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Astron. Astrophys. 358, 276-286 (2000)

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5. Discussion

The asymmetric broadening observed in the UIR bands is likely due to two effects. The first one is the distribution of the upper excitation level in RM, which should give a broadening of the absorption peaks corresponding to approximately 50 cm-1, or approximately 3% of the wavelength for the range of interest here. This will probably give a slightly asymmetric peak shape, with some tailing to longer wavelengths. The second one is the energy which ends up in the excitation of the second electron involved in the two-electron transition as sketched in Eq. (2). This would give a smaller photon energy, and could thus add to the observed long slope towards longer wavelengths of the UIR bands. The size of this effect is not known accurately, but a likely transition n = 35 [FORMULA] 25 corresponds to slightly less than 100 cm-1, which is of the same size as the half width of most of the UIR bands. Thus, this broadening mechanism is of the correct size. In the study by Allamandola et al. (1999) a broadening was also used, adding a Gaussian with FWHM of 30 cm-1 to the measured absorption lines. The reason for this broadening was stated to be intramolecular energy redistribution in the excited PAH molecules.

In both spectra in Figs. 3 and 4, a pronounced minimum exists around 10 µm. The observed signal even becomes negative in Fig. 3, which can be observed as a signal below the average background signal in Bregman et al. (1989). This effect has been attributed to an absorption in foreground silicate (Mattila et al. 1996). Thus, when the fitted spectra show the same minimum, this is due to overfitting. In the RM model, this means that the very low contributions from some of the transitions in this range are false, but this error is simple to correct when data showing the correct behavior around 10 µm become available. However, it is more difficult to correct this in the case of the PAH model. Thus, if this minimum is really due to foreground absorption, the PAH model is at variance with the correct, but not yet measured signal.

In Table 1, the band corresponding to transitions down to n = 13 close to 4.0 µm is missing. As indicated in the table, this transition is probably overlooked due to overlap with the recombination line Br[FORMULA]. In many studies, the range around 4.0 µm is not well covered, due to apparatus limitations and other expected overlaps as well. For example, Beintema et al. (1996) observe absorption bands at 4.2 µm in one of their objects.

The RM model succeeds in explaining all the UIR bands within a simple formula, using the experimental knowledge about RM. Even if the agreement is satisfactory, the astrophysical background and the actual observational details must also agree with the model if it should be trusted. The main characteristic of the UIR is that all the bands and peaks must agree with one type of molecule. The RM model agrees with this limitation, in a better way than other models. Another limitation is the required relation to the carbon concentration in space (Cohen et al. 1989). This connection is very obvious in the case of RM, since the initial atomic Rydberg states are formed during desorption from carbon particle surfaces, as described in Sect. 2.2. Another limitation often mentioned is that the molecules which should be the carrier of UIR must be very stable and should not be destroyed by high temperatures and large fluxes of ionizing radiation. At first sight, such a requirement may seem correct, but an alternative is to require that the UIR carriers should be easily formed and reformed at high temperatures and large ionizing fluxes. Since RM is formed by radiation of a small enough wavelength to cause desorption atoms or molecules and by moderate heat, and since it will certainly be reformed over and over again with no complicated dead end in the reaction flux like the PAHs (Allamandola et al. 1989), it seems to be the best choice as the UIR carrier under all circumstances. Note that in the laboratory, heating of a carbon or graphite surface always gives Rydberg states and Rydberg cluster formation of alkali metal impurities, despite the relatively high density of possible quenching gas molecules in the vacuum chambers. Thus, the conditions for RM formation are rather weak and easily fulfilled in space, with no complex reaction schemes for its formation which would imply breaking and forming strong bonds.

For a quantitative comparison of the proposed RM model with observations, both the oscillator strengths for the transitions and the column densities of the emitting particles are needed. Unfortunately, it is not possible at present to predict the probability of the processes proposed in Eqs. (1) and (2), since accurate calculations for deexcitation processes in RM are not yet possible. In fact, ordinary quantum mechanics is probably not sufficient to obtain a reliable picture of the details of the RM structure, but the pilot-wave formulation due to Bohm seems to be required. This description of quantum mechanics can describe the Rydberg states correctly in the classical limit, as shown recently by Carlsen & Goscinski (1999), which ordinary quantum mechanics is incapable of doing. A pilot-wave calculation of RM is quite demanding and has not yet been done. Experimental determinations of the oscillator strengths for the transitions will be attempted in the near future. Column densities may on the other hand be estimated from the assumed density of RM in the emitting clouds, corresponding to 106 - 1012 m -3, and from the abundances of non-H atoms for the dominating M+ mechanism in Eq. (2).

