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Observations of edge-on and face-on galaxies clearly provide complementary perspectives of the distribution of the DIG. Specifically, face-on galaxies show the surface brightness of emission lines from the DIG across the face of the galaxy, which makes it possible to explore relationships (if any) between the properties of this plasma and the locations and ionizing fluxes of the hot, massive O stars, which are the most powerful ionizing agents in disk galaxies and are the presumed ionizing source for the DIG. In general, the observations reveal a strong relationship, with the Halpha flux from the DIG comparable to that from the classical O star H II regions in the galaxy.

The presence of diffuse interstellar Halpha emission in face-on spirals was first noted by Monnet (1971), who derived a temperature of 7000 K, an emission measure of about 35 cm-6 pc, and a density near 0.5 cm-3 for the emitting gas. Modern detector technology (i.e., CCDs) has pushed the detection of diffuse H+ to fainter regions and has allowed the study of other emission lines, which has provided insight into the relationship between the diffuse ionization and the O stars.

4.1. Radiation from O stars and the surface brightness of the DIG

Although it was not understood how Lyman continuum photons could have free paths of hundreds of parsecs and more in galaxies with typical interstellar H I densities of ~1 cm-3, ever since the discovery of diffuse H+, O stars have been considered the prime candidate for the ionization. Other known energy sources simply fall short in total power (e.g., Reynolds 1984). A key observational step that connected the diffuse ionized gas to radiation from O stars was carried out by Ferguson et al. (1996), who showed a quantitative relationship between the DIG and the surface brightness distribution of the bright, O star H II regions across a galactic disk. An example of their work is given in Fig. 8 (their Fig. 4a), where it is clear that the mean radial surface brightness profile of the DIG in Halpha emission tracks that of the H II regions. Their study included a careful, quantitative comparison of the energetic requirements for the Halpha emission in the DIG with the ionizing radiation and the mechanical energy inferred to be emitted by the O stars in the H II regions of the two galaxies measured. They found that the mechanical energy clearly fell short, by more than a factor of three. They also found that the maximum contribution of local sources of ionizing radiation in the DIG from stars cooler than spectral type O8 also fell short of the luminosity required, but by a smaller factor. They concluded that the O star populations of the clusters producing the H II regions are the likeliest main source of the radiation that ionizes the DIG.

Figure 8

Figure 8. Deprojected profiles of the (solid) total Halpha surface brightness into (dashed-dotted) H II region and (dashed) DIG emission for NGC 7793. From Ferguson et al. (1996).

In two papers dedicated to testing the hypothesis that escaping Lyman continuum photons from the classical H II regions surrounding O stars can be sufficient to ionize the DIG, Zurita et al. (2000, 2002) took another important step forward by identifying and classifying the H II regions in a set of photometric maps of disk galaxies in Halpha. This process is illustrated in Fig. 9, taken from Zurita et al. (2000), which shows in the upper left, the original continuum-subtracted Halpha image of the nearly face-on spiral galaxy NGC 157, followed clockwise by a schematic representation of the positions and luminosities of the classified H II regions, a surface brightness map of the DIG in Halpha, with the H II regions subtracted off, and finally a map used for quantifying the DIG. In the case of this last frame, the DIG is measured by integrating the Halpha surface brightness over the full disk, using the values outside the H II region boundaries and local mean values inside each H II region. Some key points in the method for deriving these maps and quantifying the DIG emission include the following. First a catalog of H II regions was prepared, using a semiautomatic, but interactive method to measure their Halpha luminosities, effective radii and central positions (Rozas et al. 1999), down to a lower limiting luminosity. These H II regions were delimited and their emission subtracted from the total image by masking those pixels occupied by the H II regions, but with a final refinement that contiguous pixels with surface brightness higher than a set limit are also subtracted off.

Figure 9

Figure 9. Steps in the quantification of the total Halpha luminosity from the DIG for the representative disk galaxy NGC 157. (a) Continuum subtracted Halpha image. (b) Schematic form of H II region catalog, giving position and key to the Halpha luminosity of each region. (c) Diffuse Halpha map after subtracting off the catalogued H II regions. The brightest H II regions indicated by circles. (d) Measurement of upper limit for DIG. H II regions are blanked off, then each is assigned a local value of DIG surface brightness. Ellipse shows limit of integrated DIG flux measured. From Zurita et al. (2000).

