BOSS-EUVLG1 is the most ultraviolet (UV) and Ly$alpha$ luminous galaxy detected so far in the Universe, going through a very active starburst phase, and forming stars at a rate (SFR) of 955 $pm$ 118 M$_{odot}$ yr$^{-1}$. We report the detection of a broad H$alpha$ component carrying 25% of the total H$alpha$ flux. The broad H$alpha$ line traces a fast and massive ionized gas outflow characterized by a total mass, $log(M_{out}[M_{odot}]),$ of 7.94 $pm$ 0.15, an outflowing velocity (V$_{out}$) of 573 $pm$ 151 km s$^{-1}$, and an outflowing mass rate ($dot{M}_{out}$) of 44 $pm$ 20 M$_{odot}$ yr$^{-1}$. The presence of the outflow in BOSS-EUVLG1 is also supported by the identification of blueshifted UV absorption lines in low and high ionization states. The energy involved in the H$alpha$ outflow can be explained by the ongoing star formation without the need for an Active Galactic Nucleus. The derived low mass loading factor ($eta$= 0.05 $pm$ 0.03) indicates that although massive, this phase of the outflow can not be relevant for the quenching of the star formation. In addition, only a small fraction ($leq$ 15%) of the ionized outflowing material with velocities above 372 km s$^{-1}$ could escape the gravitational potential, and enrich the surrounding circum-galactic medium at distances above tens of kpc. The ionized phase of the outflow does not carry the mass and energy to play a relevant role neither in the evolution of the host galaxy nor in the enrichment of the intergalactic medium. Other phases of the outflow could be carrying most of the outflow energy and mass in the form of hot X-ray emitting gas as predicted by some recent simulations. The expected emission of the extended X-ray emitting halo associated with the outflow in BOSS-EUVLG1 and similar galaxies could be detected with the future X-ray observatory, {it ATHENA} but could not be resolved spatially.
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