A dynamical and radiation semi-Analytical model of pulsar-star colliding winds along the orbit: Application to LS 5039

[Context]: Gamma-ray binaries are systems that emit nonthermal radiation peaking at energies above 1 MeV. One proposed scenario to explain their emission consists of a pulsar orbiting a massive star, with particle acceleration taking place in shocks produced by the interaction of the stellar and pulsar winds. [Aims]: We develop a semi-Analytical model of the nonthermal emission of the colliding-wind structure, which includes the dynamical effects of orbital motion. We apply the model to a general case and to LS 5039. [Methods]: The model consists of a one-dimensional emitter, the geometry of which is affected by Coriolis forces owing to orbital motion. Two particle accelerators are considered: one at the two-wind standoff location and the other one at the turnover produced by the Coriolis force. Synchrotron and inverse Compton emission is studied taking into account Doppler boosting and absorption processes associated to the massive star. [Results]: If both accelerators are provided with the same energy budget, most of the radiation comes from the region of the Coriolis turnover and beyond, up to a few orbital separations from the binary system. Significant orbital changes of the nonthermal emission are predicted in all energy bands. The model allows us to reproduce some of the LS 5039 emission features, but not all of them. In particular, the MeV radiation is probably too high to be explained by our model alone, the GeV flux is recovered but not its modulation, and the radio emission beyond the Coriolis turnover is too low. The predicted system inclination is consistent with the presence of a pulsar in the binary. [Conclusions]: The model is quite successful in reproducing the overall nonthermal behavior of LS 5039. Some improvements are suggested to better explain the phenomenology observed in this source, such as accounting for particle reacceleration beyond the Coriolis turnover, unshocked pulsar wind emission, and the three-dimensional extension of the emitter.We acknowledge support by the Spanish Ministerio de Economía y Competitividad (MINECO/FEDER, UE) under grant AYA2016-76012-C3-1-P, with partial support by the European Regional Development Fund (ERDF/FEDER), and from the Catalan DEC grant 2017 SGR 643. EM acknowledges support from MINECO through grant BES-2016-076342