Ionization and maximum energy of nuclei in shock acceleration theory

TL;DR

This paper investigates how ionization during shock acceleration in supernova remnants affects the maximum energy nuclei can reach, revealing that ionization reduces maximum energy and impacts cosmic ray spectrum predictions.

Contribution

It introduces the effect of photo-ionization during DSA, showing it limits maximum ion energies and alters the expected charge dependence in cosmic ray acceleration models.

Findings

Ionization reduces maximum achievable energy of nuclei in shock acceleration.

Maximum energy depends on effective charge during acceleration, not total nuclear charge.

Ultra-heavy elements beyond Iron are unlikely to reach high energies in this process.

Abstract

We study the acceleration of heavy nuclei at SNR shocks when the process of ionization is taken into account. Heavy atoms ($Z_N >$ few) in the interstellar medium which start the diffusive shock acceleration (DSA) are never fully ionized at the moment of injection. The ionization occurs during the acceleration process, when atoms already move relativistically. For typical environment around SNRs the photo-ionization due to the background galactic radiation dominates over Coulomb collisions. The main consequence of ionization is the reduction of the maximum energy which ions can achieve with respect to the standard result of the DSA. In fact the photo-ionization has a timescale comparable to the beginning of the Sedov-Taylor phase, hence the maximum energy is no more proportional to the nuclear charge, as predicted by standard DSA, but rather to the effective ions' charge during the acceleration process, which is smaller than the total nuclear charge $Z_N$. This result can have a direct consequence in the prediction of the knee structure of the cosmic ray spectrum. Moreover the acceleration of ultra-heavy elements beyond the Iron's maximum energy is very hard to achieve making unlikely their possible contribution to the cosmic ray spectrum in the transition region between Galactic and extragalactic component.