9.1. The abundances of O, S and Cl
The values of are shown in Fig. 4. The main source of errors in this determination of the O abundance - excluding those inherent in the method - is introduced by the lines used to derive ([OII ] ) since they are very sensitive to errors in the temperature and are severely affected by sky subtraction in several positions, namely M16-2 and M20-1, 2 and 3. These positions are precisely those where the signal-to-noise ratio is rather low for many lines, and their calculated ionic abundances have the greatest uncertainties. Taking into account these considerations, which reduce the reliability of the values found for in M16-2 and M20, the results are compatible with a total abundance for all the objects in the sample, although the uncertainty of this value is difficult to estimate. This abundance ratio is the most sensitive of those presented here to errors in the temperature: a change of K in would lead to changes in of dex and dex for the positions with higher and lower ionization degree respectively. Anyway, the conclusion of a constant O abundance to within the observational errors seems solid enough and suggests that the other abundance ratios must also be similar in all the objects. This will be used as a working assumption hereafter.
The values obtained for and are presented as a function of in Fig. 5, where and . The small symbols in Fig. 5 show the predictions of the ionization models listed in Sect. 7 after scaling them to reach the best agreement between observations and models: and .
The observational results and the models are compatible with the presence of small quantities of S3+ (produced at 34.8 eV) and Cl 3+ (produced at 39.6 eV) in the areas with high ionization degree. The line [SIV ] 10.51 has been measured by Simpson et al. (1998) in spectra of M42 that sample almost all the ionized nebula. They determine (and from [SIII ] 18.71 ). This small contribution of S3+ to the total abundance can account for the observed decrease in in some areas of M42 A and in M17 and therefore agrees with the observations and the ionization models. On the other hand, there is a weak feature in the spectra of M42 A that could be [ClIV ] . The intensity of this feature implies , suggesting that the contribution of Cl 3+ to the total abundance is negligible for all the regions studied and cannot explain the slight but noticeable decrease of with the ionization degree. Noting that the collision strengths for Cl + (Krueger & Czyzak 1970) are considered to have high uncertainties (% according to Mendoza 1983), a possible explanation would be an error in the ratio . If the real values of were 40% lower than those calculated, all the regions would show a total abundance . Furthermore, note that in such case, the ionization fractions of Cl + and S+ would be similar, as can be expected from the values of their ionization potentials (23.8 and 23.2 eV, respectively).
As for the low excitation objects, the positions in NGC 7635 and M43 show unexpected underabundances in the S ratio. The line used to derive the S++ abundance ([SIII ] ) is, excluding [OII ] , the feature most sensitive to errors in the temperature: a change of K in would lead to changes in of up to dex. [The effect of this change in would be dex for and the rest of the ratios discussed hereafter.] Therefore, the decrease of the S ratio for the lower-ionization areas could be due to a systematic error in the temperature mainly affecting the S results. Note that only is available for deriving ionic abundances in NGC 7635 and M43, and that S+ and S++ have comparable contributions to the S abundance in these objects. The S++ emitting region can be characterized by temperatures below those found with the [NII ] lines, which would increase the derived ratio. The effect could also be due to a failure in the simple assumption of a two-layer emitting region.
Anyway, models and observations agree on and when , so that we can compare the total abundances of , and for the regions of lower excitation. The behaviour of the three abundance ratios for - showing greater spread when the sensitivity to the temperature is higher - agrees with the previous assumption that the values of , and are very similar for all the HII regions considered.
