Modeling the three-dimensional pair cascade in binaries

Context. LS 5039 is a Galactic binary system emitting high and very-high energy gamma rays. The gamma-ray flux is modulated on the orbital period and the TeV lightcurve shaped by photon-photon annihilation. The observed very-high energy modulation can be reproduced with a simple leptonic model but fails to explain the flux detected by HESS at superior conjunction, where gamma rays are fully absorbed. Aims. The contribution from an electron-positron pair cascade could be strong and prevail over the primary flux at superior conjunction. The created pairs can be isotropized by the magnetic field, resulting in a three-dimensional cascade. The aim of this article is to investigate the gamma-ray radiation from this pair cascade in LS 5039. This additional component could account for HESS observations at superior conjunction in the system. Methods. A semi-analytical and a Monte Carlo method for computing three-dimensional cascade radiation are presented and applied in the context of binaries. The cascade is decomposed into discrete generations of particles where electron-positron pairs are assumed to be confined at their site of creation. Both methods give similar results. The Monte Carlo approach remains best suited to calculation of a multi-generation cascade. Results. Three-dimensional cascade radiation contributes significantly at every orbital phase in the TeV lightcurve, and dominates close to superior conjunction. The amplitude of the gamma-ray modulation is correctly reproduced for an inclination of the orbit of ≈ $40^\circ$. Primary pairs should be injected close to the compact object location, otherwise the shape of the modulation is not explained. In addition, synchrotron emission from the cascade in X-rays constrains the ambient magnetic field to below 10 G. Conclusions. The radiation from a three-dimensional pair cascade can account for the TeV flux detected by HESS at superior conjunction in LS 5039, but the very-high energy spectrum at low fluxes remains difficult to explain in this model