Charge-dependent spectral softenings of primary cosmic-rays from proton to iron below the knee

Abstract

In most particle acceleration mechanisms, the maximum energy of the cosmic rays can achieve is charge dependent. However, the observational verification of such a fundamental relation is still lack due to the difficulty of measuring the spectra of individual particles from one (kind of) source(s) up to very high energies. This work reports direct measurements of the carbon, oxygen, and iron spectra from ~ 20 gigavolts to ~ 100 teravolts (~ 60 teravolts for iron) with 9 years of on-orbit data collected by the Dark Matter Particle Explorer (DAMPE). Distinct spectral softenings have been directly detected in these spectra for the first time. Combined with the updated proton and helium spectra, the spectral softening appears universally at a rigidity of ~ 15 teravolts. A nuclei mass dependent softening is rejected at a confidence level of > 99.999%. Taking into account the correlated structures at similar energies in the large-scale anisotropies of cosmic rays, one of the most natural interpretations of the spectral structures is the presence of a nearby cosmic ray source. In this case, the softening energies correspond to the acceleration upper limits of such a source, forming the so-called Peters cycle of the spectra. The results thus offer observational verification of the long-standing prediction of the charge-dependent energy limit of cosmic ray acceleration.

Figures (6)

• Figure 1: DAMPE measured rigidity spectra (red dots) of carbon, oxygen, and iron, together with the updated results of protons and helium, weighted by $R^{2.6}$. The results from AMS-02 AMS:2017seoAMS:2021lxcAMS:2021nhj, CALET Adriani:2020wygCALET:2021fksCALET:2022vroCALET:2023nif, and ISS-CREAM Choi:2022aht are overplotted for comparison.
• Figure 2: The break energy of the softening divided by $Z$ (left) or $A$ (right) as a function of particle charge for different nuclear species. The shaded regions represent the average softening energies of the particles heavier than proton. The softening energies are well proportional to the particle charge rather than the particle mass.
• Figure 3: Comparison of DAMPE proton (top-left panel) and oxygen (top-right panel) fluxes with the predictions of the two-component model, and the predicted amplitudes (bottom-left panel) and phases (bottom-right panel) of the dipole anisotropies. References of the anisotropy data are: ARGO-YBJ ARGO-YBJ:2018zoa, Baksan Alekseenko:2009ew, EAS-TOP EAS-TOP:2009nld, IceCube IceCube:2016biq, IceTop IceCube:2016biq, KASCADE-Grande 2015ICRC...34..281C, MACRO MACRO:2002qsl, Super-K Super-Kamiokande:2005plj, Tibet-AS$\gamma$Amenomori:2017jbv.
• Figure S1: The charge distributions for different $Z$ ranges in two deposited energy bins : $0.5 < E_{\rm dep} < 1$ TeV (left), and $10 < E_{\rm dep} < 100$ TeV (right). The flight data are shown by black dots. Dashed lines with different colors show the best-fit MC simulated samples of proton, helium and other nuclei. The sum of MC samples is shown by the red line.
• Figure S2: Relative uncertainties of the flux measurements from different contributions for proton (a), helium (b), carbon (c), oxygen (d) and iron (e). The systematic uncertainties in analysis, shown in black, are the quadratic sum of all systematic contributions except for the one from hadronic model.