What heats the bright HII regions in I Zw 18?

We have used the radiation field from a starburst population synthesis model appropriate for the brightest H II region of I Zw 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, one could reproduce the constraints represented by the observed ionization structure, the He II lambda 4686/H beta ratio, the Ha flux and the electron temperature indicated by the [:O III] lambda 4363/5007 ratio. We have found that, even talking 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 [O III] lambda 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 [O III] lambda 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. Several side-products of our photoionization analysis of I Zw 18 sire the following: - We have been able to reproduce the intensity of the nebular He II lambda 4686 using a stellar radiation field consistent with the observed Wolf-Rayet features in I Zw 18. - We have shown that the bright NW H rr region in I Zw 18 does not absorb all the ionizing photons from the central star cluster, and that about half of them are available to ionize an extended diffuse envelope. - The [O I] emission can easily be accounted for by condensations or intervening filaments on the line of sight. - The intrinsic H alpha/H beta ratio is enhanced by collisional excitation to a value of 3, Previous estimates of the reddening of IZw LX are therefore slightly overestimated. - We give ionization correction factors appropriate for lZw IX that can be used for more accurate abundance determinations in this object once the electron temperature problem is better understood.