Is the low-energy tail of shock-accelerated protons responsible for over-ionized plasma in supernova remnants?

Over-ionized, recombining plasma is an emerging class of X-ray bright supernova remnants (SNRs). This unique thermal state where the ionization temperature (Tz) is significantly higher than the electron temperature (Tₑ) is not expected from the standard evolution model assuming a point explosion in a uniform interstellar medium, requiring a new scenario for the dynamical and thermal evolution. A recently proposed idea attributes the over-ionization state to additional ionization contribution from the low-energy tail of shock-accelerated protons. However, this new scenario has been left untested, especially from the atomic physics point of view. We report calculation results of the proton impact ionization rates of heavy-element ions in ejecta of SNRs. We conservatively estimate the requirement for accelerated protons, and find that their relative number density to thermal electrons needs to be higher than 5~(Tₑ/ 1~keV)% in order to explain the observed over-ionization degree at Tz/Tₑ ≥ 2 for K-shell emission. We conclude that the proton ionization scenario is not feasible because such a high abundance of accelerated protons is prohibited by the injection fraction from thermal to non-thermal energies, which is expected to be ~ 1% at largest.