6. CONCLUSIONS

The best determinations of abundance ratios are those that do not depend, or depend weakly, on T_e. Therefore some of the best determinations are those derived from the ratio of two recombination lines because, to a very good approximation, the temperature dependence of the recombination lines is very similar. Unfortunately, with the exception of the He lines, the brighter recombination lines of the most abundant elements - C, N and O - are typically about three orders of magnitude fainter than H in objects with solar abundances. Consequently only a small number of high quality determinations has been carried out based on recombination lines of C, N and O. Therefore, for less abundant elements, metal poor gaseous nebulae or faint gaseous nebulae, one has to rely on collisionally excited lines to derive abundances relative to H.

The intensity of a collisionally excited line depends on the Boltzmann factor, - E / k T_e, where E is the energy difference between the excited level from which the line originates and the ground level. For UV lines and visual auroral lines, E is in the 4-13 eV range, for visual nebular lines in the 1.3-4 eV range, and for far IR lines in the 0-1 eV range. Since in gaseous nebulae k T_e ~ 1 eV, the UV and auroral lines depend strongly on T_e, the visual nebular lines depend moderately on T_e, and the IR lines are almost independent of T_e (but often their ratio relative to a H line depends strongly on N_e, see Simpson et al. 1995 and references therein). This dependence, in the presence of temperature variations over the observed volumes, produces significant errors in the abundance determinations if the nebulae are assumed to be isothermal.

More high quality abundance determinations derived from recombination lines are needed to advance in our knowledge of the chemical composition of gaseous nebulae and to estimate the effect of the temperature structure on the abundances derived from collisionally excited lines.

The photoionization models of gaseous nebulae have to be modified to include deposition of mechanical energy. Moreover further exploration of photoionization models with inhomogeneous density and chemical abundances should be carried out. Empirical abundance determination methods based on the intensity of nebular lines should be calibrated by considering objects with t² determinations; or if there are no suitable calibrators with t² determinations, the method should be calibrated with photoionization models by matching the nebular lines instead of the auroral to nebular line ratios.

From H II regions with good determinations of t² values it follows that to adopt a t² 0.04 is a reasonable approximation to use for those objects without a high quality t² determination. PN show a wider range of t² values than H II regions; typical values for PN are in the 0.03 t² 0.06 range.

Some results due to the adoption of abundances derived with t² 0.00 follow:

a) O / H values for disk PN are similar to those of the sun removing the difference between the abundances of young stars and type II PN (those that have kinematic properties typical of intermediate population I stars). There is still the standing problem of NGC 6543 and NGC 7009 that show O / H abundances two times higher than solar; more abundance determinations, based on recombination lines, are needed to find out which is the fraction of O / H rich PN and to explain their presence in the context of stellar or galactic chemical evolution.

b) The O / H values of solar vicinity H II regions become similar to those of the sun and young stars of the solar vicinity, removing a long standing discrepancy.

c) The discrepancy among the He⁺ / H⁺ abundance ratios derived from different He I lines of PN with high N_e and T_e(4363/5007) values, after considering the effects of collisional excitation and absorption from the 2³S He I level, dissapears.

d) By determining the abundances of type I PN considering their high t² values, the O / H ratios become similar to those of stars recently formed, their N / O ratios become smaller and there is no need to invoke the presence of ON cycling products in the nebular shells.

e) The Y / Z ratio derived from M17 and Y_p can be explained by chemical evolution models of the solar vicinity without the need to invoke a mass cut-off above which massive stars do not enrich the interstellar medium with heavy elements during the SN event.

f) The scatter in the Y versus N diagram present in O-poor extragalactic H II regions with WR features could be due to different t² values for each object and not to He and N pollution by WR stars.

g) The smaller Y / O ratios are in better agreement with chemical evolution models of irregular galaxies that fit other observational constraints and imply that O-rich galactic outflows are not as important as previously thought.

h) For those H II regions and PN where collisional excitations from the 2³S level are thought to be important a t² 0.00 will decrease the contribution to the He line intensities due to collisions and a higher Y value will be derived. Alternatively for O-poor extragalactic H II regions with negligible collisional effects from the 2³S level of He I (objects with low N_e), a t² = 0.04 affects the Y_p determination in the sense of reducing Y_p by about 0.003.

Acknowledgments

It is a pleasure to aknowledge important and constructive suggestions on this subject with Pedro Colín, César Esteban, Valentina Luridiana, Miriam Peña, Silvia Torres-Peimbert & Antonio Sarmiento. I also like to thank the staff of the Space Telescope Science Institute, and in particular Bob Williams and Mario Livio, for their invitation to participate in this conference and for their warm hospitality. Over the years I have had the privilege of enjoying inspiring and fruitful academic relationships with Don Osterbrock and Mike Seaton.