LS 5039 is a gamma-ray binary system observed in a broad energy range, from radio to TeV energies. The binary system exhibits both flux and spectral modulation as a function of its orbital period. The X-ray and very-high-energy (VHE, E > 100 GeV) gamma-ray fluxes display a maximum/minimum at inferior/superior conjunction, with spectra becoming respectively harder/softer, a behaviour that is completely reversed in the high-energy domain (HE, 0.1 < E < 100 GeV). The HE spectrum cuts off at a few GeV, with a new hard component emerging at E > 10 GeV that is compatible with the low-energy tail of the TeV emission. The low 10 - 100 GeV flux, however, makes the HE and VHE components difficult to reconcile with a scenario including emission from only a single particle population. We report on new observations of LS 5039 conducted with the High Energy Stereoscopic System (H.E.S.S.) telescopes from 2006 to 2015. This new data set enables for an unprecedentedly-deep phase-folded coverage of the source at TeV energies, as well as an extension of the VHE spectral range down to ~120 GeV, which makes LS 5039 the first gamma-ray binary system in which a spectral overlap between satellite and ground-based gamma-ray observatories is obtained.
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