HESS J1731-347 is a shell-type supernova remnant emitting both TeV gamma rays and non-thermal X-ray photons, spatially coincident with the radio SNR G353.6-0.7. Hadronic and leptonic scenarios (or a blend of both) are discussed in the literature to explain the TeV emission from the object. In 2011, a $gamma$-ray excess was also found in the neighborhood of the source (HESS J1729-345). Here we present results of an updated analysis obtained with the meanwhile available additional H.E.S.S. data. Beyond HESS J1731-347, the analysis reveals the morphology of the emission of the adjacent TeV source HESS J1729-345 and the emission in between the two sources in greater detail. The results permit us to correlate the TeV emission outside of the SNR with molecular gas tracers, and to confront the data with scenarios in which the TeV emission outside the SNR is produced by escaping cosmic rays.
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