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SBS0335-052E, one of the most metal-poor (Z ~ 3-4% Z$_{\odot}$) HeII-emitterstarbursts known in the nearby universe, is studied using optical VLT/MUSEspectroscopic and Chandra X-ray observations. We spatially resolved thespectral map of the nebular HeII$\lambda$4686 emission from which we derivedfor the first time the total HeII-ionizing energy budget of SBS0335-052E. Thenebular HeII line is indicative of a quite hard ionizing spectrum with photonenergies > 4 Ryd, and is observed to be more common at high-z than locally. Ourstudy rules out a significant contribution from X-ray sources and shocks to theHeII photoionization budget, indicating that the He$^{+}$ excitation is mainlydue to hot stellar continua. We discovered a new WR knot, but we also discardsingle WR stars as the main responsible for the HeII ionization. By comparingobservations with current models, we found that the HeII-ionization budget ofSBS0335-052E can only be produced by either single, rotating metal-free starsor a binary population with Z ~ 10$^{-5}$ and a 'top-heavy' IMF. Thisdiscrepancy between the metallicity of such stars and that of the HII regionsin SBS0335-052E is similar to results obtained by Kehrig et al. (2015) for thevery metal-deficient HeII-emitting galaxy IZw18. These results suggest that theHeII ionization is still beyond the capabilities of state-of-the-art models.Extremely metal-poor, high-ionizing starbursts in the local universe, likeSBS0335-052E, provide unique laboratories for exploring in detail the extremeconditions likely prevailing in the reionization era.

The extended HeII$\lambda$4686 emission in the extremely metal-poor galaxy SBS0335-052E seen with MUSE