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Context: Several binary systems hosting massive stars present gamma-rayemission. In most of these systems, despite detailed observational informationbeing available, the nature and the structure of the emitter are still poorlyknown.  Aims: We investigate the validity of the so-called one-zone approximation forthe high-energy emitter in binary systems hosting a massive star. Inparticular, the case of LS 5039 is considered.  Methods: Assuming a point-like emitter at rest, the presence of a nearbymassive star, and the observed MeV and GeV fluxes as a reference, a non-thermalleptonic model is systematically applied for different locations, magneticfields, and non-radiative losses. This allows us to identify both the emitterconfigurations that are most compatible with observations and inconsistenciesbetween model predictions and the available data.  Results: In the case of LS 5039, the best parameter combination is fastnon-radiative cooling and a low magnetic field. However, discrepancies appearwhen comparing the model results at the MeV and GeV energy ranges with theobserved fluxes. Predictions fail when the orbital motion is included in theanalysis, because emitters and energy budgets that are too large are required.Values of X-ray and TeV fluxes that are too high are predicted in such a case,along half of the orbit.  Conclusions: We show that the radiation in LS 5039 does not come from onlyone electron population, and the emitter is likely extended and inhomogeneouswith a low magnetic field. We suggest that the emitter moves at relativisticvelocities with Doppler boosting playing a significant role.  Key words. Stars: high-mass, X-rays: binaries, gamma-rays: binaries

Gamma-ray binaries beyond one-zone models: an application to LS 5039