  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 $i\approx 35^{\rm o}$.
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 $\sigma\approx 1$ and
$\Gamma_{p}\approx 5\times 10^{3}$, 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.
