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

In the context of the upcoming SRG/eROSITA survey, we present an N-body simulation-based mock catalogue for X-ray selected AGN samples. The model 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 joint X-ray -- optical extinction and classification model. We adopt a set of empirical spectral energy distributions to predict observed magnitudes in the UV, optical and NIR. With the latest eROSITA all sky survey sensitivity model, we create a high-fidelity full-sky mock catalogue of X-ray AGN. It predicts their distributions in right ascension, declination, redshift and fluxes. Using empirical medium resolution optical spectral templates and an exposure time calculator, we find that $1.1times10^6$ ($4times10^5$) fiber-hours are needed to follow-up spectroscopically from the ground the detected X-ray AGN with an optical magnitude $21<r<22.8$ ($22.8<r<25$) with a 4-m (8-m) class multi-object spectroscopic facility. We find that future clustering studies will measure the AGN 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 the baryon acoustic oscillation standard ruler will be measured using 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.