The Three Hundred Project: A fast semi-analytic model emulator of hydrodynamical galaxy cluster simulations

Next-generation photometric and spectroscopic surveys will detect faint galaxies in massive clusters, advancing our understanding of galaxy formation in dense environments. Comparing these observations with theoretical models requires high-resolution cluster simulations. Hydrodynamical simulations resolve galaxy properties in halos, but face challenges simulating low-mass galaxies due to computational limitations. In contrast, dark matter-only (DMO) simulations can provide higher resolution but need models to populate subhalos with galaxies. In this work, we introduce a fast and efficient emulator of hydrodynamical cluster simulations, based on the semi-analytic models (SAMs) SAGE and SAG. The SAMs are calibrated using cluster galaxies from hydrodynamical simulations at intermediate resolution, ensuring consistency in stellar masses and luminosities across redshifts. These SAMs are then applied to DMO simulations from The Three Hundred Project at three resolutions. We show that the SAG model, unlike SAGE, better emulates galaxy properties even at the highest resolution. This improvement is due to the treatment of orphan galaxies, which contribute significantly to the total population. SAG enables the study of dwarf galaxies down to stellar masses of 10^7 solar masses at the highest resolution, an order of magnitude smaller than those in the hydrodynamical simulations, corresponding to approximately four magnitudes fainter. This shows that SAMs can be effectively calibrated to provide fast and accurate predictions of hydrodynamical simulations, offering an efficient alternative to explore galaxy populations in dense environments.