LS 5039 is a well-known $gamma$-ray binary system which consists of an unknown compact object and a massive companion O star. It shows rather stable emissions at high energies over years and hence serves as an ideal laboratory to investigate the emission mechanism for such peculiar systems which emit prominent $gamma$-rays. To this end, we take the orbital phase resolved energy spectrum as observed by fermi over 10 years. We divide the orbit into four orbital phases, each with an orbital phase range of 0.25, centered at 0.00, 0.25, 0.50 and 0.75 respectively, where the phase 0.0 is the periastron and phase 0.5 is the apastron. The phases around 0.25 and 0.75 are symmetric and hence are supposed to have identical local acceleration environment. The spectral analysis shows that, the fermi spectra are largely different from these two symmetric orbital phases: the emission from orbital phase 0.25 turns out to be significantly stronger than that from 0.75. This result does not fit a scenario that $gamma$-rays are Doppler boosted emission from bow shock tails if LS 5039 has a shock configuration similar to PSR B1259-63, and indicates that the inverse Compton scatterings between the shock accelerated plasma and the stellar particle environment is the underline procedure. We also find that the previous report for a disappearance of the orbital modulation at 3--20 GeV is due to the similar spectral turn-over energies of the different orbital phases. The spectral properties of periastron and apastron regions are addressed in the context of the measurements in phase regions around 0.25 and 0.75.
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