9.2. The abundances of N and Ar
The variations of and as a function of are shown in Fig. 6, along with the predictions of the ionization models scaled to and . The contribution of Ar 3+ (produced at 40.7 eV) to the Ar abundance can be neglected, since the ratio could be calculated in the positions with high ionization degree (M42 A and M17), and implies (see Table 5). The models fit reasonably well the variation of with , suggesting that the value of is similar for all the objects. However, models and observations disagree in the relation of Ar ++ with . The ionization models predict that the contribution of Ar 3+ to the total abundance should be greater than that measured; the models of Stasinska (1990) predict a value as high as for the positions with high ionization degree. For those regions where , the disagreement is greater and arises from the predicted contribution of Ar + to the total abundance. This disagreement could be due to the fact that the ions and form at different conditions: the ratio is inversely proportional to the number of photons with energies above 35.1 eV, whereas the ionization potential of Ar + is 27.6 eV (the ionization potential of N+, showing better agreement with the ionization models in Fig. 6, is 29.6 eV). The ionization conditions giving rise to and are truly similar, and the models fit much better the behaviour of with respect to , as shown in Fig. 7.
On the other hand, the ratio has been calculated by Simpson et al. (1998) in M42 using [ArII ] 6.99 : they find (and from [ArIII ] 8.99 , a value similar to those measured here for M42). Taking this into account, the results found here for N and Ar imply that and in all the objects studied.
9.3. The abundances of C and He
If we continue using the ratio as a reference for the variation of the ionization degree, the disagreement between observations and models increases for C++ (produced at 24.4 eV) and He + (produced at 24.6 eV), as can be seen in Fig. 8. [The predictions of ionization models have been set arbitrarily to the solar abundances in this figure.] The ratio , whose variation reflects mainly the contribution of Cl + (with ionization potential of 23.8 eV), might be more adequate. In fact, the results for and are clearly related to those for , as shown in Fig. 9, but the only models that consider Cl (Stasinska 1990), do not reproduce these relations. Note that the results of ionization models can be expected to be more uncertain for those ions whose ionization potentials are relatively high or low, making their ionization fractions more sensitive to the assumed shape of the radiation field and the density structure of the nebula.
The tight relation between and implies that the He abundance must be the same in all the HII regions studied. However, the disagreement of the ionization models with the observations prevents us from obtaining the real abundance, and only a lower limit can be deduced from the observational results: . The case of C++ is somewhat more complicated, since the relation between and is not as clear as for He + . Taking into account the constant abundances deduced for He and the other elements, we could conclude that the results presented in Fig. 9a imply in all the objects studied, but the possibility suggested by the models cannot be excluded: in general, and an overabundance in M17.
The ratio is the only one of those derived here implying abundances above solar (at least for M17). This could be due to the fact that a recombination line is being used to derive this ratio. Several studies show that the abundances derived for ions like O++ and C++ using recombination lines are higher than those obtained from forbidden transitions (e.g. Peimbert et al. 1993; Esteban et al. 1998, 1999). The C abundance has been derived in M42 and M8 using the collisionally excited lines CII ] and CIII ] . The resulting abundances, in M42 (Walter et al. 1992) and in M8 (Peimbert et al. 1993), are clearly below the value of obtained from CII , with a factor of 2-3 difference in the C++ abundance implied by recombination and collisionally excited lines. These discrepancies are usually attributed to small-scale spatial temperature variations, that would critically affect the abundances derived from the intensity ratio of a line excited collisionally and a recombination line. The effect of considering these temperature variations would be an increase of dex in those abundances relative to H derived here from forbidden lines. On the other hand, several objections have been raised to the existence of strong temperature fluctuations in nebulae, such as (i) the similarity in the abundance ratios derived from optical forbidden lines and temperature-insensitive infrared forbidden lines and (ii) the extreme differences (up to a factor of 15) found between the abundance ratio as derived from recombination and collisionally excited lines in some planetary nebulae (see, for example, Liu 1998). Taken at face value, these objections suggest that the abundances derived from recombination lines may not be reliable. Note that if the values derived here for were scaled down (by factors of 2-3) to the values implied by the collisionally excited ultraviolet lines, the results would imply values for the C abundance close to the interstellar value, in accord with the evidence of the presence of dust grains inside HII regions mixed with the ionized gas (Münch & Persson 1971; Osterbrock 1989; Rodríguez 1996, 1999 in preparation).
© European Southern Observatory (ESO) 1999
Online publication: November 16, 1999