Comparing emission- and absorption-based gas-phase metallicities in GRB host galaxies at $z=2-4$ using JWST

Much of what is known of the chemical composition of the universe is based on emission line spectra from star forming galaxies. Emission-based inferences are, nevertheless, model-dependent and they are dominated by light from luminous star forming regions. An alternative and sensitive probe of the metallicity of galaxies is through absorption lines imprinted on the luminous afterglow spectra of long gamma ray bursts (GRBs) from neutral material within their host galaxy. We present results from a JWST/NIRSpec programme to investigate for the first time the relation between the metallicity of neutral gas probed in absorption by GRB afterglows and the metallicity of the star forming regions for the same host galaxy sample. Using an initial sample of eight GRB host galaxies at z=2.1-4.7, we find a tight relation between absorption and emission line metallicities when using the recently proposed $\hat{R}$ metallicity diagnostic (+/-0.2dex). This agreement implies a relatively chemically-homogeneous multi-phase interstellar medium, and indicates that absorption and emission line probes can be directly compared. However, the relation is less clear when using other diagnostics, such as R23 and R3. We also find possible evidence of an elevated N/O ratio in the host galaxy of GRB090323 at z=3.58, consistent with what has been seen in other $z>4$ galaxies. Ultimate confirmation of an enhanced N/O ratio and of the relation between absorption and emission line metallicities will require a more direct determination of the emission line metallicity via the detection of temperature-sensitive auroral lines in our GRB host galaxy sample.