Detailed modeling of the high-energy emission from gamma-ray binaries has been propounded as a path to pulsar wind physics. Fulfilling this ambition requires a coherent model of the flow and its emission in the region where the pulsar wind interacts with the stellar wind of its companion. We developed a code that follows the evolution and emission of electrons in the shocked pulsar wind based on inputs from a relativistic hydrodynamical simulation. The code is used to model the well-documented spectral energy distribution and orbital modulations from LS 5039. The pulsar wind is fully confined by a bow shock and a back shock. The particles are distributed into a narrow Maxwellian, emitting mostly GeV photons, and a power law radiating very efficiently over a broad energy range from X-rays to TeV gamma rays. Most of the emission arises from the apex of the bow shock. Doppler boosting shapes the X-ray and VHE lightcurves, constraining the system inclination to $iapprox 35^{rm o}$. There is a tension between the hard VHE spectrum and the level of X-ray to MeV emission, which requires differing magnetic field intensities that are hard to achieve with a constant magnetisation $sigma$ and Lorentz factor $Gamma_{p}$ of the pulsar wind. Our best compromise implies $sigmaapprox 1$ and $Gamma_{p}approx 5times 10^{3}$, respectively higher and lower than the typical values in pulsar wind nebulae. The high value of $sigma$ derived here, where the wind is confined close to the pulsar, supports the classical picture that has pulsar winds highly magnetised at launch. However, such magnetisations will require further investigations to be based on relativistic MHD simulations.
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