In Table 1, the peaks are classified according to the types proposed by Geballe (1997) and Tokunaga (1997). In terms of the peaks observed, the differences between type A and B may not appear large, but the typical shapes in Fig. 3 (type A) and Fig. 4 (type B) show large differences in the intensities of the various peaks. The most obvious difference is that the peaks at 6.2 and 7.6 µm are decreased in type B, while the bands starting at 9.2 and 11.2 µm in Table 1 are much more intense in type B. The reason for this in the RM model is quite simple, since it is only the question of the excitation state and thus also the density of the RM. In type B the transitions start at higher n values than in type A, and thus type B corresponds to a more expanded RM which can only exist if the temperature in the cloud is relatively low. This type of spectrum is usually found in proto planetary nebulas. In type A spectra, the RM is denser, and can exist under the conditions of higher temperatures and larger UV fluxes (Geballe 1997) due to the larger binding energy at the shorter internuclear distances. This corresponds to the most common form of UIR spectra, and it is found for example in planetary nebulas.

The sharp peaks at 3.29 and 11.2 µm in type A spectra indicate transitions from very high n excitation levels in the RM, while it was just concluded that type A spectra correspond to relatively dense RM with a low excitation level. Since these peaks correspond to excitation levels, which are too high to be typical of RM in space, their presence is related to capture of thermal diffusing electrons within the RM. This is also supported by the observation by Tokunaga (1997) that the type A and B spectra are similar but that type A typically show large sharp peaks at 3.3 and 11.2 µm. It should also be noted that such capture processes may as well take place as a transition in M: a diffusing electron in RM may have a low angular momentum, and it can then be captured to form M without involving the next highest electron in the core ion M+ as required for most transitions in Table 1.

One further observation from Table 1 is that it is only at 3.29 µm and at the long wavelength bands from 11.2 µm that this type of transition from a very high upper n value is observed. Such transitions are of course expected for electrons within the RM for the long wavelength transitions, since there will exist an overlap for such transitions. However, in the case of transitions to lower states, the overlap is expected to be very small, and thus the capture of diffusing electrons may be most important in the case of the 3.29 µm peak. In two objects a peak at even shorter wavelengths was observed (Beintema et al. 1996). This value, 3.25 µm is too small to come from even the ionization limit in the RM. Instead, it must correspond to capture of diffusing electrons, in this case of free electrons with an excess energy of 0.04 eV above the ionization limit. This kinetic energy corresponds to a temperature of 460 K, and this does not appear unrealistic for these proto planetary and planetary nebulae.

The very accurate measurements by Beintema et al. (1996) and Molster et al. (1996) give further results which support the RM model. Molster et al. point out that some strong peaks shift by as much as 0.05-0.18 µm between the proto planetary and planetary nebulae. These peaks are in the middle of the bands in Table 1. The shift may in itself be too small to give any precise information, but Molster et al. also note that other peaks such as 3.29, 6.01, 7.60 and 11.04 µm are stable. These peaks are seen by reference to Table 1 to lie almost at the short wavelength limit in their respective bands, and they can thus not change considerably since these limits are fundamental, not dependent of the exact conditions in the RM. This evidence is strongly in favor of the RM model.

Also in the study by Roelfsema et al. (1996) using ISO-SWS, there is very clear evidence of some of the less often observed bands and peaks. For example, the transitions RM [FORMULA] 21 are observed clearly peaking at 11.04 µm. Also, the 8.6 µm peak is shown to vary independent of 7.7 µm. As seen in Table 1, these observations agree well with the expected peaks for the RM model.

There exist two further spectral types, namely type C, which is found in only three sources according to Tokunaga (1997), and type D, which is found in two novae according to the classification by Geballe (1997). Type C shows a prominent peak at 3.53 µm, even larger than the peak at 3.2 µm. The objects showing type C spectra are slightly obscured young stellar objects in dark clouds. From Table 1, the peak at 3.53 µm indicates a very dense RM with a low excitation level, presumably due to large densities and relatively high temperature. This seems to agree with the conditions close to a young star. Type D spectra are similar to type B in the 3 µm band, thus with no sharp electron capture peaks, but agree better with type A in the 11 µm band. Since only two such novae are known, it is difficult to make a detailed interpretation.

An observation which supports the result most obvious from Table 1, namely that all the observed peaks fall within certain bands, is the one given by Roche et al. (1996a). It is shown by the authors that the peaks at 3.4, 5.25 and 11.25 µm have the same shape. From Table 1, these three peaks are close to the limit of large n, which is reasonable due to their similar shapes. All three bands have the same width, namely 50-60 cm-1, corresponding to the distance from n = 200 down to n = 80. The excitation level n = 80 is the most likely upper level of the ordinary RM in space, as also concluded from data on the diffuse interstellar bands (DIBs) (Holmlid 2000). This supports the interpretation in terms of the RM model.

