Interpreting nebular emission lines in the high-redshift Universe

One of the most remarkable outcomes from \textit{JWST} has been the exquisite UV-optical spectroscopic data for galaxies in the high-redshift Universe (\(z \geq 5\)), enabling the use of various nebular emission lines to infer conditions of the interstellar medium. In this work, we assess the reliability of commonly used diagnostics for estimating the star formation rate (SFR), the ionising photon production efficiency (\(\xi_{\rm ion}\)), and the gas-phase oxygen abundance, focusing on dust corrections based on A\({\mathstrut}_{\rm V}\) (V-band attenuation) and the Balmer decrement. Using forward-modelled galaxy spectra from idealised toy models and the FLARES cosmological hydrodynamical simulations, we examine how variations in stellar populations and star-dust geometry affect these diagnostics. We find that the clumpy nature of FLARES galaxies lead to strong internal variation in age, metallicity and dust attenuation, biasing the inferred quantities. In FLARES the SFRD at the bright-end of the SFR function can be underestimated by as much as \(30\%\) compared to the true values. While the intrinsic \(\xi_{\rm ion}\) in FLARES is nearly constant with stellar mass, estimates derived from H\(\alpha\) or H\(\beta\) can be underestimated by more than 0.5 dex at high stellar masses (\(>10^{9.5}\) M\({\mathstrut}_{\odot}\)), introducing an artificial declining trend. Similarly, the dust-corrected mass-metallicity relation inferred from line ratios is significantly flatter than the intrinsic mass-weighted relation. These systematic offsets arise from the coupling between heterogeneous stellar populations and non-uniform star-dust geometry and depend on the diagnostic and the dust-correction method employed. No single dust-correction approach yields unbiased estimates of all quantities simultaneously, highlighting the need for forward modelling and comparisons in observed space for robust high-redshift inference.