A Physical Relationship Between Electron-Proton Temperature   Equilibration and Mach Number in Fast Collisionless Shocks
  The analysis of Balmer-dominated optical spectra from non-radiative (adiabatic) SNRs has shown that the ratio of the electron to proton temperature temperature at the blast wave is close to unity at v_s <= 400 km/s, but declines sharply down to the minimum value of (m_e/m_p) dictated by the jump conditions at shock speeds exceeding 2000 km/s. We propose a physical model for the heating of electrons and ions in non-cosmic ray dominated, strong shocks (v_s > 400 km/s) wherein the electrons are heated by lower hybrid waves immediately ahead of the shock front. These waves arise naturally from the cosmic ray pressure gradient upstream from the shock. Our model predicts a nearly constant level of electron heating over a wide range of shock speeds, producing a relationship T_e/T_p ~ 1/v_s**2 (~ 1 /M**2) that is fully consistent with the observations. 
Parviz Ghavamian, J. Martin Laming and Cara E. Rakowski