Constraining Cosmic-Ray Acceleration and Escape in Middle-Aged Supernova Remnants with GeV-TeV Gamma-Ray Observations

Abstract

In this work, we perform a systematic, time-dependent study of the gamma-ray emission from four representative middle-aged SNRs (W51C, IC~443, W44, W28), incorporating both CRs within the remnant shells and escaped CRs interacting with surrounding molecular clouds. We compare our results with GeV--TeV gamma-ray observations from Fermi-LAT, H.E.S.S., MAGIC, and LHAASO, including a dedicated analysis of the Fermi-LAT data for regions A and B associated with W28. We find that the observed spectra favor steeper CR injection spectra with indices of \(\alpha\sim4.2\)--\(4.3\), maximum proton energies of $\sim$ \(100\)--\(300\) TeV, diffusion coefficients below the Galactic average, and CR acceleration efficiencies from a few to tens of percent. In particular, the VHE emission detected by LHAASO from W51C is more naturally explained by escaped CRs interacting with a nearby molecular cloud. We also investigate the contribution of escaped CRs to the VHE emission from IC~443, W44, and W28. We further demonstrate that escaped CRs can substantially enhance the TeV neutrino flux from middle-aged SNRs, improving their prospects as potential neutrino sources. These results provide new constraints on CR acceleration and escape in middle-aged SNRs and highlight the important role of escaped CRs in shaping their high-energy gamma-ray and neutrino emission.