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Context. We have presented a numerical model for the non-thermal emission ofgamma-ray binaries in a pulsar-wind driven scenario. Aims. We apply this modelto one of the best-observed gamma-ray binaries, the LS 5039 system. Methods.The model involves a joint simulation of the pulsar- and stellar-windinteraction and the transport of electronic pairs from the pulsar windaccelerated at the emerging shock structure. We compute the synchrotron andinverse Compton emission in a post-processing step, while consistentlyaccounting for relativistic beaming and $\gamma \gamma$-absorption in thestellar radiation field. Results. The stellar- and pulsar-wind interactionleads to the formation of an extended, asymmetric wind collision regiondeveloping strong shocks, turbulent mixing, and secondary shocks in theturbulent flow. Both the structure of the collision region and the resultingparticle distributions show significant orbital variation. Next to theacceleration of particles at the bow-like pulsar wind and Coriolis shock themodel naturally accounts for the reacceleration of particles at secondaryshocks contributing to the emission at very-high-energy (VHE) gamma-rays. Themodel successfully reproduces the main spectral features of LS 5039. While thepredicted lightcurves in the high-energy and VHE gamma-ray band are in goodagreement with observations, our model still does not reproduce the X-ray tolow-energy gamma-ray modulation, which we attribute to the employed magneticfield model. Conclusions. We successfully model the main spectral features ofthe observed multiband, non-thermal emission of LS 5039 and thus furthersubstantiates a wind-driven interpretation of gamma-ray binaries. Open issuesrelate to the synchrotron modulation, which might be addressed through amagnetohydrodynamic extension of our model.

Relativistic fluid modelling of gamma-ray binaries. II. Application to LS 5039