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Further analysis of nebular emission lines can be categorized as falling in two areas: (1) determination of additional properties intrinsic to the nebular gas, such as elemental abundances, geometry, or total mass; or (2) derivation of properties of the agents or mechanisms responsible for ionizing and heating the gas, such as central star temperatures or shock velocities. To address the type of question, one must first decide what mechanism is responsible for the line emission; this determines the particular parameters to be evaluated. Knowledge of the excitation mechanism is often crucial to deriving meaningful results on quantitative properties of the gas as well.

3.1. Photoionization: Characterizing the UV radiation field

For photoionized nebulae, estimates of the surface temperatures of the central stars have long been made using observations of optical/uv emission lines from ions with different ionization windows. (By "window" I mean the range between the ionization potential of the next lower ionization state chi(Xn-1), which is the minimum energy needed to create Xn, and chi(Xn), the energy it takes to ionize and thus destroy Xn.) In principle, the stellar temperatures can be calibrated empirically, from nebulae with central stars of known surface temperatures, but in practice this is rarely done. Instead, nebular ionization models are usually used at least to extend or interpolate such calibrations, and are often used as stand-alone calibrators. For example, mid-infrared spectra of obscured H II regions sample two strong ionic lines from species with very different lower bounds in chi: [Ne II] 12.8 µm (21.6-40.9 eV) and [S IV] 10.5 µm (34.8-40.7 eV). In H II regions ionized by normal thermal stellar spectra, the observed ratio of these two lines gives a first-order indication of the temperature of whether the central star (e.g., Rank et al. 1978).

When airborne or space infrared observations are available, a larger variety of ions may be sampled, and the application of detailed models is more fruitful. Sequences of model nebulae can be constructed specifically to fit observations of the infrared lines for a particular nebula (e.g., Simpson & Rubin 1984). While this may seem unnecessarily involved, nebular models developed for optical/uv observations have shown that the ionization balance in a nebula is significantly affected by nebular properties. One of the most critical is the local ratio of photons to atoms, or "ionization parameter;" changes in this parameter can mimic or mask changes in the stellar temperature (e.g., Evans & Dopita 1985). Ionization ratios formed from infrared lines are affected by the ionization parameter, the density structure and inhomogeneities, and internal non-gray opacity due to dust (Herter, Helfer, & Pipher 1983) or atoms (e.g., Rubin 1985). Geometry is another potentially important factor. Relaxing the assumption of spherical symmetry, for example in "blister" H II regions located on the edge of a dense cloud, changes the predicted ionization structure (Rubin et al. 1991). Thus, there is not always a unique correspondence between a particular observed line ratio and stellar temperature; determination of the latter will always require additional assumptions or constraints on the nebular structure.

A similar moral appears in the story of the He I 2.06 µm/H I(Br gamma) 2.16 µm line ratio, which is relatively easy to observe in moderately obscured H II regions, and is therefore attractive as a possible indicator of ionizing star properties. It is well known that the ionic abundance ratio He+ / H+ varies with the surface temperature of the ionizing star (e.g., Osterbrock 1989, Fig. 2.5). However, this does not translate in a simple way into the variation of this particular line ratio, because the energy level structure of He I makes it prone to strong radiative-transfer effects (see Osterbrock 1989, Fig. 4.4). Indeed, the strength of the 2.06 µm line is sensitive to nebular geometry, density, and velocity structure as well as to optical depth (Shields 1993). Other infrared He I lines do not suffer from as many problems, but are intrinsically weaker and hence more difficult to observe.

Geometry and density effects can only do so much; the presence of highly ionized species in a photoionized nebula requires a relatively hot source for the radiation field. Highly ionized species are often seen in the optical/uv spectra of planetary nebulae with particularly hot central stars; such nebulae are good places to look for infrared emission from ions of very high ionization potential, sometimes called "coronal lines." Examples include [Ne VI] 7.65 µm (Pottasch et al. 1985), [Si VI] 1.96 µm, and [Si VII] 2.48 µm (Ashley & Hyland 1988).

