Different spectra of cosmic ray H, He and heavier nuclei escaping compact star clusters

TL;DR

This paper investigates cosmic ray acceleration at star cluster termination shocks, showing that helium nuclei have harder spectra than hydrogen due to environmental effects, but heavy nuclei are unlikely to significantly contribute to cosmic rays at Earth.

Contribution

It provides a detailed analysis of how proton energy losses and spallation reactions influence the spectra of escaping nuclei, highlighting the spectral differences between hydrogen and helium.

Findings

Helium nuclei have systematically harder spectra than hydrogen.

Heavy nuclei undergo severe spallation, resulting in hard, low-normalization spectra.

Heavy nuclei are unlikely to significantly contribute to cosmic rays at Earth.

Abstract

Cosmic ray acceleration at the termination shock of compact star clusters has recently received much attention, mainly because of the detection of gamma ray emission from some of such astrophysical sources. Here we focus on the acceleration of nuclei at the termination shock and we investigate the role played by proton energy losses and spallation reactions of nuclei, especially downstream of the shock. We show that for a reasonable choice of the mean gas density in the cavity excavated by the cluster wind, dominated by the presence of dense clouds, the spectrum of He nuclei escaping the bubble is systematically harder than the spectrum of hydrogen, in a manner that appears to be qualitatively consistent with the observed and yet unexplained phenomenon of discrepant hardening. We also find that, in this scenario, the spallation reactions of heavier nuclei are likely to be so severe that their spectra become very hard and with a low normalization, meaning that it is unlikely that heavy nuclei escaping star clusters can provide a sizeable contribution to the spectrum of cosmic rays at the Earth. Limitations and implications of this scenario are discussed.