tokens: C iii ] upper limit). Three similar systems from Berg et al. ( 2016 ) with COS detections of all four lines are plotted as blue squares. The ratios of O iii ]/He ii are inconsistent with any AGN models – all have more flux in O iii ] 1666 than in He ii 1640. The deep ESI spectra we obtained also provide constraints on the shape of the ionizing spectrum between 10 and 50 eV. The ratio of flux between the nebular He ii and H recombination lines is closely related to the ratio of He + -ionizing (228 Å) to H-ionizing photons (912 Å). The optical He ii λ4686 and H β lines are ideal for avoiding the uncertainties introduced by dust and aperture corrections. Our ESI spectra easily resolve the nebular and broad components of the He ii line (see Fig. 5 ) and thus allow a robust simultaneous fit to both, to which H β in the same spectrum can be compared (Section 3.4 and Table 10 ). The (dust-corrected) ratio of nebular He ii /H β is plotted as a function of gas-phase metallicity in Fig. 12 . In addition to the sample presented here, we plot the published measurements of this ratio for the local WR galaxies analysed by López-Sánchez Esteban ( 2010 ). The axis on the right displays the ratio Q(He + )/Q(H) assuming ideal Case B recombination proceeds for both H and He + (and 10 4 K, 10 2 cm −3 ; Hummer Storey 1987 ; Draine 2011 ). The Case B predictions should be treated with care as collisional excitation and low ionization parameters can result in deviations from this assumption (e.g. Stasińska Izotov 2001 ; Raiter, Schaerer Fosbury 2010 ), but demonstrate clearly the effect of changing the ionizing spectrum slope at the He + ionizing edge. Figure 12. Measured nebular He ii 4686/H β values (a proxy for the ratio of He + -ionizing to H-ionizing photons) versus gas-phase metallicity. Both our galaxies (blue circles, backed by red squares if nebular C iv was detected) and the WR galaxies presented by López-Sánchez Esteban ( 2010 ) are presented. The right axis indicates the corresponding Q(He + )/Q(H) assuming Case B recombination for both species. Both observational samples show a sharp transition with metallicity, with substantially larger ratios and harder spectra below 12 + log O/H ∼ 8. The nebular He ii /H β ratio reveals a sharp transition in the ionizing spectrum with decreasing metallicity. The maximum value of He ii /H β increases as the gas-phase metallicity decreases, with a marked upturn in this envelope around 12 + log O/H ∼ 8.0–8.2. Systems below 12 + log O/H 8.2 (Z ⊙ /3) reach relative nebular He ii fluxes nearly 10 times higher than those above this metallicity. This implies an order of magnitude increase in Q(He + )/Q(HI) as the metallicity of a young stellar population is decreased from Z ⊙ to Z ⊙ /10. A similar trend towards higher He ii /H β below 12 + log O/H 8.0 was found in the full sample of SDSS spectra analysed by Brinchmann et al. ( 2008b ) and Shirazi Brinchmann ( 2012 ), though we find a far more pronounced transition. This may
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