A case of failure of Tebased abundances metalrich giant H II regions

Until recently, it was not possible to measure the electron temperature in metal-rich H II regions. The usual temperature diagnostics involve weak auroral lines, which easily fall below the detection threshold at low temperatures. With very large telescopes, such temperature-sensitive line ratios as [O iii] A4363/5007, [N ii] A5755/6584 and [S iii] A6312/9532 can now be measured even at high metallicities (e.g. Kennicutt et al. 2003, Bresolin et al. 2005, Bresolin 2007). However, due to the large temperature gradients expected to occur in high-metallicity nebulae, which are a consequence of the extremely efficient cooling in the O++ zone due to the infrared [O Ill] lines, [O Ill] A4363/5007 does not represent the temperatures of the O++ zone. As a consequence, the derived abundances can be strongly biased, as shown by Stasinska (2005). The magnitude of the bias depends on the physical properties of the HII region and on which observational temperature indicators are available.

A further problem in the estimation of Te at high metallicity is the contribution of recombination to the intensities of collisionally excited lines, which becomes important at low values of Te. For example, the contribution of recombination from O++ to the intensity of [OII] can be very important. It can be corrected for by using the formula given in Liu et al. (2000), provided that the temperature characteristic of the emission of the recombination line is known. If the temperature is measured using ratios of CELs only, that is not the case.

1.3.2.2 Statistical methods

In many cases, the weak [O Ill] A4363 or [NII] A5755 lines are not available because either the temperature is too low or the spectra are of low signal-to-noise ratio, or else the data consist of narrow-band images in the strongest lines only. Then, one may use the so-called "strong-line methods" to derive abundances. Such methods are only statistical, in the sense that they allow one to derive the metallicity of an H II region only on the assumption that this H II region shares the same properties as those of the H II regions used to calibrate the method. In practice, such methods work rather well for giant H II regions, since it appears that giant HII regions form a narrow sequence (see e.g. McCall et al. 1985), in which the hardness of the ionizing radiation field and the ionization parameter are closely linked to the metallicity. Indeed, an increased metallicity enhances the metal line blocking of the emergent stellar flux in the extreme ultraviolet and softens the ionizing spectrum. In addition, the pressure exerted on the nebular gas increases with the strength of the stellar winds, which are related to metallicity, and this in turn decreases the ionization parameter (Dopita et al. 2006).

Unlike direct methods for abundance determinations, statistical methods have to be calibrated. The reliability of these methods depends not only on the choice of an adequate indicator, but also on the quality of the calibration. This calibration can be done using grids of ab-initio photoionization models (McGaugh 1991), using a few tailored photoionization models (Pagel et al. 1979), abundances derived from direct methods (Pilyugin & Thuan 2005), or objects other than HII regions thought to have the same chemical composition (Pilyugin 2003).

The oldest and still most-popular statistical method is the one based on oxygen lines. Pagel et al. (1979) introduced the ([OII] A3727 + [O Ill] A4959,5007)/H|3 ratio (later referred to as R23 or O23) to estimate O/H. This method has been calibrated many times, with results that may differ by about 0.5 dex. McGaugh (1994) and later Pilyugin (2000, 2001) refined the method to account for the ionization parameter.

Many other metallicity indicators have been proposed: [OIll] A5007/[NII] A6584 (O3N2) by Alloin et al. (1979); [NII] A6584/H|3 (N2), by Storchi-Bergmann et al. (1994); ([SIII] A9069 + [SII] A6716, 6731)/Ha (S23) by Vilchez & Esteban (1996); [NII] A6584/[O II] A3727 (N2O2) by Dopita et al. (2000); [Ar Ill] A7135/[O Ill] A5007 (Ar3O3) and [SIII] A9069/[O Ill] A3869 (S3O3) by Stasinska (2006); and [NeIll] A9069/[O II] A3727 (Ne3O2) by Nagao et al. (2006). The metallicity indicators proposed until 2000 have been compared by Perez-Montero & Diaz (2005). However, all those methods will have to be recalibrated when the emission-line properties of the most-metal-rich H II regions are well understood, which is not the case at present.

