MAMBO -- An empirical galaxy and AGN mock catalogue for the exploitation of future surveys

Aims. We present MAMBO, a flexible and efficient workflow to build empirical galaxy and Active Galactic Nuclei (AGN) mock catalogues that reproduce the physical and observational properties of these sources. Methods. We start from simulated dark matter (DM) haloes, to preserve the link with the cosmic web, and we populate them with galaxies and AGN using abundance matching techniques. We follow an empirical methodology, using stellar mass functions (SMF), host galaxy AGN mass functions and AGN accretion rate distribution functions studied at different redshifts to assign, among other properties, stellar masses, the fraction of quenched galaxies, or the AGN activity (demography, obscuration, multiwavelength emission, etc.). Results. As a proof test, we apply the method to a Millennium DM lightcone of 3.14 $\rm deg^2$ up to redshift $z=10$ and down to stellar masses $\mathcal{M} \gtrsim 10^{7.5} \, M_\odot$. We show that the AGN population from the mock lightcone here presented reproduces with good accuracy various observables, such as state-of-the-art luminosity functions in the X-ray up to $z \sim 7$ and in the ultraviolet up to $z \sim 5$, optical/NIR colour-colour diagrams, and narrow emission line diagnostic diagrams. Finally, we demonstrate how this catalogue can be used to make useful predictions for large surveys. Using \textit{Euclid} as a case example, we compute, among other forecasts, the expected surface densities of galaxies and AGN detectable in the \textit{Euclid} $H_{\rm E}$ band. We find that \textit{Euclid} might observe (on $H_{\rm E}$ only) about $10^{7}$ and $8 \times 10^{7}$ Type 1 and 2 AGN respectively, and $2 \times 10^{9}$ galaxies at the end of its 14 679 $\rm deg^2$ Wide survey, in good agreement with other published forecasts.