The extended HeII$\lambda$4686 emission in the extremely metal-poor
  galaxy SBS0335-052E seen with MUSE
  SBS0335-052E, one of the most metal-poor (Z ~ 3-4% Z$_{\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.
