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The X-ray emission from active galactic nucleus (AGN) is a major component ofextragalactic X-ray sky. In this paper, we use the X-ray luminosity function(XLF) and halo occupation distribution (HOD) formalism to construct a halomodel for the X-ray emission from AGNs. Verifying that the two inputs (XLF andHOD) are in agreement with each other, we compute the auto-correlation powerspectrum in the soft X-ray band (0.5-2 keV) due to the AGNs potentiallyresolved by eROSITA (extended ROentgen Survey with an Imaging Telescope Array)mission and explore the redshift and mass dependence of the power spectrum.Studying the relative contribution of the Poisson and the clustering terms tothe total power, we find that at multipoles $l\lesssim 1000$ (i.e. largescales), the clustering term is larger than the Poisson term. We also forecastthe potential of X-ray auto-correlation power spectrum and X-ray-lensingcross-correlation power spectrum using eROSITA and eROSITA-LSST (Large SynopticSurvey Telescope) surveys, respectively, to constrain the HOD parameters andtheir redshift evolution. In addition, we compute the power spectrum of theAGNs lying below the flux resolution limit of eROSITA, which is essential tounderstand in order to extract the X-ray signal from the hot diffuse gaspresent in galaxies and clusters.

Constraining the X-ray AGN halo occupation distribution: implications for eROSITA