A scenario for the Galactic cosmic rays between the knee and the second-knee

Abstract

We perform a fit to measurements of the cosmic ray spectrum in the energy range between 10 15 eV and 10 18 eV using data from the TALE, Tunka and Auger experiments. We also fit the data on the depth of shower maximum, Xmax, from Tunka and Yakutsk or from Auger to constrain the cosmic ray composition. We consider a Galactic component that is a mixture of five representative nuclear species (H, He, N, Si and Fe), for which we adopt rigidity dependent broken power-law spectra, and we allow for an extragalactic component which becomes strongly suppressed for decreasing energies. The relative abundances of the Galactic components at 10 15 eV are taken to be comparable to those determined by direct measurements at 10 13 eV. The main features of the spectrum and of the composition are reproduced in these scenarios. The spectral knee results from the break of the H spectrum at E k ≃ 3 × 10 15 eV, although it is broadened by the comparable contribution from He which has a break at about 6×10 15 eV. The low-energy ankle at E la ≃ 2×10 16 eV coincides with the strong suppression of the H and He Galactic components and the increasing relative contribution of the heavier ones, but the observed hardening of the spectrum at this energy turns out to result from the growing contribution of the extragalactic component. The second-knee at E sk ≃ 26E k ≃ 8 × 10 16 eV is associated with the steepening of the Galactic Fe component. The transition to the regime in which the total cosmic ray flux is dominated by the extragalactic component takes place at an energy of about 10 17 eV. The parameters of the fit depend on the specific Xmax dataset that is considered, with the Yakutsk and Tunka data leading to a suppression of the light components being steeper beyond the knee so as to allow a faster growth of the average mass around the low-energy ankle. The results also depend on the hadronic model that is used to interpret Xmax measurements and we compare the parameters obtained with Sibyll 2.3, EPOS-LHC and QGSJET II-04. The impact of the possible existence of a maximum rigidity cutoff in the Galactic components is also discussed.

Ultrahigh energy cosmic rays from a nearby extragalactic source in the diffusive regime

“…This component is relevant only below few EeV but is anyhow subdominant above 0.1 EeV. It is taken from [36], considering the results that include an exponential Galactic cutoff at energies ∼ 40Z PeV.…”

Diffuse Galactic gamma-ray and neutrino fluxes at very high energy and the Galactic/extragalactic Cosmic Ray transition

“…Several authors have discussed models where the Galactic to extragalactic transition is at the "second Knee". Two (very similar models) of this type are those developed by Abu-Zayyad et al [14] and by Mollerach and Roulet (MR) [15]. In these models the CR Galactic component is described as an ensemble of rigidity dependent (gradually) broken power laws, with a result that is numerically very similar to the GST fit for E 10 15.5 eV.…”

“…that is a power law with a low energy exponential cutoff. In the Mollerach and Roulet (MR) model [15] the cutoff has the form 1/ cosh[(E cut /E) β ] that has a very similar (but not identical) shape. The extragalactic component emerges very rapidly for E E cut forming the spectral hardening visible at E 2 × 10 16 eV, and becomes dominant for E 10 17 eV (above the so called "second Knee").…”

“…7. The solid lines are the all-particle (black) and all-nucleon (blue) spectra of the MR model [15]. The separate contributions of Galactic and extragalactic particles to the all-nucleon flux are also shown.…”

On the relation between the astrophysical neutrino fluxes and the cosmic ray fluxes

“…In scenarios in which the suppression effects depend on the rigidity of the particles, and hence on the ratio E/Z with Z being the particle charge, the Galactic Fe component should become suppressed above an energy of about 100 PeV, which actually coincides with the observed steepening at the second knee of the spectrum. The presence of a predominant extragalactic component above this energy is then likely [8], and also the lack of significant anisotropies at EeV energies associated with the Galactic center or the Galactic plane disfavors a sizeable contribution of Galactic origin at those energies [9]. We also note that the extragalactic component relevant below a few EeV may arise from a different source population than the one dominating at higher energies, and hence to use the latter to normalize the flux of the lower energy component may not be justified.…”