Validating the clustering predictions of empirical models with the FLAMINGO simulations

Context. Mock galaxy catalogues are essential for correctly interpreting current and future generations of galaxy surveys. Despite their significance in galaxy formation and cosmology, little to no work has been done to validate the predictions of these mocks for high-order clustering statistics. Aims. We compare the predicting power of the latest generation of empirical models used in the creation of mock galaxy catalogues: a 13-parameter Halo Occupation Distribution (HOD) and an extension of the SubHalo Abundance Matching technique (SHAMe). Methods. We build GalaxyEmu-Planck, an emulator that makes precise predictions for the two-point correlation function, galaxy-galaxy lensing (restricted to distances greater than 1 $h^{-1} {\rm Mpc}$ to avoid baryonic effects), and other high-order statistics resulting from the evaluation of SHAMe and HOD models. Results. We evaluate the precision of GalaxyEmu-Planck using two galaxy samples extracted from the FLAMINGO hydrodynamical simulation that mimic the properties of DESI-BGS and BOSS galaxies, finding that the emulator reproduces all the predicted statistics precisely. The HOD showed comparable performance when fitting galaxy clustering and galaxy-galaxy lensing. In contrast, the SHAMe model showed better predictions for higher-order statistics, especially regarding the galaxy assembly bias. We also tested the performance of the models after removing some of their extensions, finding that we can withdraw two of the HOD parameters without a loss of performance. Conclusions. The results of this paper validate the current generation of empirical models as a way to reproduce galaxy clustering, galaxy-galaxy lensing and other high-order statistics. The excellent performance of the SHAMe model with a small number of free parameters suggests that it is a valid method to extract cosmological constraints from galaxy clustering.