especially their mean redshifts. We assess the effectiveness of the clustering-redshifts technique in constraining Euclid tomographic redshift bins to meet the target uncertainty of σ(⟨z⟩) < 0.002(1 + z). We inferred these mean redshifts from the small-scale angular clustering of Euclid galaxies, which were distributed into bins with spectroscopic samples localised in narrow redshift slices. Methods. We generated spectroscopic mocks from the Flagship2 simulation for the Baryon Oscillation Spectroscopic Survey (BOSS), the Dark Energy Spectroscopic Instrument (DESI), and the Euclid Near-Infrared Spectrometer and Photometer (NISP) spectroscopic survey. We evaluated and optimised the clustering-redshifts pipeline, and we introduced a new method for measuring the photometric galaxy bias (clustering), which is the primary limitation of this technique. Results. We have successfully constrained the means and standard deviations of the redshift distributions for all of the tomographic bins (with a maximum photometric redshift of 1.6). We achieved precision beyond the required thresholds. We have identified the main sources of bias, particularly the impact of the one-halo galaxy distribution, which imposed the minimal separation scale to be larger than 1.5 Mpc for evaluating cross-correlations. These results demonstrate that clustering-redshifts can meet the precision requirements for Euclid, and we highlighted several avenues for future improvements.