$L_X^{0.5-2}$/SFR as a function of galaxy gas-phase metallicity for the SFR-M_⋆-D stacks in the colour-coded with the He I/H α ratio. For comparison we overplot the empirical relations from Brorby et al. (2016) (dashed magenta line), Fornasini et al. (2020) (dashed brown line), Lehmer et al. (2021) (dashed black line), and Vulic et al. (2022) (dashed cyan line). The shaded region indicates the 1σ scatter around the latter fit. We also overlay the theoretical prediction from the XRB population synthesis best model from Fragos et al. (2013) (red dashed line).