The primary proton spectrum of the HAWC J1825-134 source

Abstract

The $\gamma$-ray spectrum of the source HAWC J1825-134 measured with the High Altitude Water Cherenkov (HAWC) observatory extends beyond 200 TeV without any evidence for a steepening or cutoff. There are some indications that the $\gamma$-rays detected with HAWC were produced by cosmic ray protons or nuclei colliding with the ambient gas. Assuming primary protons, we inquire which shape of the primary proton spectrum is compatible with the HAWC measurements. We find that the primary proton spectrum with the power-law shape of $\gamma_{p} = 2.2$ and the cutoff energy $E_{c-p} > 700$ TeV describes the data well. However, much harder spectra with $\gamma_{p}$ down to 1.3 and $E_{c-p}$ as low as 200 TeV also do not contradict the HAWC measurements. The former option might be realized if the accelerator is inside or very near to the $\gamma$-ray production zone. The latter option is viable for the case of a cosmic ray source which effectively confines low-energy ($E_{p} < 100$ TeV) accelerated protons.