A few comments are in order. First, any method based on the ratio of an optical CEL and a recombination line (e.g. O23 or S23) is bound to be double-valued, as illustrated e.g. by Figure 7 of Stasinska (2002). This is because, at low metallicities, such ratios increase with increasing metallicity, whereas at high metallicities they decrease with increasing metallicity due to the greater cooling by infrared lines, which lowers the temperature below the excitation threshold of optical CELs. In such circumstances, external arguments must be relied upon to find out whether the object under study is on the "high-abundance" or "low-abundance" branch. The commonest argument is based on the [NII] A6584 line. The reason why this argument works is that the N/O ratio is observed to increase as O/H increases, at least at high metallicities. Besides, high-metallicity H II regions tend to have lower ionization parameters, favouring low-excitation lines such as [NII] A6584. The biggest problem is at intermediate metallicities, where the maxima of O23 and S23 occur and the metallicity is very ill-determined. By using both O23 and S23 indices at the same time, it would perhaps be possible to reduce the uncertainty.

Methods that use the [NII] A6584 lines have another potential difficulty. The chemical evolution of galaxies changes the N/O ratio in a complicated and non-universal way. Therefore, a calibration is not necessarily relevant for the group of objects under study.

Perhaps the most satisfactory methods, on the theoretical side, are the ones using the Ar3O3 or S3O3 indicators, since these indicators are monotonic and work for well-understood reasons, which are directly linked to metallicity.

Conversely, the Ne3O2 index, which is seen to decrease as metallicity decreases, behaves in such a way only because metal-richer giant H II regions happen to be excited by a softer radiation field and have a lower ionization parameter. This is a very indirect metallicity indicator!

It is important to be aware that, in principle, strong-line methods can be safely used only when applied to the same category of objects as was used for the calibration. The meaning of the results in the case of integrated spectra of galaxies, for example, is far from

Figure 1.1. Spectral energy distributions (SEDs) for effective temperatures corresponding to massive stars (left) and central stars of planetary nebulae (right). The dotted line indicates the position of the ionization potential of hydrogen; the full line indicates the wavelength of the V filter.

Figure 1.1. Spectral energy distributions (SEDs) for effective temperatures corresponding to massive stars (left) and central stars of planetary nebulae (right). The dotted line indicates the position of the ionization potential of hydrogen; the full line indicates the wavelength of the V filter.

obvious in an absolute sense. Such spectra contain the light from HII regions differing in chemical composition and extinction as well as the light from the diffuse ionized interstellar medium. In addition, inclination effects may be important. A few studies have addressed these issues from an observational point of view (Zaritsky et al. 1994, Kobulnicky et al. 1999, Moustakas & Kennicutt 2006), but clearly the subject is not closed.

A further step in strong-line abundance determinations has been made by using ratios of line equivalent widths (EWs) instead of intensities (Kobulnicky et al. 2003). The advantage of using equivalent widths is that they are almost insensitive to interstellar reddening, which allows one to apply the method even when reddening corrections are not available, especially at redshifts larger than 1.6. The reason why equivalent widths work well for integrated spectra of galaxies is that there is empirically a very close correlation between line intensities and equivalent widths, meaning that, statistically, stellar and nebular properties as well as the reddening are closely interrelated.

1.3.3 Estimation of the effective temperature of the ionizing stars T* from the Zanstra method. This method, proposed by Zanstra (1931), makes use of the fact that the number of stellar quanta in the Lyman continuum, normalized with respect to the stellar luminosity at a given wavelength, is an increasing function of the effective temperature. This is illustrated in Figure 1.1 (based on modern stellar model atmospheres). In practice, it is the luminosity of the Hp line which is the counter of Lyman-continuum photons. This assumes that all the Lyman-continuum photons are absorbed by hydrogen. This assumption breaks down in the case of density-bounded nebulae or of nebulae containing dust mixed with the ionized gas. In real nebulae, some Lyman-continuum photons are also absorbed by He0 and He+. However, recombination of these ions produces photons that are able to ionize hydrogen, so the basic assumption of the Zanstra method is generally remarkably well fulfilled. Of course, the value of the effective temperature, T*, obtained by the Zanstra method will depend on the model atmosphere used in the derivation.

For very hot stars, such as the central stars of planetary nebulae, one can also define a He+ Zanstra temperature, using the He II A4686 flux as a measure of the number of photons with energies above 54.4 eV.

100 200 T [kK]
100 200 T. [kK]
100 200 t. [kK]

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