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

Context. We have presented a numerical model for the non-thermal emission of gamma-ray binaries in a pulsar-wind driven scenario. Aims. We apply this model to one of the best-observed gamma-ray binaries, the LS 5039 system. Methods. The model involves a joint simulation of the pulsar- and stellar-wind interaction and the transport of electronic pairs from the pulsar wind accelerated at the emerging shock structure. We compute the synchrotron and inverse Compton emission in a post-processing step, while consistently accounting for relativistic beaming and $\gamma \gamma$-absorption in the stellar radiation field. Results. The stellar- and pulsar-wind interaction leads to the formation of an extended, asymmetric wind collision region developing strong shocks, turbulent mixing, and secondary shocks in the turbulent flow. Both the structure of the collision region and the resulting particle distributions show significant orbital variation. Next to the acceleration of particles at the bow-like pulsar wind and Coriolis shock the model naturally accounts for the reacceleration of particles at secondary shocks contributing to the emission at very-high-energy (VHE) gamma-rays. The model successfully reproduces the main spectral features of LS 5039. While the predicted lightcurves in the high-energy and VHE gamma-ray band are in good agreement with observations, our model still does not reproduce the X-ray to low-energy gamma-ray modulation, which we attribute to the employed magnetic field model. Conclusions. We successfully model the main spectral features of the observed multiband, non-thermal emission of LS 5039 and thus further substantiates a wind-driven interpretation of gamma-ray binaries. Open issues relate to the synchrotron modulation, which might be addressed through a magnetohydrodynamic extension of our model.