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The measurement of nebular chemical abundances that are free of significant systematic uncertainties remains an unsolved problem in astrophysics, despite decades of observational efforts to investigate the emission-line properties of Galactic and extragalactic H ii regions. Many authors (among others: Bresolin, Garnett and Kennicutt 2004, Kewley and Ellison 2008; López-Sánchez et al. 2012) have addressed this issue, showing how the various emission line diagnostics and the different calibrations proposed in the literature for these diagnostics are afflicted by systematic variations on the derived oxygen abundances, that reach up to 0.7 dex. 1 This problem, of course, affects not only the investigation of ionized nebulae in the local Universe, e.g., for the analysis of abundance gradients in spiral galaxies (Vila-Costas and Edmunds 1992; Zaritsky, Kennicutt and Huchra 1994; Kennicutt, Bresolin and Garnett 2003; Sánchez et al. 2014; Ho et al. 2015; Bresolin and Kennicutt 2015), but also the myriad of studies concerning the chemical composition of star-forming galaxies, notably those at high redshifts (e.g., to investigate the mass-metallicity relation), that rely on the local calibrations, and the cosmic evolution of metals (Tremonti et al. 2004; Erb et al. 2006; Maiolino et al. 2008; Mannucci et al. 2010; Zahid et al. 2013; Sanders et al. 2015, to cite only a few).

In order to derive reliable chemical abundances of ionized nebulae it is necessary to have a good knowledge of the physical conditions of the gas, in particular of the electron temperature Te, because of the strong temperature sensitivity of the line emissivities of the various ions. An excellent source on the subject of deriving oxygen abundances in ionized nebulae is the monograph published by Stasińska et al. (2012). Nebular electron temperatures can be obtained through the classical, so-called direct method (Menzel, Aller and Hebb 1941), utilizing emission lines of the same ions that originate from different excitation levels, and in particular from the ratio of the (collisionally excited) auroral [O iii] λ4363 and nebular [O iii] λλ4959, 5007 lines. In the case of high-excitation (low-metallicity) extragalactic H ii regions and planetary nebulae the [O iii] λ4363 line is often detected, but it becomes unobservable as the cooling of the gas becomes efficient at high metallicity, or whenever the objects are faint, so that properly calibrated strong-line abundance diagnostics become necessary in order to infer the oxygen abundances. However, even for nebulae where [O iii] λ4363 can be observed, a poorly understood discrepancy exists between the nebular abundances based on the direct method and those obtained from emission line strengths calibrated via photoionization model grids (McGaugh 1991; Blanc et al. 2015; Vale Asari et al. 2016). A 0.2–0.3 dex discrepancy (Te-based abundances being lower) is also found when using the weak metal recombination lines, in particular the O ii lines around 4650 Å, instead of the collisionally-excited lines (García-Rojas and Esteban 2007; Esteban et al. 2009; Toribio San Cipriano et al. 2016). On the other hand, comparisons of stellar (B and A supergiants) and nebular chemical compositions in a handful of galaxies (see Bresolin et al. 2009a) provide a generally good agreement when the nebular abundances are calculated from the direct method, at least for sub-Solar metallicities.

Despite the somewhat unsatisfactory situation illustrated above, we can still derive robust results concerning the metallicities of outer disk H ii regions. As will become apparent later on, it is important to highlight two results. Firstly, radial abundance trends in spiral disks are generally found to be qualitatively invariant relative to the selection of nebular abundance diagnostics, although different methods can yield different gradient slopes (see Bresolin et al. 2009a; Arellano-Córdova et al. 2016). Secondly, O/H values that are derived from direct measurements of Te or from strong-line diagnostics that are calibrated based on [O iii] λ4363 detections, lie at the bottom of the possible abundance range, when compared to metallicities derived from other diagnostics, such as those based on theoretical models.

The literature on nebular abundance diagnostics is vast (a recent discussion can be found in Brown, Martini and Andrews 2016), and for the purposes of this review it is important only to recall a few of the most popular ones, and (some of) their respective calibrations:

  1. O3N2 ≡ log[([O iii] λ5007 / Hβ) / ([N ii] λ6583/Hα)], calibrated empirically (i.e., based on Te-detections in H ii regions of nearby galaxies) as given by Pettini and Pagel (2004) and, more recently, by Marino et al. (2013).
  2. N2O2 ≡ [N ii] λ6583 / [O ii] λ3727, calibrated from photoionization models by Kewley and Dopita (2002) and empirically by Bresolin (2007). Bresolin et al. (2009b) showed that these two calibrations yield abundance gradients in spiral disks that have virtually the same slopes, despite a large systematic offset.
  3. N2 ≡ [N ii] λ6583 / Hα, calibrated by Pettini and Pagel (2004) and Marino et al. (2013).
  4. R23 ≡ ([O ii] λ3727 + [O iii] λλ4959, 5007) / Hβ (Pagel et al. 1979). Many different calibrations have been proposed through the years (e.g., McGaugh 1991; Kobulnicky and Kewley 2004). This diagnostic can be important in order to verify whether the metallicity gradients derived from other strong-line techniques, mostly involving the nitrogen [N ii] λ6583 line, are corroborated by considering only oxygen lines instead. Unfortunately, the use of this indicator for abundance gradient studies is complicated by the non-monotonic behaviour of R23 with oxygen abundance. The simultaneous use of a variety of diagnostics, when the relevant emission lines are available, alleviates this problem. The empirically calibrated P-method (Pilyugin and Thuan 2005), and some related diagnostics (e.g., Pilyugin and Grebel 2016) also make use of both the [O ii] and [O iii] strong emission lines.

To summarize, a variety of optical emission-line diagnostics are available to derive the metallicities (oxygen abundances) of extragalactic H ii regions. Due to poorly known aspects of nebular physics (e.g., temperature fluctuations), absolute metallicities remain a matter of debate, especially at high (near Solar) values. On the other hand, relative abundances within galaxy disks are quite robust. Te-based oxygen abundances lie at the bottom of the distribution of values obtained from the set of metallicity diagnostics currently available.

1 In the literature measuring the metallicity of an H ii region is equivalent to measuring its oxygen abundance O/H, since O constitutes (by number) approximately half of the metals. The standard practice is to report the value of 12 + log(O/H). The Solar value used for reference is taken here to be 12 + log(O/H) = 8.69, from Asplund et al. (2009). Back.

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