4.3. Complications in emission-line analysis

Although the hydrogen and helium lines are basically due to a simple recombination process, there are various complications in the precise interpretation of their relative intensities (cf. Davidson & Kinman 1985) even when the non-trivial problems of detector linearity, flux calibration and correction for interstellar reddening have been overcome. These are the following:

1. Unobservable neutral helium in the H⁺ region. Because He is abundant enough to soak up its own ionising photons, the degree of ionisation of trace elements like oxygen or sulphur is not a straightforwardly good guide to this effect, which is mainly governed by the effective temperature(s) of the ionising star(s) (Osterbrock 1974) and negligible when this exceeds 40,000 K or so. Vilchez & Pagel (1988), following earlier work by Shields & Searle (1978) and Mathis (1982, 1985), use a radiation softness parameter (O⁺ / O⁺⁺) / (S⁺ / S⁺⁺) as a measure of the effective temperature and the more recent work avoids cases where the parameter is so large that the corresponding ionisation correction factors (icf) read off from photo-ionisation models (Mathis 1982; Stasinska 1982, 1990) exceed a few per cent and become model-dependent. Because stellar effective temperatures tend to be higher in objects with the lowest heavy-element abundances (e.g. Campbell 1988), there is a danger of a spurious dY / dZ correlation when objects with a large icf are included. Our method could underestimate the icf in cases where one sees two H II regions superposed, a hot one with HeI, H I and [O III] and a cooler one with H I and [O II] but no, or less, HeI (Pena 1986; Dinerstein & Shields 1986; Dufour, Garnett & Shields 1988), but in our hottest objects [O II] is in any case so weak compared to [O III] that this problem cannot lead to an error as large as 5 per cent (Pagel & Simonson 1989). He⁺⁺ is directly seen by virtue of the 4686 line in the hottest objects and is easily allowed for.

2. Collisional contributions to the emission lines. Because the 2³S state of HeI is highly metastable, it builds up a substantial population in H II regions and can be excited by electron collisions to the upper states of the relevant optical lines (Cox & Daltabuit 1971). This possibility was generally discounted because of agreement between triplets and the singlet 6678 in dense planetary nebulae (Peimbert & Torres-Peimbert 1971) until Ferland (1986) drew attention to new quantum-mechanical calculations by Berrington et al. (1985) which implied that the singlet states can also be excited from 2³S. Ferland deduced some remarkably low helium abundances from 5876 after correcting for the effect; these resulted in part from an overestimate of the rates by Berrington et al. (since more exact computation including resonances from enough higher levels is expensive) but in large part also from a poor selection of data from the literature on Ferland's part. Anyway, his results were sensational enough to provoke new, more accurate quantum-mechanical calculations by Berrington & Kingston (1987), giving about half the previous rates, which have been used by Clegg (1987) to provide what seem to be reliable correction formulae depending on electron temperature and density (which therefore need to be accurately measured). Peimbert & Torres-Peimbert (PTP 1987a, b) find that, compared to these formulae, 10830 (2³P^o - 2³S) is still anomalously weak by a factor 2 or so. Clegg & Harrington (1989) consider various effects that could act to depopulate the 2³S state, finding that radiative processes do not do so appreciably at moderate or low densities. They accordingly suggest the presence in the planetaries studied by PTP of a hitherto unknown destruction mechanism (like charge exchange) which would be inoperative at the low densities of extragalactic H II regions. The corrections for 4471 and 6678 do not usually exceed a few per cent, in any case.

3. Fluorescence effects. The large population of 2³S can also lead to enhanced production of emission lines by multiple scattering of ultra-violet photons (Robbins 1970). A line especially sensitive to this is 7065 (3³S - 2³P^o), which is also relatively strongly affected by collisional excitation, but can still be used as a test when this is allowed for. Existing measurements of 7065 (listed by Pagel 1987a) show no evidence for significant fluorescence enhancement of the helium lines from extragalactic H II regions.

4. Underlying absorption lines in the stellar continuum. When an H II region is well resolved, it may be possible to place the slit of the spectrograph in such a way as to record purely nebular emission, in which case this problem does not arise. With H II galaxies, however, which are apparently (and sometimes also intrinsically) very compact, it is impossible to avoid including the spectrum of the embedded star cluster with absorption lines of both hydrogen and helium that are usually unresolved from the nebular emission lines. This problem particularly affects 4471 and it can be quantified in high signal:noise spectra by looking for the neighbouring line 4388, which is comparable or stronger in absorption-line spectra but only 1/7 as strong in emission. Absorption equivalent widths of hydrogen and helium lines relevant to this problem have been calculated from evolutionary stellar population synthesis models by Olofsson (1990).

5. Effects of internal dust. While extinction effects of external dust along the line of sight are readily allowed for by comparison of observed and theoretical Balmer decrements using a standard reddening law, internal dust, when present even in small amounts, can cause substantial complications, e.g. by swallowing up Lyman line photons and invalidating the standard assumption of Case B recombination. This problem is quite significant in the case of the Orion Nebula (Cota & Ferland 1988; Baldwin et al. 1991) but probably much less so in extragalactic H II regions with lower densities and lower abundances. The effect, if present, must vanish in the limit Z = 0, but it gives yet another reason for not including Orion in the regression (12) (cf. Pagel 1982).

6. Absorption by intervening gas. Both the Milky Way and the Earth's atmosphere have absorption lines that can affect HeI 5876 at certain red-shifts, and a particular problem is presented by Galactic NaI for objects with red-shifts in the range 0.002 to 0.004 in which many of the known H II galaxies lie, including both I Zw 18 (Davidson, Kinman & Freedman 1989) and II Zw 40 (discussed above). Because of this, and because of somewhat greater sensitivity to collisional excitation, it is not advisable to try to deduce a helium abundance from 5876 alone.