3.9 day orbital modulation in the TeV γ-ray flux and spectrum from the X-ray binary LS 5039

Aims. LS 5039 is a High Mass X-ray Binary (HMXRB) comprising a compact object in an eccentric 3.9 day orbit around a massive O6.5V star. Observations at energies above 0.1 TeV (1011 eV) by the High Energy Stereoscopic System (HESS) in 2004 revealed that LS 5039 is a source of Very High Energy (VHE) $\gamma$-rays and hence, is able to accelerate particles to multi-TeV energies. Deeper observations by HESS were carried out in 2005 in an effort to probe further the high energy astrophysics taking place. In particular, we have searched for orbital modulation of the VHE $\gamma$-ray flux, which if detected, would yield new information about the complex variation in $\gamma$-ray absorption and production within X-ray binary systems. Methods. Observations at energies above 0.1 TeV (1011 eV), were carried out with the High Energy Stereoscopic System (HESS) of Cherenkov Telescopes in 2005. A timing analysis was performed on the dataset employing the Lomb-Scargle and Normalised Rayleigh statistics, and orbital phase-resolved energy spectra were obtained. Results. The timing analysis reveals a highly significant (post-trial chance probability <10-15) peak in the TeV emission periodogram at a frequency matching that of the 3.9 day orbital motion of the compact object around the massive stellar companion. This is the first time in $\gamma$-ray astronomy that orbital modulation has been observed, and periodicity clearly established using ground-based $\gamma$-ray detectors. The $\gamma$-ray emission is largely confined to half of the orbit, peaking around the inferior conjunction epoch of the compact object. Around this epoch, there is also a hardening of the energy spectrum in the energy range between 0.2 TeV and a few TeV. Conclusions. The $\gamma$-ray flux vs. orbital phase profile suggests the presence of $\gamma$-ray absorption via pair production, which would imply that a large fraction of the $\gamma$-ray production region is situated within ~1 AU of the compact object. This source size constraint can be compared to the collimated outflows or jets observed in LS 5039 resolved down to scales of a few AU. The spectral hardening is however not explained exclusively by the absorption effect, indicating that other effects are present, perhaps related to the $\gamma$-ray production mechanism(s). If the $\gamma$-ray emission arises from accelerated electrons, the hardening may arise from variations with phase in the maximum electron energies, the dominant radiative mechanism, and/or the angular dependence in the inverse-Compton scattering cross-section. Overall, these results provide new insights into the competing $\gamma$-ray absorption and production processes in X-ray binaries.