The supernova remnant (SNR) HESS J1731-347 is a young SNR which displays a non-thermal X-ray and TeV shell structure. A molecular cloud at a distance of 3.2 kpc is spatially coincident with the western part of the SNR, and it is likely hit by the SNR. The X-ray emission from this part of the shell is much lower than from the rest of the SNR. Moreover, a compact GeV emission region coincident with the cloud has been detected with a soft spectrum. These observations seem to imply a shock-cloud collision scenario at this area, where the stalled shock can no longer accelerate super-TeV electrons or maintain strong magnetic turbulence downstream, while the GeV cosmic rays (CRs) are released through this stalled shock. To test this hypothesis, we have performed a detailed Fermi-LAT reanalysis of the HESS J1731-347 region with over 9 years of data. We find that the compact GeV emission region displays a spectral power-law index of -2.4, whereas the GeV emission from the rest of the SNR (excluding the cloud region) has an index of -1.8. A hadronic model involving a shock-cloud collision scenario is built to explain the -ray emission from this area. It consists of three CR sources: run-away super-TeV CRs that have escaped from the fast shock, leaked GeV CRs from the stalled shock, and the local CR sea. The X-ray and -ray emission of the SNR excluding the shock-cloud interaction region is explained in a one-zone leptonic model. Our shock-cloud collision model explains well the GeV-TeV observations from both cloud regions around HESS J1731-347, i.e. from the cloud in contact with the SNR and from the more distant cloud which is coincident with the nearby TeV source HESS J1729-345. We find however that the leaked GeV CRs from the shock-cloud collision do not necessarily dominate the GeV emission from the clouds, due to a comparable contribution from the local CR sea.
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