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 $1.1\times10^6$ ($4\times10^5$) 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.
