Constraining the position of the knee in the galactic cosmic ray spectrum with ultra-high-energy diffuse $\gamma$-rays

Abstract

The diffuse $\gamma$-ray emission was measured up to $957$ TeV by the Tibet-AS$\gamma$ experiment recently. Assuming that it is produced by the hadronic interaction between cosmic ray nuclei and the interstellar medium, it requires that the cosmic ray nuclei should be accelerated well beyond PeV energies. Measurements of the cosmic ray spectra for different species show diverse results at present. The Tibet experiments showed that the spectrum of proton plus helium has an early knee below PeV. If this is correct, the diffuse $\gamma$-ray emission would suggest an additional component of Galactic cosmic rays above PeV energies. This second component may originate from a source population of so-called PeVatrons revealed by recent ultra-high energy $\gamma$-ray observations, and could contribute to the cosmic ray fluxes up to the energy of the second knee. On the other hand, the KASCADE measurement showed that the knee of protons is higher than PeV. In this case, the diffuse $\gamma$-rays observed by Tibet-AS$\gamma$ can be well accounted for by only one cosmic ray component. These two scenarious (ie. the Tibet and KASCADE knees) could be distinguished by the spectral structures of diffuse $\gamma$-rays and cosmic ray nuclei. Future measurements of spectra of individual nuclei by HERD and LHAASO experiments and diffuse $\gamma$-rays by LHAASO can jointly constrain these two scenarios.