SBS0335-052E, one of the most metal-poor (Z ~ 3-4% Z$_{odot}$) HeII-emitter starbursts known in the nearby universe, is studied using optical VLT/MUSE spectroscopic and Chandra X-ray observations. We spatially resolved the spectral map of the nebular HeII$lambda$4686 emission from which we derived for the first time the total HeII-ionizing energy budget of SBS0335-052E. The nebular HeII line is indicative of a quite hard ionizing spectrum with photon energies > 4 Ryd, and is observed to be more common at high-z than locally. Our study rules out a significant contribution from X-ray sources and shocks to the HeII photoionization budget, indicating that the He$^{+}$ excitation is mainly due to hot stellar continua. We discovered a new WR knot, but we also discard single WR stars as the main responsible for the HeII ionization. By comparing observations with current models, we found that the HeII-ionization budget of SBS0335-052E can only be produced by either single, rotating metal-free stars or a binary population with Z ~ 10$^{-5}$ and a top-heavy IMF. This discrepancy between the metallicity of such stars and that of the HII regions in SBS0335-052E is similar to results obtained by Kehrig et al. (2015) for the very metal-deficient HeII-emitting galaxy IZw18. These results suggest that the HeII ionization is still beyond the capabilities of state-of-the-art models. Extremely metal-poor, high-ionizing starbursts in the local universe, like SBS0335-052E, provide unique laboratories for exploring in detail the extreme conditions likely prevailing in the reionization era.
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