High ionization species are also found in the ejecta of recent classical nova events. Indeed, infrared coronal lines were first identified in a nova (Grasdalen & Joyce 1976). Since then it has been found that many, if not all, novae show high-ionization infrared lines such as [Si VI], [Si VII], [Al XIII], [Ne VI], etc., starting about 10 to 300 days after visual maximum (see reviews by Gehrz 1988; Dinerstein & Benjamin 1993). The record-setting infrared line is [Si IX] 3.92, requiring 401 eV to produce (Greenhouse et al. 1990). The origin of the coronal ions has been controversial. Greenhouse et al. argue that they arise from gas in collisional ionization equilibrium at coronal temperatures. However, the observed near-infrared line-to-continuum ratios in several recent novae (Benjamin & Dinerstein 1990) support the view that the gas is thermally cool, and the coronal ions are produced through photoionization by the hard radiation field of the hot white dwarf (Williams 1991).

Novae also provide a fascinating opportunity to watch a nebular spectrum evolve, in response to the changing surface temperature of the white dwarf and declining density of the ejecta. During the first year or two after visual maximum, both of these effects drive the ionization balance towards higher ionization states. Figure 6 shows a particularly dramatic example of spectral evolution: Nova Cyg 1992 in the K-band during its transition to the "coronal" phase. If conditions in the ejecta can be properly modeled, the changing spectrum can be used to infer the spectral evolution of the white dwarf. The composition of the ejecta, which are enriched in metals due to the thermonuclear runaway and in some cases may also include material originating from the interior of the white dwarf, is also of interest (Section IV).

Figure 6

Figure 6. Evolution of the spectrum of N Cyg 1992 near 2.0 µm, during the transition to the "coronal phase." Note the declining strength of H I Br delta 1.94 µm and dramatically increasing strength of [Si VI] 1.96 µm on a timescale of a few weeks. (From Dinerstein & Benjamin 1993)

The presence of lines from species with a wide range in ionization potential is often taken as an indicator of ionization by a power-law continuum, for example from an active galactic nucleus (AGN). Several groups have predicted intensity ratios for infrared emission lines, for various models of AGN's, starburst galaxies, and other related objects (Voit 1992; Spinoglio & Malkan 1992). The idea is to construct diagnostic diagrams, by plotting pairs of line ratios against each other, in which these different types of regions can be easily separated and distinguished. The technique is similar to indicators based. on optical and far red lines developed by Baldwin et al. (1981) and Osterbrock, Tran, & Veilleux (1992) respectively. It has also been suggested that the intensities of some infrared coronal lines can be enhanced by laser effects in AGNs (Greenhouse et al. 1993).

3.2. Photodissocation regions

The collisionally excited emission lines in ionized nebulae are populated by interactions with free electrons that are produced by the photoionization of atoms, primarily hydrogen. Photons with energies slightly less than 13.6 eV penetrate somewhat farther, and dominate the energetics of the region just beyond the edge of the Strömgren sphere. The last decade has seen a dramatic growth of interest in such transition regions between ionized nebulae and adjacent molecular clouds, where the gas is warm but mostly neutral. In these regions, the electrons are photoelectrons from grains, or from gaseous Species with ionization potentials lower than that of H, of which the most abundant is neutral atomic carbon. Models of these so-called "photodissociation regions" or PDRs (Tielens & Hollenbach 1985, hereafter TH) predict that their temperatures are of order approx 100-1000K, and that they cool primarily through infrared and submillimeter spectral lines. There are also significant H2 populations in excited vibration-rotation levels in these regions.

