In order to provide a firm identification of the newly discovered Galactic TeV sources, a search for counterparts in a broad band from soft X-ray to soft gamma rays is crucial as data in these wave bands allow us to distinguish between different types of suggested models (for example, leptonic vs. hadronic) and, in turn, to disentangle their nature. In this paper we report the results of a set of follow-up observations performed by the Swift X-Ray Telescope (XRT) on seven sources recently discovered by HESS, in the range from a few hundred GeV to about 10 TeV, during the inner Galaxy survey. In all but one case, we detect X-ray sources inside or close by the extended TeV-emitting region. All of these putative X-ray counterparts have an accurate arcsecond location and are consistent with being point sources. The main result of our search is the discovery that three of them are located at the center of the diffuse radio emission of the supernova remnants, which have been spatially associated with these TeV objects. HESS J1640-465, HESS J1834-087, and HESS J1813-178 show this evidence, suggestive of a possible pulsar wind nebula association.
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