The eROSITA X-ray luminosity function of active galactic nuclei

The X-ray luminosity function (XLF) of active galactic nuclei (AGN) provides an observational probe of the growth of supermassive black holes (SMBHs) across cosmic time. With its large survey grasp, Spectrum Roentgen Gamma (SRG)/eROSITA samples the luminosity--redshift plane with a depth--area balance complementary to pencil-beam surveys, providing the volume needed to detect rare luminous AGN, previously limited by small-number statistics. We measure the soft XLF, leveraging an eROSITA sample spanning approximately eight orders of magnitude in luminosity out to z 6. This enables us to study luminosity-dependent evolution with improved constraints, and to infer both the SMBH accretion history and optical/UV missed AGN population. We introduce a new redshift-dependent smoothly broken power-law parameterisation in which all XLF model parameters are allowed to evolve continuously with redshift. We find lower space densities for moderately and very luminous AGN at low redshift, while the abundance is higher than previously found at the highest redshifts. Comparisons to optical/UV quasar LFs converted to rest-frame 2!-!10, keV show that the UV-missed fraction decreases with luminosity, and, in the most luminous bin, increases with redshift. Integrating the XLF yields a black-hole accretion-rate density peaking at z 1.5, with the corresponding cumulative black-hole mass density indicating about80+11-23% obscured growth relative to locally-inferred BH mass estimates derived from scaling relations and missed by the soft X-ray selection of our sample. With this work, we release the eROSITA DR2 AGN catalogue, including counterparts and their redshift information. We then discuss how these results can inform future spectroscopic, photometric, and X-ray survey strategies aimed at improving AGN demographic constraints.