3.4. Aperture correction, nebular geometry and density inhomogeneities

Observations are made with apertures or slits that often have a smaller projected size on the sky than the objects under study. When combining data obtained with different instruments, one needs to correct for aperture effects. To merge spectra obtained by IUE with optical spectra, one can use pairs of lines of the same ion such as He II 1640 and He II 4686. However, ionization stratification and reddening make the problem difficult to solve. One can also use C III] 1909 and C II 4267, but this involves additional difficulties (see Sect. 3.6). Summarizing, aperture corrections can be wrong by a factor as large as 2 (Kwitter & Henry 1998, van Hoof et al. 2000).

Interpretation of emission line ratios should care whether the observing slit covers the entire nebula, at least in the estimation of error bars on derived quantities. This is especially important when the observations cover only a small fraction of the total volume. Gruenwald & Viegas (1992) have published line of sight results for grids of H II region models, that can be used to estimate the ionization correction factors relevant to H II region spectra observed with small apertures. Alexander & Balick (1997) and Gruenwald & Viegas (1998) have considered the case of PNe, and shown that traditional ionization correction factors may strongly overestimate (or underestimate) the N/H ratio in the case when the slit size is much smaller than the apparent size of the nebula. The ratio N/O is less affected by line of sight effects. The problem is of course even worse in real nebulae than in those idealized models, due to the presence of small scale density variations. Integrated spectra have the merit on being less dependent on local conditions and of being more easily comparable to models. For extended nebulae, they can be obtained by scanning the slit across the face of the nebula (van Hoof et al. 2000, Liu et al. 2000), or by using specially designed nebular spectrophotometers (Caplan et al. 2000).

Tailored modelling taking explicitly into account departure from spherical symmetry is still in its infancy. One may mention the work of Monteiro et al. (2000) who constructed a 3D photoionization model to reproduce the narrow band HST images and velocity profiles of the PN NGC 3132 and concluded that this nebula has a diabolo shape despite its elliptical appearance. For the abundance determination however, which is the topic of this review, their finding has actually no real incidence.

More relevant for abundance determinations are the works of Sankrit & Hester (2000) and Moore et al. (2000), who modelled individual filaments in large nebulae, trying to reproduce the emission line profiles in several lines. Such a method uses many more constraints than classical T_e-based methods to derive abundances, but would need additional line ratios, and especially the T_e indicators, to be validated.

If large density contrasts occur in ionized nebulae, the use of forbidden lines for abundance determinations may induce some bias if collisional deexcitation is important. These biases have been explored by Rubin (1989) and his "maximum bias table" can be used to confine errors in abundances due to these effects.