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LS 5039 and LSI +61$\degr$303 are two binaries that have been detected in theTeV energy domain. These binaries are composed of a massive star and a compactobject, possibly a young pulsar. The gamma-ray emission would be due toparticle acceleration at the collision site between the relativistic pulsarwind and the stellar wind of the massive star. Part of the emission may alsooriginate from inverse Compton scattering of stellar photons on the unshocked(free) pulsar wind. The purpose of this work is to constrain the bulk Lorentzfactor of the pulsar wind and the shock geometry in the compact pulsar windnebula scenario for LS 5039 and LSI +61$\degr$303 by computing the unshockedwind emission and comparing it to observations. Anisotropic inverse Comptonlosses equations are derived and applied to the free pulsar wind in binaries.The unshocked wind spectra seen by the observer are calculated taking intoaccount the gamma-gamma absorption and the shock geometry. A pulsar windcomposed of monoenergetic pairs produces a typical sharp peak at an energywhich depends on the bulk Lorentz factor and whose amplitude depends on thesize of the emitting region. This emission from the free pulsar wind is foundto be strong and difficult to avoid in LS 5039 and LSI +61$\degr$303. If theparticles in the pulsar are monoenergetic then the observations constrain theirenergy to roughly 10-100 GeV. For more complex particle distributions, the freepulsar wind emission will be difficult to distinguish from the shocked pulsarwind emission.

Spectral signature of a free pulsar wind in the gamma-ray binaries LS 5039 and LSI +61$\degr$303