The literature contains two types of theoretical studies of PDR's: those that focus on the details of the near-infrared H2 quadrupole emission spectrum, and those that emphasize the energetics, chemistry, and longer-wavelength lines. The first type of model treats the populations of each excited H2 vibrational-rotational level individually, in order to predict accurate intensities of observable emission lines (Black & van Dishoeck 1987; Steinberg & Dalgarno 1989). The two main mechanisms for populating these levels are collisions (as in a thermalized, shock-heated gas), and fluorescence or "uv-pumping." The latter operates by the absorption of uv photons (with 912 Å < lambda < 1100 Å) which excite the molecules to higher electronic states, followed by a radiative cascade through the levels that give rise to the infrared lines. This process was discussed 20 years ago (i.e., Black & Dalgarno 1976), but not actually observed in the interstellar medium until 10 years later (Hayashi et al. 1985; Sellgren 1986). Both the absolute efficiency (line brightness per unit mass) and the relative line intensities of fluorescent H2 emission are dramatically different from those of a thermalized, collisionally-excited spectrum. In particular, only a fluorescent spectrum will show significant emission in lines from high vibrational levels v geq 3. Two examples of "pure" or "radiative" fluorescent regions are the reflection nebula NGC 2023 (Gatley et al. 1987) and the planetary nebula Hubble 12 (Dinerstein et al. 1988; Ramsay et al. 1993). However, if the illuminated material is sufficiently dense, the spectrum will be modified by collisional effects, which tend to thermalize the lowest-lying energy levels (v leq 2) but not the higher vibrational states. This is called a "collisional fluorescent" spectrum by Steinberg & Dalgarno (1989). Another complicating factor is that gas illuminated by X-rays (a harder radiation field than that from ordinary hot stars) may also produce line ratios that are intermediate between the "pure" collisional and fluorescent cases (see article by A. Dalgarno in this volume).

Several techniques have been used to distinguish fluorescent excitation of the H2 lines from emission produced entirely by collisions in shock-heated gas. One method that has been popular because of its simplicity and ease of measurement is to simply take the ratio of the v = 2-1 S(1) line at 2.247 µm to the v 1-0 S(1) line at 2.121 µm. These lines are sufficiently close in wavelength that they can be observed simultaneously with some instruments. Under typical collisional excitation conditions, this ratio is about 1/10; for fluorescence, it is about 1/2. However, this diagnostic is fallible; in particular, at densities approaching 104 cm-3 the v = 2 level may be depopulated by collisions, even if the original "pump" was uv radiation. A more sophisticated approach that requires additional data is to plot the data in a level-population vs. excitation energy diagram (e.g., Hasegawa et al. 1987). In such a diagram, collisionally populated levels will fall along a straight line defined by a single excitation temperature, or a smooth curve for a mixture of thermalized components with a range in temperature (a more realistic case for shocked gas). For a fluorescently excited gas, the vibration or rotation temperatures calculated from different pairs or sets of lines will have different slopes. The difference is illustrated in Fig. 7. A more efficient approach for simply detecting fluorescent emission (as opposed to studying its spectrum) is to observe lines arising from very high v levels, that are absent from a thermal spectrum (e.g., Luhman et al. 1994). Most of the strongest high-v lines, such as the v = 6-4 lines, fall in the J and H bands.

Figure 7

Figure 7. Population/excitation-energy diagrams for fluorescent H2 emission (left), and for shock-excited emission (right). Note the disparate values of Tvib and Trot for fluorescence, and the smooth slope of the thermalized gas. (From Hasegawa et al. 1987).

