A Minimal Interpretation of the Galactic Cosmic-Ray Proton and Helium Spectra from GeV to PeV Energies

Abstract

High-precision measurements of the cosmic-ray (CR) proton and helium spectra have revealed significant deviations from a simple power law, characterized by multiple spectral features, including a hardening above $\sim$100~GeV, a broad excess in the multi-TeV range, and a pronounced structure at PeV energies. We propose a minimal phenomenological two-cosmic-ray-population framework that consistently accounts for the observed spectra of protons and helium across six decades in energy, with agreement at the level of $\sim 10 \%$ or better over most of the explored energy range. In this scenario, the spectral complexity arises from a transition between two Galactic CR populations in the 10~TeV-1~PeV energy range. The low-energy proton population exhibits a sharp cutoff at tens of TeV, while a second, higher-energy population emerges and dominates above 100~TeV, terminating with a smooth exponential cutoff at $\sim$6.5~PeV. The same two-component model applied to CR helium, with a slightly harder first component extending effectively to several hundred TeV and a second component that scales with the proton spectrum in magnetic rigidity, provides a consistent description of both the helium spectrum and the p/He ratio. This framework reproduces the main observed spectral features of CR protons and helium without invoking contributions from nearby sources or non-standard assumptions about CR acceleration or propagation. Recent gamma-ray observations of supernova remnants, star-forming regions, and microquasars offer plausible astrophysical sites for these two CR components.