Counting pairs in Euclid. The self-calibration observation sequence and the impact of the interlopers on the two-point correlation function.

My PhD research has been carried out in the framework of the preparation activities of the ESA Euclid satellite mission, to which I have contributed in two different areas as a member of the Euclid Consortium. This thesis explores these two crucial aspects of the Euclid experiment: the calibration activities and the impact of observational systematics on the galaxy clustering analysis. In the first part of this thesis, I detail my contribution to the mission calibration activities. In this context, I collaborated with the Euclid Calibration Team to establish the best sequence of sky pointings needed for the Euclid satellite's self-calibration process. This step is crucial to ensure that the telescope's focal plane receives uniform illumination. While it was understood that a pseudo-random pointing pattern was necessary, there hadn't been systematic testing or optimization of such a sequence. I introduced criteria to evaluate different pointing sequences and identified the most effective one, which closely mimicked ideal pseudo-random sampling. Using an algorithm that I had developed during my master thesis, I validated this selected sequence's ability to accurately reconstruct illumination variations. The Euclid Calibration Team endorsed this sequence for operational use. Initial assessments during in-flight testing confirmed that it met the mission's requirements, indicating the successful functioning of the Euclid reconstruction algorithm. In the second part of this thesis, I report my investigations on the impact of interlopers on the galaxy clustering analysis. Interlopers are galaxies whose redshift was not correctly measured. Such sources represent contaminants in the Euclid spectroscopic sample, since they introduce distortions in the amplitude and shape of the measured statistics of the galaxy density field. Specifically, I analyzed the impact of an incorrect redshift determination for a fraction of the observed galaxies on the two-point correlation function, the statistics which quantifies the excess probability of finding pairs of galaxies at a certain separation with respect to a uniform distribution without clustering effects. I show three different analyses. First of all, I validated the exact model for the two-point correlation function in presence of different types of interlopers. In second place, I quantified the systematic effect induced by considering an incomplete parameterization, made of only those terms that we think will have a major impact on the measured signal. This study has highlighted how the simplified model used so far within the Euclid Consortium is not sufficient to correctly parameterize the measured two-point correlation function in presence of the expected types and fractions of interlopers. My analysis provides clear indications on the statistical significance of line interlopers' auto correlation signals when a galaxy sample is contaminated by about 10% of strong emission line galaxies. In order to quantify the relevance of the other potential contaminants, a larger number of simulations is required to increase the precision on the estimate of any systematic effect. Further simulations and analysis are also required to asses the impact of a poor modelling of the two-point correlation function on the measurements of the cosmological parameters.