5. Physical conditions
Temperatures and densities were calculated with the nebular package implemented in IRAF, with the atomic parameters referenced therein (updated May 1997). The physical conditions were determined from intensity ratios that could be measured with precision, i.e. by comparing relatively bright lines that appear in the same wavelength range.
Electron densities have been obtained from the intensity ratios of the [SII ] and [ClIII ] lines and ; the derived values are listed in Table 3. Because of the weakness of the [ClIII ] lines, the values of are considered more reliable and are used hereafter to determine abundances.
Table 3. Physical conditions
The values of the temperatures and have been calculated from the intensity ratios and , respectively, and are listed in Table 3.
Some of the abundance ratios derived here are very sensitive to temperature; hence, the accuracy of the values of and must be taken into account. The electron temperatures are affected by uncertainties of the atomic data (especially the collision strengths) and by observational errors. The uncertainty affecting existing atomic data cannot be estimated precisely, but the comparison of a given and with other values derived by different methods and numerical schemes, may provide an idea of the overall reliability of those values. In this paper the collision strengths of Lennon & Burke (1994) have been used to derive both temperatures. For comparison, the collision strengths of Baluja et al. (1980, 1981) for O++, and those of Seaton (1975) and Stafford et al. (1994) for N+, will be considered. All these calculations are based on the close-coupling approximation and on the configuration interaction method, but differ in the assumed ionic structure (the number of terms or states) and in the numerical procedures followed. The two sets of data for O++, calculated for the same 12 ionic states, lead to essentially identical results for . However, the calculations available for N+ are based on varied ionic representations: three terms (Seaton 1975), 12 terms (Lennon & Burke 1994) or 13 terms (Stafford et al. 1994). The results of Seaton (1975) are thought to be accurate within 10% (Mendoza 1983; Pradhan & Gallagher 1992), but the three sets of N+ collision strengths differ from each other up to 20% for some transitions and lead to differing : the results of Lennon & Burke (1994) imply temperatures 200 K higher than those from Stafford et al. (1994) and 400 K higher than those of Seaton (1975). Referring to abundances, it should be borne in mind that a 6% uncertainty in both and (implied by 10% uncertainty in the collision strengths) translates into uncertainties between 0.1 and 0.2 dex for most of the abundance ratios determined here.
The effect of random observational errors in the values derived for and is estimated to be below K for most positions. The exceptions are M20 and M16, objects whose spectra show the lowest signal-to-noise ratio. The most extreme case is M16-2, where an uncertainty of K is estimated. On the other hand, the values of are likely to be affected by a systematic error due to the blending of [OIII ] with [FeII ] and OII . The contribution of these lines to the total intensity can be % in M42 (Esteban et al. 1998) and % in M8 (Esteban et al. 1999): such contributions imply that the values of can be 200-300 K lower than those presented here. The effect of this change in is small for most of the abundance ratios discussed here, and remains below 0.1 dex in any case.
The values found for , and are presented as a function of in Fig. 3. No apparent trends can be seen in the relation of with , but both temperatures show loose correlations with the density, which is especially clear for . These loose correlations are satisfied by areas belonging to different HII regions characterized by various excitation conditions (although sharing similar chemical abundances, as shown below) and could be reflecting a real phenomenon. The temperature in a static nebula is determined by the equilibrium between the heating rate due to ionization and the cooling rate due to recombination processes and the nebular radiation, mainly the collisionally excited line radiation. At a given metallicity, the value of the equilibrium temperature is rather insensitive to the stellar radiation field (Osterbrock 1989), and can be expected to increase with density - as in Fig. 3a and 3b - reflecting the effects of collisional de-excitation on the cooling rate.
All the areas show . This result is usually obtained for HII regions and is generally accepted as real, it being considered a consequence of both the hardening of the radiation field in the lower ionization zones where the [NII ] lines are emitted and the low concentration in these zones of O++, whose fine-structure transitions cool the gas very efficiently (Stasinska 1980).
© European Southern Observatory (ESO) 1999
Online publication: November 16, 1999