A theoretical investigation of far-infrared fine structure lines at z > 6 and of the origin of the [O III]_88 μm/[C II]_158 μm enhancement

¹ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
² Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Box 43 SE-221 00 Lund, Sweden

^⋆ Corresponding author: camilla.nyhagen@fysik.lu.se

Received: 23 October 2024
Accepted: 17 July 2025

Abstract

The far-infrared (FIR) fine structure lines [C II]_158 μm, [O III]_88 μm, [N II]_122 μm, and [N III]_57 μm are excellent tools for probing the physical conditions of the interstellar medium (ISM). The [O III]_88 μm/[C II]_158 μm and [O III]_88 μm/[N II]_122 μm luminosity ratios have shown to be promising tracers of the ionisation state and gas-phase metallicity of the ISM. Observations of galaxies at redshift z > 6 show unusually high [O III]_88 μm/[C II]_158 μm luminosity ratios compared to local sources. The origin of the enhanced ratios has been investigated in the literature with different theoretical modelling approaches. However, no model has to date successfully managed to match the observed emission from both [O III]_88 μm and [C II]_158 μm, as well as their ratio. For this study we used CLOUDY to model the [C II]_158 μm, [O III]_88 μm, [N II]_122 μm, and [N III]_57 μm emission lines of PONOS, a high-resolution (m_gas = 883.4 M_⊙) cosmological zoom-in simulation of a galaxy at redshift z = 6.5, which is post-processed using KRAMSES-RT. We modify carbon, nitrogen, and oxygen abundances in our CLOUDY models to obtain C/O and N/O abundance ratios respectively lower and higher than solar, more in line with recent high-z observational constraints. We find [O III]_88 μm/[C II]_158 μm luminosity ratios that are a factor of ∼5 higher compared to models assuming solar abundances. Additionally, we find an overall better agreement of the simulation with high-z observational constraints of the [C II]_158 μm-SFR and [O III]_88 μm-SFR relations. This shows that a lower C/O abundance ratio is essential to reproduce the enhanced [O III]_88 μm/[C II]_158 μm luminosity ratios observed at z > 6. By assuming a super-solar N/O ratio, motivated by recent z > 6 JWST observations, our models yield an [O III]_88 μm/[N II]_122 μm ratio of 1.3, which, according to current theoretical models, would be more appropriate for a galaxy with a lower ionisation parameter than the one we estimated for PONOS. Most current simulations adopt solar abundance patterns that are not adequate for recently observed high-z predictions. Our results showcase the importance of theoretical modelling efforts, coupled with high-resolution zoom-in simulations, and with parallel multi-tracer observations to understand the physical and chemical conditions of the ISM at z > 6.