Identification of the cosmic-ray (CR) “PeVatrons,” which are sources capable of accelerating particles to $\sim {10}^{15}\mathrm{eV}$ energies and higher, may lead to resolving the long-standing question of the origin of the spectral feature in the all-particle CR spectrum known as the “knee.” Because CRs with these energies are deflected by interstellar magnetic fields identification of individual sources and determination of their spectral characteristics is more likely via very high energy $\gamma$-ray emissions, which provide the necessary directional information. However, pair production on the interstellar radiation field (ISRF) and cosmic microwave background (CMB) leads to steepening of the high energy tails of $\gamma$-ray spectra, and should be corrected for to enable true properties of the spectrum at the source to be recovered. Employing recently developed three-dimensional ISRF models this paper quantifies the pair-absorption effect on spectra for sources in the Galactic center (GC) direction at 8.5 and 23.5 kpc distances, with the latter corresponding to the far side of the Galactic stellar disc where it is expected that discrimination of spectral features $>10\mathrm{TeV}$ is possible by the forthcoming Cherenkov Telescope Array (CTA). The estimates made suggest spectral cutoffs could be underestimated by factors of a few in the energy range so far sampled by TeV $\gamma$-ray telescopes. As an example to illustrate this, the recent HESS measurements of diffuse $\gamma$-ray emissions possibly associated with injection of CRs nearby Sgr A* are ISRF corrected, and estimates of the spectral cutoff are reevaluated. It is found that it could be higher by up to a factor of $\sim 2$, indicating that these emissions may be consistent with a CR accelerator with a spectral cutoff of at least 1 PeV at the 95% confidence level.

• Received 26 February 2018
• Revised 3 April 2018

DOI:https://doi.org/10.1103/PhysRevD.98.041302