Optical Strong Line Ratios Cannot Distinguish Between Stellar Populations and Accreting Black Holes at High Ionization Parameters and Low Metallicities

High-redshift observations from JWST indicate that optical strong line ratios do not carry the same constraining power as they do at low redshifts. Critically, this prevents a separation between stellar- and black hole-driven ionizing radiation, thereby obscuring both active galactic nuclei demographics and star formation rates. To investigate this, we compute a large suite of photoionization models from Cloudy powered by stellar populations and accreting black holes over a large grid of ages, metallicities, initial mass functions, binarity, ionization parameters, densities, and black hole masses. We use these models to test three rest-frame optical strong line ratio diagnostics which have been designed to separate ionizing sources at low redshifts: the [NII]-BPT, VO87, and OHNO diagrams. We show that the position of a model in these diagrams is strongly driven by the ionization parameter (log U) and the gas-phase metallicity, often more so than the ionizing spectrum itself; in particular, there is significant overlap between stellar population and accreting black hole models at high log U and low Z. We show that the OHNO diagram is especially susceptible to large contamination of the AGN region defined at z=1 for stellar models with high log U and low Z, consistent with many observed JWST spectra at high redshift. We show that the optical line ratio diagnostics are most sensitive to the shape of the <54 eV ionizing continuum, and that the derived ionizing sources for a given set of optical strong line ratios can be highly degenerate. Finally, we demonstrate that very high ionization (>54 eV) emission lines that trace ionizing sources harder than normal stellar populations help to break the degeneracies present when using the strong line diagnostics alone, even in gas conditions consistent with those at high redshifts.