The observational constraints were provided by narrow-band imaging in nebular lines and the stellar continuum, together with optical spectra giving nebular line intensities. The ionizing-radiation field was given by a stellar-population synthesis model aimed at reproducing the observed features from hot Wolf-Rayet stars. The conclusion from the modelling exercise was that, even taking into account strong deviations from the adopted spectral energy distribution of the ionizing radiation and the effect of postulated additional X-rays, the photoionization models yield an [O III] A4363/5007 ratio that is too low by about 30%.* This significant discrepancy cannot be solved by invoking expected inaccuracies in the atomic data. The missing energy is of the same order of magnitude as the one provided by the stellar photons.
Interestingly, this paper was rejected by a first referee on the ground that "the temperature of the nebula, as indicated by the ratio [O III] A4363/5007, is in all trial t The lack of variation of the [O III] A5007/4959 ratio among quasars at various redshifts shows that the fine-structure constant, a, does not depend on cosmic time (Bahcall et al. 2003). A far-reaching application of emission-line astrophysics!
* Note that the observed geometrical constraint provided by the images was important in reaching this conclusion, since the authors also showed that, by assuming a simpler geometry with no central hole - but in complete disagreement with the observations - one could obtain a higher electron temperature, due to a reduced H Lya cooling.
models out of the observed range by 30%. The authors seem to have tried everything possible [...] but still ... no secure results". A second referee accepted the paper without changes, emphasizing that "The results are of highest interest for future studies of ionized regions, mainly by the identification of a serious problem in the interpretation of the [O Ill] A4363/5007 ratio, which cannot be consistently reproduced by the models"!
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