  We have used the radiation field from a starburst population synthesis model
appropriate for the brightest HII region of IZw 18 to perform a photoionization
model analysis of this object. We have investigated whether, with the observed
nebular density distribution as revealed by the HST images and a total stellar
radiation compatible with the observed UV flux, the constraints represented by
the observed ionization structure, the HeII/Hbeta ratio, the Halpha flux and
the electron temperature indicated by the [OIII] 4363/5007 ratio can be
reproduced. We have found that, even taking into account strong deviations from
the adopted spectral energy distribution of the ionizing radiation and the
effect of additional X-rays, the photoionization models yield too low a
4363/5007 ratio by about 30 %. This discrepancy is significant and poses an
interesting problem, which cannot be solved by expected inaccuracies in the
atomic data. The missing energy may be of the same order of magnitude as the
one provided by the stellar photons or lower, depending on the way it acts on
the 4363 line. Elemental abundance determinations in I Zw 18 are affected by
this problem. Before the nature of the missing heating source and its
interactions with the nebular gas are better understood it is, however, not
possible to estimate the typical uncertainties by which standard empirical
methods are affected. Other topics discussed include: nebular HeII emission,
photon leakage, [OI] 6300 emission, reddening, ionization correction factors.
(abridged abstract)
