We compute synthetic optical and ultraviolet (UV) emission-line properties of galaxies in a full cosmological framework by coupling, in post-processing, new-generation nebular-emission models with high-resolution, cosmological zoom-in simulations of massive galaxies. Our self-consistent modelling accounts for nebular emission from young stars and accreting black holes (BHs). We investigate which optical- and UV-line diagnostic diagrams can best help to discern between the main ionizing sources, as traced by the ratio of BH accretion to star formation rates in model galaxies, over a wide range of redshifts. At low redshift, simulated star-forming galaxies, galaxies dominated by active galactic nuclei and composite galaxies are appropriately differentiated by standard selection criteria in the classical [OIII]$lambda$5007/H$beta$ versus [NII]$lambda$6584/H$alpha$ diagram. At redshifts $z gt 1$, however, this optical diagram fails to discriminate between active and inactive galaxies at metallicities below $0.5 Z_odot$. To robustly classify the ionizing radiation of such metal-poor galaxies, which dominate in the early Universe, we confirm 3 previous, and propose 11 novel diagnostic diagrams based on equivalent widths and luminosity ratios of UV emission lines, such as EW(OIII]$lambda$1663) versus OIII]$lambda$1663/HeII$lambda$1640, CIII]$lambda$1908/HeII$lambda$1640 versus OIII]$lambda$1663/HeII$lambda$1640, and CIV$lambda$1550/CIII]$lambda$1908 versus CIII]$lambda$1908/CII$lambda$2326. We formulate associated UV selection criteria and discuss some caveats of our results (e.g., uncertainties in the modelling of the HeII$lambda$1640 line). These UV diagnostic diagrams are potentially important for the interpretation of high-quality spectra of very distant galaxies to be gathered by next-generation telescopes, such as the James Webb Space Telescope.
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