## Abstract

*Euclid*imaging 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 ten

*Euclid*tomographic redshift bins can be calibrated to the

*Euclid*target uncertainties of

*σ*(⟨

*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), and

*Euclid*’s NISP spectroscopic survey. We construct mock

*Euclid*and spectroscopic galaxy samples from the Flagship simulation and measure small-scale clustering redshifts up to redshift

*z*< 1.8 with an algorithm that performs well on current galaxy survey data. The clustering measurements are then fitted to two

*n*(

*z*) models: one is the true

*n*(

*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 expected

*Euclid*, BOSS, and DESI overlap region of approximately 6000 deg

^{2}, the uncertainties attainable by clustering redshifts exceeds the

*Euclid*requirement by at least a factor of three for both

*n*(

*z*) models considered, although systematic biases limit the accuracy. Clustering redshifts are an extremely effective method for redshift calibration for

*Euclid*if 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.

Original language | English |
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Article number | A149 |

Journal | Astronomy and Astrophysics |

Volume | 670 |

Number of pages | 14 |

ISSN | 0004-6361 |

DOIs | |

Publication status | Published - 2023 |

## Keywords

- Methods: data analysis
- Techniques: photometric
- Large-scale structure of Universe