MNRAS 000, 1–16 (2018) Preprint 30 July 2020 Compiled using MNRAS L A T E X style file v3.0 An analytic model for [O iii] fine structure emission from high redshift galaxies Shengqi Yang, 1⋆ Adam Lidz 2 1 Center for Cosmology and Particle Physics, Department of physics, New York University, 726 Broadway, New York, NY, 10003, U.S.A. 2 Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA Accepted XXX. Received YYY; in original form ZZZ ABSTRACT Recent ALMA measurements have revealed bright [O iii] 88 micron line emission from galax- ies during the Epoch of Reionization (EoR) at redshifts as large as z ∼ 9. We introduce an analytic model to help interpret these and other upcoming [O iii] 88 micron measurements. Our approach sums over the emission from discrete Str¨ omgren spheres and considers the total volume of ionized hydrogen in a galaxy of a given star-formation rate. We estimate the relative volume of doubly-ionized oxygen and ionized hydrogen and its dependence on the spectrum of ionizing photons. We then calculate the level populations of OIII ions in different fine-structure states for HII regions of specified parameters. In this simple model, a galaxy’s [O iii] 88 µm lu- minosity is determined by: the typical number density of free electrons in HII regions (n e ), the average metallicity of these regions (Z ), the rate of hydrogen ionizing photons emitted (Q HI ), and the shape of the ionizing spectrum. We cross-check our model by comparing it with de- tailed CLOUDY calculations, and find that it works to better than 15% accuracy across a broad range of parameter space. Applying our model to existing ALMA data at z ∼ 6 - 9, we derive lower bounds on the gas metallicity and upper bounds on the gas density in the HII regions of these galaxies. These limits vary considerably from galaxy to galaxy, with the tightest bounds indicating Z  0.5Z ⊙ and n H  50 cm −3 at 2 - σ confidence. Key words: galaxies: evolution – galaxies: high-redshift – submillimetre: ISM 1 INTRODUCTION Observations of far-infrared fine structure emission lines have en- abled spectrosopic redshift determinations for some of the highest redshift galaxies detected thus far at z ∼ 6 − 9 (e.g., Willott et al. (2015); Inoue et al. (2016); Marrone et al. (2018)). These measure- ments probe into the Epoch of Reionization (EoR) when early gen- erations of luminous sources form, emit ultraviolet light, and grad- ually photo-ionize neutral hydrogen in the intergalactic medium (IGM). Fine-structure emission lines provide valuable information regarding the interstellar medium (ISM) in star-forming galaxies and the new high redshift measurements have started to probe ISM properties back into the EoR. Among other quantities, fine-structure lines may be used to constrain the gas phase metallicities, gas den- sities, and the spectral shape of the ionizing radiation from early stellar populations. Thus far, ALMA observations have yielded a handful of detec- tions of [C ii] 158 µm and [O iii] 88 µm emission lines at z ∼ 6 − 9 (e.g., Pentericci et al. 2016; Laporte et al. 2017; Carniani et al. 2017; Smit et al. 2018; Carniani et al. 2018a,b; Hashimoto et al. 2018, 2019; Tamura et al. 2019; Harikane et al. 2019a; Novak et al. 2019). An interesting result from these measurements is that the galaxies’ ⋆ E-mail:sy1823@nyu.edu [O iii] luminosity is comparable or brighter than that of local galax- ies with similar star-formation rates (SFRs) (De Looze et al. 2014; Moriwaki et al. 2018). Further, the luminosity ratio LOIII /LCII ap- pears quite high, as much as ten times larger than in local galaxies (Harikane et al. 2019a). 1 Finally, the overall success rate of detect- ing the [O iii] 88 µm line via ALMA follow-up observations of pho- tometric z  6 galaxy candidates is quite high (see e.g. Harikane et al. 2019a and references therein). That is, the [O iii] 88 µm line has emerged as a valuable probe of reionization-era galaxy popula- tions, as anticipated by Inoue et al. (2014). Future ALMA observa- tions may also detect [O iii] 52 µm emission lines (e.g Jones et al. 2020), while the JWST will enable the detection of rest-frame opti- cal transitions from OIII ions into the EoR (Moriwaki et al. 2018). An emerging technique, complementary to the targeted ALMA observations, is line-intensity mapping (Kovetz et al. 2017). In this method, one measures the spatial fluctuations in the combined emis- sion from many individually unresolved galaxies. A number of sur- veys are underway to measure the [C ii] 158 µm emission from EoR era galaxies (see e.g. Kovetz et al. 2017 for a description of some 1 Recent work suggests, however, that the [C ii] emission is more extended than that in [O iii]; the current observations may consequently underesti- mate the [C ii] luminosity and overestimate the L OIII /L CII luminosity ra- tio (Carniani et al. 2020). c  2018 The Authors arXiv:2007.14439v1 [astro-ph.GA] 28 Jul 2020