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We report on detailed analysis of the hard X-ray and GeV gamma-ray spectra ofLS 5039, one of the brightest gamma-ray binary system in the Galaxy. The NuSTARobservation covering its entire orbit in 2016 allowed us for the first time tostudy the orbital variability of the spectrum above 10 keV. The hard X-rayspectrum is well described with a single power-law component up to 78 keV. TheX-ray flux showed a slight deviation from those observed previously with Suzakuin 2007. The fast X-ray brightening observed with Suzaku, around the inferiorconjunction, was not observed in this observation. We also analyzed 11 years ofFermi Large Area Telescope data of LS 5039. The GeV spectrum around theinferior conjunction was well described with two non-thermal components; apower law with a photon index of $\sim 3$ and a cut-off power law with a cutoffenergy of $\sim 2$ GeV. The orbital flux variability also changed graduallyaround a few GeV. These results indicate that there are two emission componentsin the GeV band, and the dominant component above $\sim 1$ GeV does not dependon the orbital phase. By combining these results, we update the spectral energydistribution of LS 5039 with the highest available statistics. Theoreticalmodels proposed so far cannot explain the obtained multi-wavelength spectrum,especially the emission from $\sim$ 1 MeV to $\sim$ 400 MeV, and we discuss apossibility that particle acceleration in LS 5039 is different from the shockacceleration.

Broad-Band High-Energy Emission of the Gamma-ray Binary System LS 5039: Spectral and Temporal Features using NuSTAR and Fermi Observations