Difficulties at high metallicity

Obtaining a direct measurement of chemical abundances in H11 regions requires that we have a good idea of the value of the electron temperature, Te. The strengths of the forbidden emission lines (collisionally excited) from various metal ions commonly detected in nebular spectra are strongly sensitive to Te, besides being sensitive to the abundance of the originating ionic species, N(X+i):

since the line emissivity has essentially an exponential dependence on Te:

Taking the ratio of forbidden lines corresponding to atomic transitions that originate from widely separated energy levels, such that their relative population is sensitive to the electron temperature, provides a measure of Te. One uses the ratio of the auroral lines (transitions from the second-lowest excited level to the lowest excited level) to the corresponding nebular lines (transitions from the first excited level to the ground level). The auroral lines are generally quite faint, and relatively high temperatures are required to excite enough atoms via collisions to the energy levels from which these lines originate. The case of oxygen is probably the most well known; specifically, for [O iii] one uses the ratio of X4363 (auroral) to H4959, 5007 (nebular; the ground level is actually split by spin-spin interactions, hence the two nebular lines).

The heart of the problem in the high-metallicity nebular business is illustrated in Figure 17.1. An increase in the metallicity has the effect of increasing the cooling in the nebula, which occurs mostly via line emission from metals, mostly oxygen, first through the [O iii] optical forbidden lines and, at higher abundances (lower temperatures), through the far-IR [O iii] hyperfine transitions at A.A.52, 88 |^m. Figure 17.1 shows that as one moves to low temperatures (say Te < 8,000 K) the [O iii] 4363/(4959 + 5007) line ratio soon becomes very small, due to its exponential dependence. In fact, for extragalactic work the ratio hits the typical limit imposed by the capabilities of current 8-10-m telescopes (represented by the horizontally streched rectangle in Figure 17.1) already for metallicities well below the Solar value (notice the position of the Solar symbol on the dotted curve, around 6,000 K).

Qualitatively the picture remains the same when considering auroral-to-nebular line ratios for other ions; however, we can consider cases in which these ratios are larger, at a given temperature, than in the case of [O iii]. This happens for ions for which the upper level (from which the auroral transition originates) lies at a lower energy above the ground level with respect to the [O iii] X4363 case (5.3 eV), for example for [N ii] X5755 (4.0 eV) and [S iii] A6312 (3.4 eV). Observationally

Figure 17.1. Dependences of commonly used auroral-to-nebular line ratios on electron temperature Te. The arrow points in the direction of increasing metallicity (increased cooling results in lower Te). In the high-metallicity regime, Te is typically below 8,000 K. The Solar symbols on each of the three curves indicate the line ratios observed for extragalactic H ii regions of approximately Solar metallic-ity. The open rectangle represents the current observational limit reached with an 8-m-class telescope. Although there is no hope of being able to measure electron temperatures of metal-rich nebulae from observations of the [O iii] X4363 auroral line, it is possible to derive Te (and therefore abundances) using the auroral lines [S iii] X63l2 and [N ii] X5755 even at metallicities above Solar.

Figure 17.1. Dependences of commonly used auroral-to-nebular line ratios on electron temperature Te. The arrow points in the direction of increasing metallicity (increased cooling results in lower Te). In the high-metallicity regime, Te is typically below 8,000 K. The Solar symbols on each of the three curves indicate the line ratios observed for extragalactic H ii regions of approximately Solar metallic-ity. The open rectangle represents the current observational limit reached with an 8-m-class telescope. Although there is no hope of being able to measure electron temperatures of metal-rich nebulae from observations of the [O iii] X4363 auroral line, it is possible to derive Te (and therefore abundances) using the auroral lines [S iii] X63l2 and [N ii] X5755 even at metallicities above Solar.

this situation creates a big advantage: even at supersolar metallicities ratios such as [S iii] 6312/(9069 + 9532) and [N ii] 5755/(6548 + 6583) are measurable in bright extragalactic H ii regions with current instrumentation. The Solar symbols on the [S iii] and [N ii] curves, representing the typical line ratios measured for Solar-metallicity extragalactic H ii regions (e.g. Bresolin etal. 2005) lie well above the typical observational limit of 8-10-m telescopes. Note that some of the coolest extragalactic nebulae for which a direct Te determination exists have temperatures in the range 5,000-6,000 K.

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