Similarity of $\gamma$-ray spectrum in middle aged supernova remnants interacting with molecular clouds: challenge for current models

Middle aged supernova remnants (SNRs) interacting with molecular clouds (MCs) are an important class of objects in $\gamma$-ray which are crucial for understanding the hadronic emission in SNRs from accelerated protons. In this work, we compare the $\gamma$-ray spectrum available in literature from these remnants and then demonstrate the similarity in the shape of spectra. We also clarify a few points about the $\pi^0$-decay signatures claimed in a few SNRs recently. Next, we discuss the escaping scenario and direct interaction scenario, which have been proposed to interpret the observed $\gamma$-ray emission with hadronic origin. We show the similarity presented in $\gamma$-ray spectra is inconsistent with the prediction from escaping scenario in a statistical way. The inconsistency implies that the widely used free escape boundary might not be a good prescription to investigate the spatial distribution of escaping CRs. The direct interaction scenario involving re-acceleration of pre-existing ambient CRs can explain the similarity in $\gamma$-ray spectra. But the model suggests a transition in seed particles during the SNR evolution, which is from thermal injected particles in young SNRs to pre-existing ambient CRs in middle aged SNRs. Whether such transition in seed particles indeed exists in SNRs has to be tested by future multi-wavelength observation. In the end, we discuss about the possibility for a hybrid model and the challenges confronted by current models.