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From the study of the emission lines produced in galactic and extragalactic gaseous nebulae it has been possible to derive abundances of H, He, C, N, O, Ne, S and Ar. The chemical composition of these gaseous nebulae is needed to understand their physical conditions as well as their evolution. These abundances are also paramount to constrain evolutionary models of stars, galaxies and the universe.

Reviews and textbooks on the physical processes taking place in ionized nebulae have been presented by many astronomers, classic ones are those by Seaton (1960), Aller (1984) and Osterbrock (1989).

Some abundances have been determined based on detailed photoionization models while most abundances have been determined based on simple empirical methods. The input of a photoionization model consists of: a) a stellar radiation field, b) an electron density distribution, Ne(r), (which defines the geometry of the nebula, c) a dust distribution, Nd(r), and d) abundance distributions, which in most cases have been assumed homogeneous. The output consists of: a) a set of line intensities, b) the electron temperature distribution, Te(r), and c) the ionization structure.

The input of an empirical method consists of a set of observed line intensities (in some cases also some continuum intensities). The output consists of quantities averaged over the observed volumes like: a) < Te >, usually derived from the auroral to nebular intensity ratios of [O III] and [N II] lines, b) < Ne >, usually derived from nebular intensity ratios of the [O II], [S II] and [Ar IV] lines, c) a set of average ionic abundances. Not all the ionization stages are observed, therefore to derive the total abundances, ionization correction factors, icf, have to be estimated based on photoionization models or on observations at different distances from the ionizing stars. Some of the icf are almost model independent.

There are discrepancies among different photoionization models of a given object. There are also discrepancies between results derived from photoionization models and empirical methods. Apparently, the main source of the discrepancy is due to the temperature structure of the gaseous nebulae.

In Section 2 I will discuss the temperature structure of gaseous nebulae and its relevance in abundance determinations. Some recent results on planetary nebulae, galactic H II regions and extragalactic H II regions are reviewed in Section 3, 4 and 5 respectively. The conclusions on the physical conditions of gaseous nebulae and on the constraints for the evolution of stars, galaxies and the universe are presented in Section 6.

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