Interpreting nebular emission lines in the high-redshift Universe

TL;DR

High-redshift galaxies probed by JWST yield nebular emission lines that constrain SFR, $ξ_{\rm ion}$, and metallicity, but the reliability of these diagnostics at $z \ge 5$ is unclear. The authors use forward modelling with toy galaxies and FLARES simulations to quantify biases caused by varying stellar populations and non-uniform star–dust geometry. They find that no single dust-correction approach yields unbiased results for all quantities; SFR, $ξ_{\rm ion}$, and the mass-metallicity relation can be systematically distorted, and biases depend on the diagnostic and dust-correction method. They advocate forward modelling and observable-space comparisons for robust high-redshift inferences and discuss future directions including FIR lines and spatially resolved observations.

Abstract

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 ($ξ_{\rm ion}$), and the gas-phase oxygen abundance, focusing on dust corrections based on A$_{\rm V}$ (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 $ξ_{\rm ion}$ in FLARES is nearly constant with stellar mass, estimates derived from H$α$ or H$β$ can be underestimated by more than 0.5 dex at high stellar masses ($>10^{9.5}$ M$_{\odot}$), 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.

Figures (19)

• Figure 1: The star formation and metal enrichment history of the 4 toy model galaxies.
• Figure 2: Top: The total intrinsic (black) and the dust-attenuated (for different spread in the dust attenuation, in coloured) SEDs of the 'Varying only A$_{\rm V}$' model galaxy, truncated to $0.1-1$ µm. Bottom: Attenuation curves of the resultant galaxy when varying the spread in the dust attenuation across the different star-forming clumps. We also show the power-law extinction curve (slope $=-1$) that was used for each stellar clumps, as well as the SMC and Calzetti (for slope$=0,0.5$) attenuation curve.
• Figure 3: Fraction of the recovered SFR after correcting for dust obscuration for the different toy galaxies in the model. The different markers denote the different models, with the different colours denoting the spread in the obscuration along the line-of-sight to the different stellar clumps within the galaxy. The filled and open markers denote the SFR fraction recovered using the A$_{\rm V}$ method and the Balmer decrement method respectively. It is easier to follow the plot by concentrating on the same colour and shape (along the same A$_{\rm V}$); one can see the pattern that the A$_{\rm V}$ method recovers a higher fraction of the SFR, while the Balmer decrement method recovers a lower fraction.
• Figure 4: The different panel shows the star formation rate function for the galaxies in FLARES using different dust corrections for $z\in[5,10]$. We also plot the observed and intrinsic SFRF. The black scatter points with the errorbars are the densities taken directly from the simulation, shown for comparing to the Schechter fit. We also plot the SFR derived by directly summing up the mass of stars formed in the last 10 Myr, denoted as 'SFR (10 Myr)'. We do not plot the corresponding Schechter fit for this.
• Figure 5: The recovered SFRD fraction for FLARES galaxies using different dust corrections for $z\in [5,10]$. We also plot the unobscured fraction and SFR (10 Myr) for comparison. The shaded region indicate the $1-\sigma$ scatter associated with the fit obtained by sampling the covariance matrix of the fit.