Euclid: Calibrating photometric redshifts with spectroscopic cross-correlations

Abstract

Cosmological constraints from key probes of theEuclidimaging survey rely critically on the accurate determination of the true redshift distributions,n(z), of tomographic redshift bins. We determine whether the mean redshift, ⟨z⟩, of tenEuclidtomographic redshift bins can be calibrated to theEuclidtarget uncertainties ofσ(⟨z⟩) < 0.002 (1 + z) via cross-correlation, with spectroscopic samples akin to those from the Baryon Oscillation Spectroscopic Survey (BOSS), Dark Energy Spectroscopic Instrument (DESI), andEuclid’s NISP spectroscopic survey. We construct mockEuclidand spectroscopic galaxy samples from the Flagship simulation and measure small-scale clustering redshifts up to redshiftz < 1.8 with an algorithm that performs well on current galaxy survey data. The clustering measurements are then fitted to twon(z) models: one is the truen(z) with a free mean; the other a Gaussian process modified to be restricted to non-negative values. We show that ⟨z⟩ is measured in each tomographic redshift bin to an accuracy of order 0.01 or better. By measuring the clustering redshifts on subsets of the full Flagship area, we construct scaling relations that allow us to extrapolate the method performance to larger sky areas than are currently available in the mock. For the full expectedEuclid, BOSS, and DESI overlap region of approximately 6000 deg2, the uncertainties attainable by clustering redshifts exceeds theEuclidrequirement by at least a factor of three for bothn(z) models considered, although systematic biases limit the accuracy. Clustering redshifts are an extremely effective method for redshift calibration forEuclidif the sources of systematic biases can be determined and removed, or calibrated out with sufficiently realistic simulations. We outline possible future work, in particular an extension to higher redshifts with quasar reference samples.