This procedure is illustrated in Fig. 10 (Zurita et al. 2000), which shows how this criterion for separating H II region from DIG emission coincides very well with an alternative criterion in which the boundaries of an H II region are defined by a limiting value of surface brightness gradient. Having separated the H II regions, one can then define the total DIG luminosity in one of three ways: (a) integrating the remaining surface luminosity after applying the H II region mask; (b), as in (a) but then adding a contribution from the areas of the H II regions, assuming this is proportional to their projected areas times their local DIG surface brightness, or (c), as in (a) but making the contribution proportional to the area of the H II regions times the mean DIG surface brightness outside the regions across the disk of the galaxy. Modes (a), (b), and (c) give respectively lower limits, upper limits, and approximate estimates for the total DIG emission from the observed galaxies. In Fig. 11, we show the results of this method of estimating the DIG, for six galaxies, shown as the ratio of the DIG Halpha luminosity to the total luminosity for the galaxy plotted in terms of galactocentric radius.

Figure 10

Figure 10. Technique used for separating H II region emission from DIG emission. (a) Portion of Halpha image of NGC 157 with crowded field (on a spiral arm). Grey scale in emission measure. Circles show mean catalogued radii of H II regions. Dashed line at 73 pc cm-6, cut-off applied to avoid contamination of DIG by H II regions. (b) Diffuse emission after subtracting off H II regions and applying surface brightness cut-off. (c) Same portion of image in units of Halpha surface brightness gradient. Applying uniform cut-off at 12.4 pc cm-3 pixel-1 (0.28"/pix) yields H II region boundaries equal to those found in (a), which confirms this separation technique. (d) Map as in (b), but with H II region mask filled at level of local DIG, giving upper limit case for total galaxy DIG luminosity (see text). From Zurita et al. (2000).

We can see that the DIG emits around a half of the total Halpha output, that there are systematic modulations of this tendency with radius, and that there is slight tendency for the fraction to increase with radius. We also note that the projected area of the disk occupied by the DIG is of order 80(± 10)% for all the objects shown in Fig. 11. In a separate study of over 100 galaxies, Oey et al. (2007) found that the amount of DIG Halpha to total Halpha from a galaxy ranged from 20% to nearly 100% with a mean near 60%. Voges (2006) has presented results suggesting an inverse correlation between the DIG Halpha fraction and the star formation rate per unit area.

Figure 11

Figure 11. Radial variation of the ratio of integrated DIG luminosity in Halpha to the total luminosity for six spiral galaxies (within 0.15R / R25 crowding precludes accurate estimates). A canonical value for the integrated ratio of geq 50% is found, with a total fractional area subtended by the DIG of ~ 80%. From Zurita et al. (2000).

4.2. An escape model for Lyman continuum propagation

Given a full catalog of H II region positions and luminosities for a galaxy, one can test the hypothesis that escaping photons from the H II regions cause the ionization of the DIG by modeling the transfer of these photons from their points of origin. This was done in considerable detail by Zurita et al. (2002) for NGC 157. This galaxy was selected because of the availability of a VLA H I map of reasonable resolution, as we will explain shortly. In Fig. 12, we show a comparison between the observed surface brightness distribution in the DIG and one of the simplest models used. In this model 30% of emitted Lyman continuum photons escape from each H II region, and propagate through the DIG isotropically.

Figure 12

Figure 12. Comparison of a DIG model with observations. (left) Modeled surface brightness in Halpha of the DIG in the disk of NGC 157 assuming 30% of Lyc photons escape from each H II region, and a simple propagation law through a (macroscopically) uniform slab model for the disk. The result is a projection in the plane of the predicted 3D Halpha column density. (right) Deprojected image of the galaxy with H II regions masked, and a cut-off of 73 × cosi pc cm-6 applied to limit the H II region contamination of the DIG. This shows the basic similarity between these models and the observed DIG, though further refinements are important (see Fig. 13). From Zurita et al. (2002).

