  The nature of the sources powering nebular HeII emission in star-forming
galaxies remains debated, and various types of objects have been considered,
including Wolf-Rayet stars, X-ray binaries, and Population III stars. Modern
X-ray observations show the ubiquitous presence of hot gas filling star-forming
galaxies. We use a collisional ionization plasma code to compute the specific
HeII ionizing flux produced by hot gas and show that if its temperature is not
too high (less than 2.5 MK), then the observed levels of soft diffuse X-ray
radiation could explain HeII ionization in galaxies. To gain a physical
understanding of this result, we propose a model that combines the
hydrodynamics of cluster winds and hot superbubbles with observed populations
of young massive clusters in galaxies. We find that in low-metallicity
galaxies, the temperature of hot gas is lower and the production rate of HeII
ionizing photons is higher compared to high-metallicity galaxies. The reason is
that the slower stellar winds of massive stars in lower-metallicity galaxies
input less mechanical energy in the ambient medium. Furthermore, we show that
ensembles of star clusters up to 10-20 Myr old in galaxies can produce enough
soft X-rays to induce nebular HeII emission. We discuss observations of the
template low-metallicity galaxy I Zw 18 and suggest that the HeII nebula in
this galaxy is powered by a hot superbubble. Finally, appreciating the complex
nature of stellar feedback, we suggest that soft X-rays from hot superbubbles
are among the dominant sources of HeII ionizing flux in low-metallicity
star-forming galaxies.
