Euclid preparation. LXXVI. Simulating thousands of Euclid spectroscopic skies

We present two extensive sets of 3500+1000 simulations of dark matter haloes on the past light cone and two corresponding sets of simulated (mock) galaxy catalogues that represent the spectroscopic sample of Euclid. The simulations were produced with the latest version of the code Pinocchio and provide the largest public set of simulated skies. The mock galaxy catalogues were obtained by populating haloes with galaxies using an halo occupation distribution (HOD) model extracted from the Flagship galaxy catalogue provided by Euclid Collaboration. The Geppetto set of 3500 simulated skies was obtained by tiling a 1.2 h−1 Gpc box to cover a light cone whose sky footprint is a circle with a radius of 30◦ for an area of 2763 deg2 and a minimum halo mass of 1.5 × 1011 h−1 M⊙. The relatively small size of the box means that this set is unsuitable for measuring very large scales. The EuclidLargeBox set consists of 1000 simulations of 3.38 h−1 Gpc and has the same mass resolution and a footprint that covers half of the sky. It excludes the Milky Way zone of avoidance. From this, we produced a set of 1000 EuclidLargeMocks on the 30◦ radius footprint, whose comoving volume is fully contained in the simulation box. We validated the two sets of catalogues by analysing number densities, power spectra, and two-point correlation functions to show that the Flagship spectroscopic catalogue is consistent with being one of the realisations of the simulated sets. We noted small deviations, however, that are limited to the quadrupole at k > 0.2 hMpc−1. We infer the cosmological parameters from these catalogues and demonstrate that using one realisation of EuclidLargeMocks in place of the Flagship mock produces the same posteriors to within the expected shift given by the sample variance. These simulated skies will be used for the galaxy clustering analysis of the Euclid Data Release 1 (DR1), and an even larger set of simulations is planned for the next releases.