Relativistic hydrodynamical simulations of the eccentric gamma-ray binary HESS J0632$+$057, show that the energy of a putative pulsar wind should accumulate in the binary surroundings between periastron and apastron, being released by fast advection close to apastron. To assess whether this could lead to a maximum of the non-thermal emission before apastron, we derive simple prescriptions for the non-thermal energy content, the radiation efficiency, and the impact of energy losses on non-thermal particles, in the simulated hydrodynamical flow. These prescriptions are used to estimate the non-thermal emission in radio, X-rays, GeV, and TeV, from the shocked pulsar wind in a binary system simulated using a simplified 3-dimensional scheme for several orbital cycles. Lightcurves at different wavelengths are derived, together with synthetic radio images for different orbital phases. The dominant peak in the computed lightcurves is broad and appears close to, but before, apastron. This peak is followed by a quasi-plateau shape, and a minor peak only in gamma rays right after periastron. The radio maps show ejection of radio blobs before apastron in the periastron-apastron direction. The results show that a scenario with a highly eccentric high-mass binary hosting a young pulsar can explain the general phenomenology of HESS J0632$+$057: despite its simplicity, the adopted approach yields predictions that are robust at a semi-quantitative level and consistent with multiwavelength observations.
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