The recent discovery of the radio shell-type supernova remnant (SNR), G353.6-0.7, in spatial coincidence with the unidentified TeV source HESS J1731-347 has motivated further observations of the source with the High Energy Stereoscopic System (H.E.S.S.) Cherenkov telescope array to test a possible association of the gamma-ray emission with the SNR. With a total of 59 hours of observation, representing about four times the initial exposure available in the discovery paper of HESS J1731-347, the gamma-ray morphology is investigated and compared with the radio morphology. An estimate of the distance is derived by comparing the interstellar absorption derived from X-rays and the one obtained from 12CO and HI observations. The deeper gamma-ray observation of the source has revealed a large shell-type structure with similar position and extension (r~0.25{deg}) as the radio SNR, thus confirming their association. By accounting for the H.E.S.S. angular resolution and projection effects within a simple shell model, the radial profile is compatible with a thin, spatially unresolved, rim. Together with RX J1713.7-3946, RX J0852.0-4622 and SN 1006, HESS J1731-347 is now the fourth SNR with a significant shell morphology at TeV energies. The derived lower limit on the distance of the SNR of 3.2 kpc is used together with radio and X-ray data to discuss the possible origin of the gamma-ray emission, either via inverse Compton scattering of electrons or the decay of neutral pions resulting from proton-proton interaction.
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