In Table 1, the three last entries correspond to the broader features observed in some objects. The final one, the broad band with its peak at 30 [FORMULA]m (Justtanont et al. 1996, Omont et al. 1995), is proposed to be due to transitions from very high excitation levels or by capture of diffusing electrons down into the lower RM states, not into atomic or ionic states. This may also explain its slightly different, more symmetric shape.

One of the objects studied by Beintema et al. (1996) and Molster et al. (1996) is HR4049, which is a proto planetary nebula. It may be classified with a type C spectrum. This spectrum contains some rather unusual UIR peaks, like 3.25, a large 3.53, 6.01, 8.67, 9.7, 11.05 µm which provide evidence for some of the not so often observed bands in Table 1. It is interesting that it is in these very young stellar objects that all the RM bands appear, while older objects show type A spectra, with just a few of the bands preserved. This may indicate that the ISM is in RM form, and that the star formation with strong UV radiation destroys most of the RM material or the carbon particles required for RM formation. The typical sharp peaks in type A spectra are probably partly due to electron capture of diffusing electrons, and this may indicate that many charged particles reach the RM in type A objects. Thus, the typical type A objects are depleted in their UIR characteristics due to the strong radiation and do not show the full richness of transitions found in the younger objects.

A very interesting study with spatial resolution of the IR emission in one object is reported by Sloan et al. (1993). It is shown that no UIR peaks are observed in the center of the object HD 44179. At about one arcsec from the center, peaks at 7.9 ("7.7"), 8.6, 11.3 and 12.7 µm suddenly appear with relative intensities in this order, and then decay further out. The authors interpret their observations within the PAH model, but the RM model may fit the results even better. RM is formed from hydrogen and other gases at some distance from the object where the temperature and density has fallen enough. Further out, the RM becomes less dense and colder, thus the excitation level is higher giving a more expanded RM. The observed peaks according to Table 1 correspond to transitions 70 [FORMULA] 18, 84 [FORMULA] 19, 140 [FORMULA] 22 (or 70 [FORMULA] 21) and 60 [FORMULA] 22. That the intensity of the 7.7 µm peak drops more quickly than the longer wavelength peaks is expected, since the RM will occupy higher states further out, giving less overlap to low states. The 7.9 µm peak also changes to 7.4 µm further out, which may indicate mainly electron capture at long distance from the center, and the 11.3 µ m peak has an intermediate maximum at some distance from the center of the object, which may indicate that 70 [FORMULA] 21 and 140 [FORMULA] 22 both contribute. The last one of these should contribute more at longer distance, since it corresponds to large excitation levels.

Similar studies with spatial resolution of the UIR bands have also been made on galaxies, for example by Metcalfe et al. (1996) on the dwarf galaxy Haro 3. They show maps of emission in the ranges 7-8.5 µm and 12-18 µm, as well as a ratio map of the intensities in these two spectral ranges. Several UIR peaks are observed, most of them indicating RM of low density and no capture processes, which of course will be unlikely to be observed in such an extended object. The maps of the IR emission are very similar to the H[FORMULA] light maps, which agrees with the description that the RM mainly contains hydrogen. The ratio map shows that the emission around 7.7 µm is stronger in the inner parts of the galaxy, which is the same feature as described above for a much smaller object, caused by the higher excitation level of RM at lower temperature and lower densities further out in the galaxy.

A comparison of peak heights in Mattila et al. (1996) shows that the ratio between the peaks of the 11.3 and 7.7 µm bands is constant for different astronomical objects, while the ratio between the peaks at 6.2 and 7.7 µm is considerably smaller in the emission from the galactic disk. By reference to Table 1 one can conclude that the 6.2 µm peak is due to a transition from a rather low excitation level n = 65. In the galactic disk, the radiation field should be relatively low, and the density and temperature should be low as well. Thus it is likely that the long-lived states at high excitation levels should be more populated, and thus that transitions with longer wavelengths are more probable, which agrees with the observations.

There also exist studies which correlate the UIR band strength to the FIR (far-IR) intensity measured in the range of 100 µm wavelength (Onaka 1997). A very good correlation is found. This is of course difficult to understand if two different types of particles give these contributions, and even more so if PAH gives the UIR bands and small silicate particles give the FIR radiation. From Dwek (1997) it seems that it is not obvious which particle type gives the main contribution at 100 µm. If RM is also the main emitter giving the FIR intensity, the correlation is obvious.

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Online publication: June 26, 2000