[OIII] 88 μm over [NII] 122 μm line ratio as a function of metallicity. The colour shaded areas mark the range of ratios predicted by the CLOUDY models of Pereira-Santaella et al. (2017) with the same ionization parameter but different densities (circles n = 10 cm⁻³ and squares n = 10⁴ cm⁻³). The colour coding (grey, red, orange, yellow, and green) indicates the ionization parameter (log U = −4.0, −3.5, −3.0, −2.5, and −2.0, respectively). The solid horizontal purple line marks the observed ratio in SPT 0418−47 with the uncertainty range delimited by dashed lines. The thick part of the horizontal line indicates the allowed range of log U as derived from the continuum SED (Fig. 4).