Strong nebular HeII emission induced by He$^+$ ionizing photons escaping through the clumpy winds of massive stars

The origin of nebular HeII-emission in both local and high-redshift galaxies remains an unsolved problem. Various theories have been proposed to explain it, including HeII-ionization by high mass X-ray binaries, ultra-luminous X-ray sources, or "stripped" He stars, shock ionization, and hidden AGNs. All these theories have shortcomings, however, leaving the cause of nebular HeII emission unclear. We investigate the hypothesis that the photons responsible for driving nebular HeII emissions are produced by the evolution of single massive stars and/or WR stars. We combine models of stellar evolution with population synthesis and nebular models to identify the most favorable scenarios for producing nebular HeII via this channel. We find that, if WR winds are clumpy enough to become close to optically thin, stellar populations with a wide range of metallicities and rotation rates can produce HeII ionizing photons at rates sufficient to explain the observed nebular $I(HeII)/I(\mathrm{H}\beta)$ ratio $\sim 0.004-0.07$ found in HeII-emitting galaxies. Metal-poor, rapidly rotating stellar populations ($[\mathrm{Fe}/\mathrm{H}]=-2.0$, $v/v_\mathrm{crit}=0.4$) also reach these levels of HeII production even for partially clumpy winds. These scenarios also yield HeII, H$\beta$, and "Blue-Bump" line equivalent widths comparable to those observed in HeII emitters. Only for laminar, non-clumpy winds, do we fail to find combinations of metallicity and stellar rotation rate that yield $I(HeII)/I(\mathrm{H}\beta)$ values as high as those observed in HeII-emitters. Contrary to previous findings, we conclude that single WR stars can be a strong source for nebular HeII emission if their winds are sufficiently clumpy allowing significant escape of hard ionizing photons.