The predicted Halpha surface brightness is derived by summing the contributions to the ionizing radiation field from each of the H II regions. We can see that the result is remarkably similar globally to the observed distribution, and is itself a fair verification of the initial hypothesis. However a more quantitative look at the comparison shows that the ratio between the predicted and observed DIG surface brightness is not uniform on large scales, as would be expected since the initial model assumes a uniform slab structure for the H I involved in converting the Lyman continuum photons to Halpha. The missing structural parameter can be supplied by using the observed H I column density, as shown in Fig. 13, where we can see that in zones of low H I column density the ratio of observed to predicted DIG surface brightness is reduced. Maps of these two quantities give excellent coincidence of features, and go a step further in showing that the principal DIG ionization sources must be the O stars in luminous H II regions. Modeling the effect of clustered supernovae on the distribution of the H I, Clarke and Oey (2002) also found that the resulting clumpiness of the medium had a significant effect on the escape fraction of the ionizing radiation. Zurita et al. (2002) carried out a number of different modeling tests of the basic hypothesis, varying the law relating the escape fraction of ionizing photons with the luminosity of an H II region, and varying the mean absorption coefficient of the inhomogeneous neutral fraction of the DIG. However, they concluded that it was not possible without H I data of improved angular resolution to go further in testing different photon escape laws, or to estimate what fraction of the DIG ionization could be due to mechanisms other than that tested.

Figure 13

Figure 13. Ratios of observed to modeled DIG of NGC 157, for three variant models of photon escape from H II regions, assuming a slab structure to the H I in the disk. (a) Constant fraction of photons emitted by the O stars escape from each H II region. (b) Only H II regions with luminosities higher than a critical value show significant Lyc photon escape. (c) A constant underlying escape fraction for all H II regions plus an increasing increment for H II regions above a set Halpha luminosity. The results are similar for all three. (d) Observed H I column density map (with catalogued H II regions overlaid in black). Note complete coincidence of low zones of observed/modeled ratio with zones of low H I column density, as predicted if photon escape from the H II regions is the main ionizer of the DIG. From Zurita et al. (2002).

4.3. Line ratio studies

There have been relatively few quantitative spectroscopic studies of the DIG in face-on galaxies. A pioneering study of [N II] and Halpha across the face of NGC 1068 was carried out by Bland-Hawthorn et al. (1991), who found very high [N II] / Halpha ratios and discussed possible causes for this high excitation. Hoopes and Walterbos (2003) and Voges and Walterbos (2006) have made the most careful and detailed examinations to date. In Fig. 14, we show the observations of the DIG close to the luminous H II region NGC 604 in the nearby spiral M33 (Hoopes and Walterbos 2003), obtained by placing a slit across the H II region so that it sampled the DIG on either side. This example is representative of their study of the three local face-on galaxies, M33, M51, and M81. We can see that the line ratios, [N II] / Halpha, He I / Halpha, and [O III] / Hbeta, all tend to show higher values in the DIG. The full study includes measurements of these ratios as well as [S II] / Halpha and [S II] / [N II] in H II regions and in the DIG, both in the spiral arms and in the interarm zones in each galaxy. The results were compared with predictions made with "standard" H II region ionizing fields, with varying ionization parameters and stellar photospheric temperatures between 20000 K and 50000 K. There is good agreement for the H II regions but poor agreement for the DIG. They then considered more realistic radiation fields, which take into account the fact that the spectrum of the radiation escaping from H II regions may be different from that from a pure O star (see next section). They modified their spectra accordingly, varying the modeled escape fraction between 30% and 60%, where a lower escape fraction implies a harder spectrum. These results showed better agreement with the DIG observations than the previous set, but the agreement was only fair.

Figure 14

Figure 14. Selected emission line ratios from long slit spectra across the luminous H II region NGC 604 in M33. The solid line is the Halpha surface brightness showing rising to the center of the H II region, and falling to low values in the DIG outside it. Note the tendency of the line ratios to rise in the DIG. From Hoopes and Walterbos (2003).

The authors reached the tentative conclusion that O star photoionization is not the sole mechanism for ionizing and/or heating the DIG, the same conclusion reached by others who have studied these line ratios both in our Galaxy and others (e.g., Wood and Mathis 2004, Reynolds et al. 1999, Rand 1998). This may indeed well be the case; however, before reaching a definitive conclusion, it would be useful to test a modification of the types of models proposed in Hoopes and Walterbos (2003) based on the assumption that not only is the DIG itself inhomogeneous, but so also are the H II regions. The effects of clumping of the interstellar gas on the escape fraction and the spectrum of the ionizing radiation is discussed in more detail below.

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