  Finding and elucidating the properties of Lyman-continuum(LyC)-emitting
galaxies is an important step for our understanding of cosmic reionization.
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. We hence construct
one- and two-zone photoionization models accounting for the observed LyC
escape, which we compare to the observed emission line measurements. We find
that one-zone density-bounded photoionization models cannot reproduce the
emission lines of the LyC leakers because they systematically underpredict the
lines of species of low ionization potential, as [OI] and [SII]. 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 and escape fractions of the LyC emitters are well
reproduced. The [OI] excess, which is observed in some LyC leakers, can be
naturally explained in this model, e.g., by emission from low-ionization and
low-filling-factor gas. LyC emitters with a high escape fraction (fesc > 38%)
are deficient both in [OI]6300A and in [SII]6716,6731A. We also confirm that a
[SII] deficiency can be used to select LyC emitter candidates. 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. 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. These models provide a first step towards the use of optical emission
lines and their ratios as quantitative diagnostics of LyC escape from galaxies.

Astrophysics of Galaxies