Abstract
We compare the $\gamma$-ray spectra from 10 middle-aged supernova remnants (SNRs), which are interacting with molecular clouds (MCs), with the model prediction from widely used escaping scenario and direct interaction scenario. It is found that the $\gamma$-ray data is inconsistent with the escaping scenario statistically, as it predicts a diversity of spectral shape which is not observed. The inconsistency suggests that the free escape boundary adopted in the escaping model is not a good approximation, which challenges our understanding of cosmic ray (CR) escaping in SNRs. In addition, we show that ambient CRs is potentially important for the $\gamma$-ray emission of illuminated MCs external to W28 and W44. In direct interaction scenario, the model involving re-acceleration of pre-existing CRs and adiabatic compression is able to explain the emission from most SNRs. The dispersion shown in the TeV data is naturally explained by different acceleration time of CR particles in SNRs. Re-acceleration of pre-existing CRs suggests a transition of seed particles, which is from thermal injected seed particle in young SNRs to ambient CRs in old SNRs. The transition needs to be tested by future multi-wavelength observation. In the end, we propose that radiative SNR without MC interaction is also able to produce a significant amount of $\gamma$-ray emission. A good candidate is S147. With accumulated Fermi data and CTA in future we expect to detect more remnants like S147.
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