Predicted relative emission line intensity ratios of nebular He II λ4686 (top) and [Ne V]λ3426 (bottom) as a function of L_X/SFR for different SEDs. Each colour represents a different X-ray model. The horizontal grey area shows the typical range of the observed He II line intensity, when detected. The vertical dashed line indicates the L_X/SFR value of our ‘base model’. The dispersion in each SED model is due to changes in the ionisation parameter. It can be seen that an increase in the X-ray component produces stronger He II emission, overlapping with the observational area for L_X/SFR ≃ 10⁴⁰ − 10⁴¹ erg s⁻¹/(M_⊙ yr⁻¹), depending on the adopted ULX SED. For comparison, the value for the LEB models are overplotted, showing that the LEB SED can reproduce the observed He II strength. In approximately two-thirds of the galaxies, HeII emission is not detected with relative intensities below I(4686)/I(Hβ) ∼ (2−3) × 10⁻³. The models with L_X/SFR <  10⁴⁰ erg s⁻¹/(M_⊙ yr⁻¹) do not produce significant [NeV] emission (i.e. I([NeV])/I(Hβ) < 10⁻⁴), and they are therefore not included.