  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. 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. A
semi-analytical and a Monte Carlo method for computing three-dimensional
cascade radiation are presented and applied in the context of binaries.
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 about 40 degrees. 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. 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.
