Building robust AGN mock catalogs to unveil black hole evolution and for survey planning

The statistical distributions of active galactic nuclei (AGN), i.e. accreting supermassive black holes (BHs), in mass, space and time, are controlled by a series of key properties, namely the BH-galaxy scaling relations, Eddington ratio distributions and fraction of active BHs (duty cycle). Shedding light on these properties yields strong constraints on the AGN triggering mechanisms whilst providing a clear baseline to create useful mock catalogues for the planning of large galaxy surveys. We here delineate a robust methodology to create mock AGN catalogs built on top of large N-body dark matter simulations via state-of-the-art semi-empirical models. We show that by using as independent tests the AGN clustering at fixed X-ray luminosity, galaxy stellar mass and BH mass, along with the fraction of AGN in groups and clusters, it is possible to significantly narrow down the choice in the relation between black hole mass and host galaxy stellar mass, the duty cycle, and the average Eddington ratio distribution, delivering well-suited constraints to guide cosmological models for the co-evolution of BHs and galaxies. Avoiding such a step-by-step methodology inevitably leads to strong degeneracies in the final mock catalogs, severely limiting their usefulness in understanding AGN evolution and in survey planning and testing.