Examining a hadronic γ-ray scenario for the radiative shell & molecular clouds of the old GeV supernova remnant G298.6$-$0.0

Based on the 13.7~yr Fermi-LAT data, Yeung et al. (2023) claimed detection of two γ-ray sources (Src-NE and Src-NW) associated with the supernova remnant (SNR) G298.6$-$0.0, and interpreted it as an old GeV SNR interacting with molecular clouds (MCs). In this follow-up study, we refine the flux measurements below 2~GeV with Fermi-LAT event types of better angular reconstruction. Then, we report our cosmic-ray phenomenology in a hadronic scenario, considering both the shell and MC regions of SNR G298.6$-$0.0. We confirm that both the γ-ray spectra of Src-NE and Src-NW exhibit spectral breaks at 1.50-0.50+0.60~GeV and 0.68-0.11+0.32~GeV, respectively. Src-NW has a harder broadband photon index than Src-NE, suggesting an appreciable difference between the physical separations of their respective emission sites from SNR G298.6$-$0.0. The cosmic-ray spectrum responsible for Src-NE starts with a minimum energy ECR,min=1.38-0.16+0.47~GeV, and has a proton index ΓCR=2.57-0.21+0.18 below the exponential cutoff energy ECR,max=240₋₁₅₀⁺²⁴⁰~GeV. Accordingly, we argue that Src-NE is dominated by the SNR shell, while only a minor portion of lower-energy emission is contributed by the MCs interacting with the SNR. The cosmic-ray population for Src-NW starts at a higher energy such that the ECR,min ratio of Src-NW to Src-NE is 2. The high ECR,min, as well as the high cosmic-ray energy density required (~26~eV~cm⁻³), supports the interpretation that Src-NW is predominantly the γ-ray emission from the farther MCs being bombarded by protons that had earlier escaped from SNR G298.6$-$0.0. By comparing the high-energy features of G298.6$-$0.0 with those of analogical SNRs, especially SNR W28 and SNR W44, we further constrain the age of SNR G298.6$-$0.0 to be 10--30~kyr.