Euclid preparation: LXXXIII. The impact of redshift interlopers on the two-point correlation function analysis

Context. The Euclid galaxy survey is designed to measure the spectroscopic redshift of emission-line galaxies (ELGs) by identifying the Hα emission line in their slitless spectra. The efficacy of this approach crucially depends on the signal-to-noise ratio (S/N) of the line, as sometimes noise fluctuations in the spectrum continuum can be misidentified as Hα. In addition, other genuine strong emission lines can be mistaken for Hα, depending on the redshift of the source. Both effects lead to ambiguities in the redshift measurement that can result in catastrophic redshift errors and the inclusion of interloper galaxies in the sample. Aims. This paper forecasts the impact on the galaxy clustering analysis of the expected redshift errors in the Euclid spectroscopic sample. Specifically, it investigates the effect of the redshift interloper contamination on the galaxy two-point correlation function (2PCF) and, in turn, on the inferred growth rate of structure f8 and Alcock Paczynski (AP) parameters α and α. Methods. This work is based on the analysis of 1000 synthetic spectroscopic catalogues, the EuclidLargeMocks, which mimic the area and selection function of the Euclid Data Release 1 (DR1) sample. We estimated the 2PCF of contaminated catalogues and separated the different contributions, particularly those coming from galaxies with correctly measured redshift and from contaminants. We explored different models of increasing complexity to describe the measured 2PCF at a fixed cosmology, with the aim of identifying the most efficient model to reproduce the data. Finally, we performed a cosmological inference and evaluated the systematic error on the inferred f8, α, and α values associated with different models. Results. Our results demonstrate that a minimal modelling approach, which only accounts for an attenuation of the clustering signal regardless of the type of contaminants, is sufficient to recover the correct values of f8, α, and α at DR1. The accuracy and precision of the estimated AP parameters are largely insensitive to the presence of interlopers. The adoption of a minimal modelling induces a 1% 3% systematic error on the growth rate of structure estimation, depending on the considered redshift. However, this error remains smaller than the statistical error expected for the Euclid DR1 analysis.