GLAST testing of a pulsar model matching H.E.S.S. observations of LS 5039

LS 5039 is one of a handful of X-ray binaries that have been recently detected at high-energy $\gamma$-rays, in this case, by the High-Energy Stereoscopy Array (H.E.S.S.). The nature of this system is unknown: both a black hole and a pulsar have been invoked as possible compact object companions. Here we work with a model of the high energy phenomenology of the system in which it is assumed that the companion object is a pulsar rotating around an O6.5V star in the $\sim 3.9$ days orbit. The model assumes two different sets of power-law spectral parameters of the interacting primary leptons corresponding to the two orbital phase intervals defined by H.E.S.S. as having different gamma-ray spectra and very-high-energy (VHE) cutoffs. We show the H.E.S.S. phenomenology is completely explained by this model. We present predictions for photons with lower energies (for $E>1 $ GeV), subject to test in the forthcoming months with the GLAST satellite. We find that GLAST is able to judge on this model within one year.