What can cosmic-ray knees reveal about source populations?

TL;DR

The paper addresses whether the cosmic-ray knee phenomenology can be explained by a single population of accelerators with a fixed-rigidity cutoff or requires more complex physics. Using a minimal model with a single source and a population characterized by distributions in the cutoff energy E_{p,max} and the slope γ, the authors derive robust trends for the knee observables, including a near-0.5 slope change and a pattern where composition breaks first, with break energies E_A and E_b moving apart as population diversity increases. Comparing these trends to data, they find that the primary knee around ~4×10^{15} eV is compatible with a fixed-rigidity cutoff only for some datasets, while the second knee around ~5×10^{17} eV likely demands additional physics, and a high-energy Auger feature around ~10^{19} eV may be consistent only if there is substantial diversity in population properties. Overall, the work provides exclusion tests for the single-population hypothesis and clarifies where population diversity or multi-population dynamics must enter to reproduce the observed cosmic-ray knee and ankle features.

Abstract

Cosmic ray (CR) knees (spectral steepenings) encode information on CR accelerator populations. We seek population features that imprint onto knee observables in a manner that is robust enough to be discernible even in the presence of significant systematics in CR data. In particular, we explore how diversity among population members could imprint on the knee phenomenology, under the assumption that a knee is due to a fixed-rigidity cutoff in the source spectra. We use a simple theoretical model for a population of CR accelerators. Each population member accelerates CR to a power-law spectrum, up to a cutoff rigidity. We allow for variance among members, in cutoff rigidity and power-law slope. We find that: (a) the slope step of the spectrum is $\sim 0.5$, decreasing weakly with increasing spread in either property; (b) composition always breaks first; (c) the difference between the break energies in composition and flux increases with increasing diversity; (d) composition and flux break together only if population diversity is minimal. These trends are robust under our assumptions; deviations from them would indicate more complex physics than encoded in our simple model. Comparing these trends with observed CR knees, we conclude that: (i) the primary knee at $\sim 4\times10^{15}$ eV is consistent with a constant-rigidity cutoff according to KASCADE-Grande data processed with post-LHC hadronic models, but not according to other datasets; (ii) the second knee at $\sim 5 \times 10^{17}$ eV requires more complexity than our model; (iii) the spectral feature identified by Auger at $\sim 10^{19}$ eV is consistent with a constant-rigidity source cutoff only if there is a substantial spread in both cutoff rigidity and slope. Interestingly, a significant spread in slope would also result in spectral curvature before the break, which would in turn be contributing to the ankle feature.

Figures (8)

• Figure 1: All-particle flux and composition spectra in the case of a lognormal $p(E_{p,{\rm max}})$. Upper-left panel: all-particle flux spectrum flattened by $E^{\gamma}$. Upper-right panel: composition spectrum. Lower-left panel: broken power-law fit around the knee for the flux spectrum. Crosses correspond to mock observations obtained from our model. The solid line is the fit of Eq. (\ref{['12']}). Lower-right panel: low- and high-energy asymptotic logarithmic fits to the composition spectrum (green and red solid lines respectively). Points again correspond to mock data obtained from our model. The composition break energy given by the intersection of the two lines (black star).
• Figure 2: Values of the spectral power indices $\gamma_1$ and $\gamma_2$, indicated with red and blue points respectively, as a function of $\sigma_{E p,{\rm max}}/\bar{E}_{p,{\rm max}}$.
• Figure 3: Energies of the composition break (red) and the flux break (blue) in units of $\bar{E}_{p,{\rm max}}$ as a function of $\sigma_{E p,{\rm max}}/\bar{E}_{p,{\rm max}}$.
• Figure 4: As in Fig. \ref{['fig:fig3']}, but using initial CR composition taken from New_composition, which is more appropriate for energies above the knee.
• Figure 5: As in Fig. \ref{['fig:fig4']}, but using initial CR composition taken from New_composition, which is more appropriate for energies above the knee.