Context. Finding and elucidating the properties of Lyman-continuum(LyC)-emitting galaxies is an important step in improving our understanding of cosmic reionization. Aims. Although the z ∼ 0.3 − 0.4 LyC emitters found recently show strong optical emission lines, no consistent quantitative photoionization model taking into account the escape of ionizing photons and inhomogenous interstellar medium (ISM) geometry of these galaxies has yet been constructed. Furthermore, it is unclear to what extent these emission lines can be used to distinguish LyC emitters. Methods. To address these questions we construct one- and two-zone photoionization models accounting for the observed LyC escape, which we compare to the observed emission line measurements. The main diagnostics used include lines of [O III], [O II], and [O I] plus sulfur lines ([S II], [S III]) and a nitrogen line ([N II]), which probe regions of different ionization in the ISM. Results. We find that single (one-zone) density-bounded photoionization models cannot reproduce the emission lines of the LyC leakers, as pointed out by earlier studies, because they systematically underpredict the lines of species of low ionization potential, such as [O I] and [S II]. Introducing a two-zone model, with differing ionization parameter and a variable covering fraction and where one of the zones is density-bounded, we show that the observed emission line ratios of the LyC emitters are well reproduced. Furthermore, our model yields LyC escape fractions, which are in fair agreement with the observations and independent measurements. The [O I] λ6300 excess, which is observed in some LyC leakers, can be naturally explained in this model, for example by emission from low-ionization and low-filling-factor gas. LyC emitters with a high escape fraction (fesc ≳ 38%) are deficient both in [O I] λ6300 and in [S II] λλ6716,6731. We also confirm that a [S II] λλ6716,6731 deficiency can be used to select LyC emitter candidates, as suggested earlier. Finally, we find indications for a possible dichotomy in terms of escape mechanisms for LyC photons between galaxies with relatively low (fesc ≲ 10%) and higher escape fractions. Conclusions. We conclude that two-zone photoionization models are sufficient and required to explain the observed emission line properties of z ∼ 0.3 − 0.4 LyC emitters. This is in agreement with UV absorption line studies, which also show the co-existence of regions with high hydrogen column density (i.e., no escape of ionizing photons) and density-bounded or very low column density regions responsible for the observed escape of LyC radiation. These simple but consistent models provide a first step towards the use of optical emission lines and their ratios as quantitative diagnostics of LyC escape from galaxies.
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