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2.1.4. Photoionization Models

Some have said that the use of photoionization models to estimate nebular abundances is the "last resort of scoundrels", so to speak. I admit that I have used photoionization models to commit offenses in the past. Since Grazyna Stasinska will cover the mechanics of photoionization modeling in detail in her lectures, I will confine my remarks to what I feel are major uncertainties and observational considerations that need to be addressed.

Gas-star geometry: This is an observational consideration, since the geometry influences the ionization parameter. The classical model of an H II region is a uniform sphere with a point source of ionizing photons. High-resolution images of real H II regions show that they are anything but this. The Orion Nebula is better modeled as a blister, with the brightest areas being the photoevaporating surface of molecular cloud. Hubble Space Telescope images of giant H II regions show them to resemble bubbles more than filled spheres, often with a surrounding halo of superbubbles. Young star clusters can often be found outside the main H II region associated with the superbubbles (Hunter et al. 1996). In many cases the ionizing cluster is not centrally condensed, but rather quite loose and extended (for example, NGC 604 and I Zw 18). Even the 30 Doradus nebula, which is dominated by the compact cluster R136a, also includes an extended distribution of O giants, supergiants and Wolf-Rayet stars, plus luminous embedded, possibly pre-main-sequence stars (see Walborn 1991, Bosch et al. 1999). To my knowledge, there has been no investigation of the effect of an extended distribution of ionizing sources on H II region spectra.

The effects of density and density variations are related to this problem. Te, and thus the optical forbidden line strengths, are very sensitive to density because of collisional de-excitation of the far-IR fine structure cooling lines (Oey & Kennicutt 1993). This is most true for metal-rich H II regions, so, for example the relation between R23 and O/H from ionization models depends on the average density asssumed. It is not clear yet that observed integrated densities from, say, the [S II] line ratio accurately reflect mean densities. It is highly likely that a range of densities is more representative of nebular structure, although a functional form is not yet known.

A great deal of work needs to be done in this area.

Wolf-Rayet stars: There are a number of myths about Wolf-Rayet stars and their influence on the H II regions. The first myth is that the presence of Wolf-Rayet stars indicates an age of at least 3 Myr for the ionizing OB association, which is the result obtained from stellar evolution and spectrum synthesis modeling. However, this idea is demonstrated to be not true specifically in the case of 30 Doradus, which contains numerous W-R stars, yet has a color-magnitude age of 1.9 Myr (Hunter et al. 1995). This contradiction is the result of a new population of hydrogen-rich W-R stars noted by de Koter, Heap & Hubeny (1997). Thus we need to reconsider our ideas about using W-R stars to constrain the ages of stellar populations.

The second myth is that W-R stars add a hard component of photons with energies greater than 54 eV to the ionizing radiation field. Again, this is a result from the combination of stellar atmosphere models for Wolf-Rayet stars and spectrum synthesis models. The reality is that only about 1 in 100 W-R stars emits significant amounts of radiation beyond 54 eV. Those W-R stars that are associated with nebular He II emission in nearby galaxies tend to be rare high excitation WN and WO types (Garnett et al. 1991). X-ray binaries are also implicated in nebular He II emission (Pakull & Angebault 1986). We do not yet understand the evolutionary status of these stars, so it is premature to predict them from the stellar evolution models. Indeed, a comparison of photoionization models with the spectral sequence of H II regions indicates that OB cluster models that include such hot W-R stars produce results that are not consistent with observed emission-line trends (Bresolin, Kennicutt, & Garnett 1999).

It is not clear that we know very well at all the ionizing spectral energy distribution of Wolf-Rayet stars, or of O stars for that matter. Stellar atmosphere models which incorporate stellar winds, departures from LTE and plane-parallel geometry, and realistic opacities are still in the development stage, and the effective temperature scale of O stars is still in flux (Martins, Schaerer, & Hillier 2002).

A great deal of work needs to be done in this area.

Dust: Dust has three major effects on the H II region spectrum. First, dust grains mixed with the ionized gas absorb Lyman-continuum radiation. Second, obscuration by dust is typically patchy; differential extinction between stars and gas can affect the emission line equivalent widths. Third, dust can affect the heating and cooling by emitting and recombining with photoelectrons.

The absorption cross-section for standard interstellar dust grains extends well into the EUV spectral region with a peak near 17 eV. Dust grains are thus quite capable of absorbing ionizing photons in the H II regions, and in fact can compete with H and He. When this occurs, the flux of Balmer line emission is reduced over the dust-free case. Figure 3 displays a set of ionization models showing the reduction in Hbeta line emission over that expected from the number of ionizing photons for dusty H II regions. I have assumed standard interstellar grains (Martin & Rouleau 1990), with a dust-to-gas ratio that varies linearly with metallicity over the range 0.1-2.0 solar O/H. The models show that grains can reduce the emitted Hbeta flux by as much as 50%. The amount lost depends strongly on the ionization parameter, increasing for higher ionization parameters. A region with high U is likely to be a young one where the gas is close to the star cluster; thus more Hbeta photons are missed, and EW(Hbeta) reduced the most, for the youngest clusters.

Figure 3

Figure 3. The ratio of emitted Hbeta emission to that predicted from the stellar ionizing photon luminosity as a function of the nebular abundances, showing the effects of absorption of ionizing photons by dust grains. The models are for a stellar temperature of 40,000 K and assume a linear increase of the dust-to-gas ratio with metallicity. From Garnett (1999).

Incidentally, the same phenomenon leads one to underestimate the number of ionizing photons. Therefore, claims of leakage of ionizing photons from H II regions, based on comparing N(Ly-c) from Balmer lines fluxs with that estimated from the OB star population, must be viewed with some skepticism.

Differential extinction between the stars and the gas can also affect EW(Hbeta). Calzetti et al. (1994) found that the obscuration toward starburst clusters tended to be lower than that toward the ionized gas. They determined that, on average, AV toward the stars was about one-half of that toward the gas. This is understandable if the stars have evacuated a cavity in the ionized gas through the combined effects of radiation pressure and stellar winds. The average derived obscuration for H II regions in spirals is AV approx 1 mag. If AV(stars) is only 0.5 mag, then the observed EW(Hbeta) will be about 40% lower than the intrinsic value.

These results suggest that dust effects can easily cause one to underestimate the intrinsic EW(Hbeta), even for metallicities as low as 0.1 solar O/H. This would lead to a systematic bias toward larger ages for the stellar population. One should therefore exercise caution in weighting EW(Hbeta) as a constraint on the synthesis models.

By contrast, the effects of dust on the relative forbidden-line strengths are modest (Figure 4), except at high metallicities (Shields & Kennicutt 1995). One exception is in the case of very hot ionizing stars (for example the central stars of planetary nebulae), where ionization of grains can lead to additional photoelectric heating of the nebula (e.g., Ferland 1998, Stasinska & Szczerba 2001).

Figure 4

Figure 4. The effects of dust grains on forbidden-line strengths in H II regions. Three sequences of models are shown, with Teff = 40,000 K and log U = -3. Solid line plus squares: dust-free models; dashed line + crosses: models with standard ISM grains; dotted line plus triangles: models with Orion-type grains. The effects of grains on the emission-line ratios are seen to be modest. From Garnett (1999).

A great deal of work is needed in this area.

Note on atomic data for ionization calculations: the vast majority of the values used for photoionization and recombination cross-sections are computed, not experimental. This does not mean that their uncertainties are zero! In fact, the best values are probably not accurate to better than 15-20%. Thus, it is unreasonable to expect photoionization models to match real H II region spectra to an accuracy much better than this.

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