Electron-ion temperature ratio as a function of cosmic ray acceleration efficiency. The efficiency is defined here as the fraction w₂ of post-shock cosmic-ray pressure (assumed here to be characterised by an adiabatic index of γ_cr = 1.5) to the overall pressure. The cosmic-ray efficiency is linked to the Mach number at the sub-shock, which has been affected by the compression of the plasma in the cosmic-ray precursor. See Vink et al. (2010) and Vink & Yamazaki (2014) for details.