Active Galactic Nuclei and their Large-scale Structure: an eROSITA mock catalogue

In the context of the upcoming SRG/eROSITA survey, we present a methodology to construct mock catalogues for X-ray selected AGN samples based on dark matter only N-body simulations. We create a model that reproduces the observed hard X-ray AGN luminosity function (XLF) and the soft X-ray logN-logS from redshift 0 to 6. The XLF is reproduced to within $\pm5\%$ and the logN-logS to within $\pm20\%$. We develop a model of extinction and AGN classification in both the X-ray and optical bands. We predict observed AGN magnitudes in the UV optical and NIR bands by adopting a set of empirical spectral energy distributions. We imprint the latest eROSITA all sky survey sensitivity model to create a high fidelity full-sky mock catalogue, predicting the expected distribution of X-ray AGN in right ascension, declination, redshift and flux (X-ray and optical). Using empirical medium resolution optical spectral templates and an exposure time calculator, we find that $1.2\times10^6$ ($1.1\times10^6$) fiber-hours are needed to follow-up spectroscopically from the ground all of the detected X-ray AGN with a 4-m (8-m) class multi-object spectroscopic facility. We find that future clustering studies will measure the bias to the percent level at redshift $z<1.2$ and should discriminate possible scenarios of galaxy-AGN co-evolution. We predict the accuracy to which it will be possible to measure the baryon acoustic oscillation standard ruler with X-ray AGN: better than 3\% for AGN between redshift 0.5 to 3 and better than 1\% using the Ly$\alpha$ forest of X-ray QSOs discovered between redshift 2 and 3. eROSITA will provide an outstanding set of targets for future galaxy evolution and cosmological studies.