2021MNRAS.504..723Y

The [O III] 88 µm fine-structure emission line has been detected into the Epoch of Reionization (EoR) from star-forming galaxies at redshifts 6 < z <= 9 with ALMA. These measurements provide valuable information regarding the properties of the interstellar medium (ISM) in the highest redshift galaxies discovered thus far. The [O III] 88 µm line observations leave, however, a degeneracy between the gas density and metallicity in these systems. Here, we quantify the prospects for breaking this degeneracy using future ALMA observations of the [O III] 52 µm line. Among the current set of 10 [O III] 88 µm emitters at 6 < z <= 9, we forecast 52 µm detections (at 6σ) in SXDF-NB1006-2, B14-6566, J0217-0208, and J1211-0118 within on-source observing times of 2-10 h, provided their gas densities are larger than about n_H >= 10²-10³ cm^–3. Other targets generally require much longer integration times for a 6σ detection. Either successful detections of the 52 µm line or reliable upper limits will lead to significantly tighter constraints on ISM parameters. The forecasted improvements are as large as ∼3 dex in gas density and ∼1 dex in metallicity for some regions of parameter space. We suggest SXDF-NB1006-2 as a promising first target for 52 µm line measurements. We discuss how such measurements will help in understanding the mass-metallicity relationship during the EoR.