The production of orbitally modulated UHE photons in LS 5039

Conntext. Gamma-ray binaries present emission that is variable and can reach ultra-high energies. The processes behind the acceleration of the particles that produce this very energetic radiation are yet to be understood. Aims. We probe the properties of the particle accelerator and the ultra-high-energy photon emitter in the gamma-ray binary LS 5039. Methods. From the properties of the binary system and the ultra-high-energy radiation detected by HAWC, we used analytical tools to investigate how these properties constrain the emission and acceleration regions, namely the role of synchrotron losses, particle confinement, and the accelerated particle spectrum, and propose an acceleration scenario that can relax the derived constraints. Results. The modest target densities for hadronic processes and the overall gamma-ray orbital variability favor inverse Compton scattering of ultraviolet photons from the massive companion star by highly relativistic electrons. The acceleration of the highest energy electrons implies a constraint on synchrotron cooling in the acceleration region, which can set an upper limit on its magnetic field. Moreover, the detected variability requires very strong particle confinement in both the acceleration and emission regions, which sets a lower limit on their magnetic fields that is barely consistent with the synchrotron cooling constraint from acceleration. Synchrotron losses may be higher in the emitting region if it is separated from the accelerator, but this requires a very hard particle injection spectrum. An accelerator based on an ultrarelativistic magnetized outflow can alleviate these requirements. Conclusions. A scenario for LS 5039 of the kind proposed by Derishev and collaborators, in which an ultrarelativistic magnetized outflow accelerates leptons injected within the outflow by γγ absorption, provides a viable mechanism to accelerate very energetic electrons. This mechanism relaxes the acceleration and confinement requirements by reducing the impact of synchrotron cooling, and can generate the required particle spectrum.