S26 is an extragalactic microquasar with the most powerful jets ever discovered. They have a kinetic luminosity of $L_ j $. This implies that the accretion power to the black hole should be super-Eddington, of the order of $L_ acc j $. However, the observed X-ray flux of this system indicates an apparent very sub-Eddington accretion luminosity of $L_ X We aim to characterize the nature of S26, explain the system emission, and study the feasibility of super-Eddington microquasars as potential PeVatron sources. We first analyze multi-epoch X-ray observations of S26 obtained with XMM-Newton and model the super-Eddington disk and its wind. We then develop a jet model and study the particle acceleration and radiative processes that occur in shocks generated near the base of the jet and in its terminal region. We find that the discrepancy between the jet and the apparent disk luminosities in S26 is caused by the complete absorption of the disk radiation by the wind ejected from the super-Eddington disk. The non-thermal X-rays are produced near the base of the jet, and the thermal X-rays are emitted in the terminal regions. The radio emission observed with the Australia Telescope Compact Array can be explained as synchrotron radiation produced at the reverse shock in the lobes. We also find that S26 can accelerate protons to PeV energies in both the inner jet and the lobes. The ultra-high energy protons accelerated in the lobes of S26 are injected into the interstellar medium with a total power of $ We conclude that S26 is a super-Eddington microquasar with a dense disk-driven wind that obscures the X-ray emission from the inner disk, and that the supercritical nature of the system allows the acceleration of cosmic rays to PeV energies.
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