  Gamma-ray binaries could be compact pulsar wind nebulae formed when a young
pulsar orbits a massive star. The pulsar wind is contained by the stellar wind
of the O or Be companion, creating a relativistic comet-like structure
accompanying the pulsar along its orbit. The X-ray and the very high energy
(>100 GeV, VHE) gamma-ray emissions from the binary LS 5039 are modulated on
the orbital period of the system. Maximum and minimum flux occur at the
conjunctions of the orbit, suggesting that the explanation is linked to the
orbital geometry. The VHE modulation has been proposed to be due to the
combined effect of Compton scattering and pair production on stellar photons,
both of which depend on orbital phase. The X-ray modulation could be due to
relativistic Doppler boosting in the comet tail where both the X-ray and VHE
photons would be emitted. Relativistic aberrations change the seed stellar
photon flux in the comoving frame so Doppler boosting affects synchrotron and
inverse Compton emission differently. The dependence with orbital phase of
relativistic Doppler-boosted (isotropic) synchrotron and (anisotropic) inverse
Compton emission is calculated, assuming that the flow is oriented radially
away from the star (LS 5039) or tangentially to the orbit (LS I +61 303, PSR
B1259-63). Doppler boosting of the synchrotron emission in LS 5039 produces a
lightcurve whose shape corresponds to the X-ray modulation. The observations
imply an outflow velocity of 0.15-0.33c consistent with the expected flow speed
at the pulsar wind termination shock. In LS I +61 303, the calculated Doppler
boosted emission peaks in phase with the observed VHE and X-ray maximum.
Doppler boosting might provide an explanation for the puzzling phasing of the
VHE peak in this system.
