The high and very-high energy spectrum of gamma-ray binaries has become a challenge for all theoretical explanations since the detection of powerful, persistent GeV emission from LS 5039 and LS I +61 303 by Fermi/LAT. The spectral cutoff at a few GeV indicates that the GeV component and the fainter, hard TeV emission above 100 GeV are not directly related. We explore the possible origins of these two emission components in the framework of a young, non-accreting pulsar orbiting the massive star, and initiating the non-thermal emission through the interaction of the stellar and pulsar winds. The pulsar/stellar wind interaction in a compact orbit binary gives rise to two potential locations for particle acceleration: the shocks at the head-on collision of the winds and the termination shock caused by Coriolis forces on scales larger than the binary separation. We explore the suitability of these two locations to host the GeV and TeV emitters, respectively, through the study of their non-thermal emission along the orbit. We focus on the application of this model to LS 5039 given its well determined stellar wind with respect to other gamma-ray binaries. The application of the proposed model to LS 5039 indicates that these two potential emitter locations provide the necessary conditions for reproduction of the two-component high-energy gamma-ray spectrum of LS 5039. In addition, the ambient postshock conditions required at each of the locations are consistent with recent hydrodynamical simulations. The scenario based on the interaction of the stellar and pulsar winds is compatible with the GeV and TeV emission observed from gamma-ray binaries with unknown compact objects, such as LS 5039 and LS I +61 303.
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