Nebular HeII emission implies the presence of energetic photons (E$ge$54 eV). Despite the great deal of effort dedicated to understanding HeII ionization, its origin has remained mysterious, particularly in metal-deficient star-forming (SF) galaxies. Unfolding HeII-emitting, metal-poor starbursts at z ~ 0 can yield insight into the powerful ionization processes occurring in the primordial universe. Here we present a new study on the effects that X-ray sources have on the HeII ionization in the extremely metal-poor galaxy IZw18 (Z ~ 3 % Zsolar), whose X-ray emission is dominated by a single high-mass X-ray binary (HMXB). This study uses optical integral field spectroscopy, archival Hubble Space Telescope observations, and all of the X-ray data sets publicly available for IZw18. We investigate the time-variability of the IZw18 HMXB for the first time; its emission shows small variations on timescales from days to decades. The best-fit models for the HMXB X-ray spectra cannot reproduce the observed HeII ionization budget of IZw18, nor can recent photoionization models that combine the spectra of both very low metallicity massive stars and the emission from HMXB. We also find that the IZw18 HMXB and the HeII-emission peak are spatially displaced at a projected distance of $simeq$ 200 pc. These results reduce the relevance of X-ray photons as the dominant HeII ionizing mode in IZw18, which leaves uncertain what process is responsible for the bulk of its HeII ionization. This is in line with recent work discarding X-ray binaries as the main source responsible for HeII ionization in SF galaxies.
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