The second class of PDR models trace the chemistry, heating, and cooling of uv-irradiated molecular clouds, from the ionization front to deep into the cloud. The path length is specified either by N(H) or by AV; the latter is closely related to the increasing extinction seen by the uv photons. Temperatures in these regions range from as high as 1000K to as low as 50K, depending on the physical conditions, and the strongest emission lines are the far-infrared fine-structure lines of [O I] and [C II]. These are the main cooling lines for atomic gas over a very wide range of physical conditions, approximately 20K < T < 2000K and 2 < log n < 6 (see Fig. 10 of TH). As discussed above, the intensity ratios among these lines are diagnostics of temperature and density (e.g., Fig. 3). The two key parameters of PDR models are the intensity of the uv radiation field, expressed in multiples of a "standard" interstellar intensity, denoted chi or G = IUV / IUV(IS), and the gas density in. The model yields the run of temperature for given values of G and n. PDR models have been computed for conditions ranging from dense, clumpy media (Burton, Hollenbach, & Tielens 1990) to low-density extended gas in galaxies (Hollenbach, Takahashi, & Tielens 1991). The predictions of how the line intensity ratios map into parameters G and n have been applied to situations as diverse as galactic nuclei (Wolfire, Tielens, & Hollenbach 1990; Carnal et al. 1994) and planetary nebulae (Dinerstein et al. 1995b).

3.3. Shocks

The ultimate energy source for the collisionally excited emission lines in ionized nebulae and photodissociation regions is the radiation field, although collisions are the proximate cause of the line emission. An alternate heating mechanism is the mechanical action of interstellar shocks (supersonic compressions). Conditions in the "post-shock" region, the material that has already passed through the shock, depend on the shock velocity vs and the "pre-shock density" n0 (the initial density of the gas before it encounters the shock). These are the two primary parameters that are usually extracted from attempts to fit observations of shock-produced emission lines. The ionization, chemical, and thermal structures of the shock and post-shock zone are also affected by the magnetic field strength. Shocks are classified as "J-type" or "C-type" depending on whether there is a discontinuity or "jump" (J) in the gas properties at the interface, or a gradual or "continuous" (C) transition between the pine- and post-conditions (Draine 1980; McKee, Cheinnoff, & Hollenbach 1984). Recent reviews of the theory of interstellar shocks have been presented by Shull & Draine (1987) and Draine & McKee (1993).

Relatively slow shocks (vs leq 50 km s-1) moving into molecular clouds cool primarily through infrared and submillimeter lines of neutral and molecular species, such as [O I] 63, 145 µm, [C I] 370, 610 µm, and, at vs geq 10 km s-1, pure-rotation transitions of H2 (Draine, Roberge, & Dalgarno 1983). The relative strengths of the different lines vary with vs, n0, and the shock type and structure. Given a set of models, the shock parameters can be constrained by plotting the loci of observed line ratios in (vs, n0) phase space (e.g., Fig. 6 of McKee, Chernoff, & Hollenbach 1984). Faster shocks dissociate the H2 molecules, produce a high-temperature zone that illuminates the pine-shock gas with uv radiation (the radiative "precursor"), and ionize some species (Hollenbach & McKee 1989). In such cases the H2 molecules may re-form on the grain surfaces after the shock passes, and be released into the gas phase. When a number of different lines are observed, the level populations can be compared with the predictions of shock models in order to estimate the magnetic field strength and probe the detailed shock physics (e.g., Brand et al. 1988).

Supernova remnants (SNRs) are an obvious site of fast interstellar shocks. An interesting, still unsolved, puzzle is the extreme strength of the near-infrared [Fe II] lines in SNRs. This phenomenon was first noticed in IC 443, where the 1.64 µm [Fe II] line vastly outshines H I Br gamma (Graham, Wright, & Longmore 1987). Indeed, the value of this ratio in SNRs exceeds its value in H II regions by a factor of about 500! The dilemma is: can the strength of the [Fe II] lines be explained entirely by the ionization structure of the post-shock region, or it is necessary to invoke grain destruction by the shock, liberating Fe atoms and thereby enhancing the gas-phase Fe abundance? A further complication is that strong [Fe II] emission may also be produced by photoionization by a power-law continuum, as in the Crab Nebula (Graham, Wright, & Longmore 1990), and possibly AGN (see Section V). Observations of multiple [Fe II] lines can constrain the physical conditions (Section II), and in combination with H2 lines, may make it possible to distinguish among the different proposed mechanisms for enhancing the [Fe II] emission (Graham et al. 1991; Oliva, Moorwood, & Danziger 1991).

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