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

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4. Results

There exist good surveys over the UIR bands in the literature (Tokunaga 1997, Geballe 1997) and several other recent studies, like the ones taken with SWS onboard the ISO. The values found for the various peaks of the spectra are collected in Table 1, using the UIR spectral classification schemes from the UIR surveys. Note that the peaks observed are not very sharp, with typical FWHM of 0.05-0.5 µm depending on the wavelength range and the astronomical object. In Table 1, the values given in the publications as the peaks of the broad bands are collected. These peaks are found in different objects, and it should be noted that all these peaks for one band are not found in the same object.


[TABLE]

Table 1. Assignment and classification of the various UIR peaks. Each section of the table indicates one band with transitions from the RM states to an intermediate Rydberg state in M+ (see the text). The spectral types follow the scheme by Geballe (1997) with some additions due to Tokunaga (1997). The wavelengths where peaks are observed are in bold print. The italicized entries are lower wavelength limits for each band. The transitions 200 [FORMULA] for M+ (100 [FORMULA] for M) are considered to be capture of diffusing electrons.


The energy changes following the deexcitation from the RM to a relatively low nR state as in Eqs. (1) and (2) can easily be calculated from the Bohr formula. In the case of the process in Eq. (2), the final state for the electron in a state with quantum number [FORMULA] is the second highest in the atom. Thus, a double charge on the core ion must be used to take into account that the final state is a low Rydberg level, inside the orbit of the highest electron ending up in state [FORMULA]. In Table 1, the transitions in M and M+ matching the observed peaks are given. It is seen that the observed features fall into bands, which are limited towards short wavelengths by a transition from a very high n number around n = 200 to a certain lower n number, between 10 and 22 for most of the bands. This means that there exists a type of band heads at the wavelengths 3.29, 3.87, 4.49, 5.16, 5.87, 6.64, 7.45, 8.30, 9.21, 10.16, and 11.17 µm. Just a few of these low wavelength limits have been observed directly, but the largest UIR peaks which correspond to transitions from n [FORMULA] 60 are just above these values, like 3.3-3.4, 4.6, 5.6, 6.2, 6.9, 7.6, and 11.5 [FORMULA]m. Each band is limited towards long wavelengths by a transition from the lowest stable RM state, of the order of n = 50 (Svensson & Holmlid 1999). The most apparent such peaks are normally 3.53, 5.6, 8.59, 10.4 and 12.7 µm, which correspond to RM excitation states of n = 45, 51, 48, 57 and 60 respectively. These values increase with the lower n value (n = 12, 15, 18, 20 and 22), which is reasonable if the overlap between the two states is considered. It is easily seen that all the observed UIR peaks fall within these bands. The differences in the spectra between different objects and spectral types A - D are believed to be due to real differences in the conditions of the RM. This will be discussed below.

The possible transitions from RM levels down to states in M+ or M thus fall within broad bands, as shown in Table 1. The actual peaks observed in any object must lie within these bands, and that is the case for all observed peaks. However, the actual peak observed in any object is due to the excitation state and other parameters like the density of the RM phase, and can not be predicted at present. The short wavelength limits of the bands can be predicted quite accurately. For example, if the RM level would be n = 300 instead of 200 as in Table 1, the wavelength at 5.16 µm would shift very slightly to 5.14 µm. The long wavelength limit is however more uncertain: a change from n = 46 to 50 for the 6.2 µm band means a change in wavelength of the long wavelength limit from 6.63 to 6.50 µm.

A few special features can be observed directly from Table 1. Peaks have been detected for all the bands with lower n = 12-22, with only n = 13 missing (see further in the discussion section). That also so many odd n values are found means that the transitions definitely are in the ions M+ within the RM. In space, RM is thought to have an excitation level around n = 80, with a lower limit at approximately n = 50. The highest upper level is not known so well, but high excitation levels can only exist at low temperatures due to the low bond strength for high excitation levels. Thus, transitions from n = 200 are considered to correspond to direct electron capture of diffusing electrons within the RM.

To make a detailed comparison with observed UIR spectra, reasonable band shapes have to be used together with band centers from Eqs. (1) and (2). (The observed peak structure interpreted in Table 1 is not used in this case). Since the RM deexcitation bands are expected to be asymmetric (see below), a Gaussian function is not really useful, and a Lorentzian shape is not in agreement with the model assumptions of two-electron processes. Instead, a function similar to a Weibull function is used here, with the form

[EQUATION]

which means that the integral over [FORMULA] from zero to infinity is normalized to unity. Here, [FORMULA] is used in wave numbers. The peak of this distribution is at q. The parameter determining the width of the skewed function in [FORMULA] is t. At t = 60, the FWHM of the distribution is +15,-20 cm-1 at q = 800 cm-1, and +30,-40 cm-1 at 1800 cm-1. This width is reasonable for the simple deexcitations in Eq. (1), while a slightly broader distribution with t = 30 or 20 has been used for the transitions involving also a second electron. In these cases, the distribution for t = 30 has a FWHM of +25,-40 cm-1 at q = 800 cm-1, and +60,-80 cm-1 at q = 1800 cm-1, and for t = 20 a FWHM of +40,-60 cm-1 at q = 800 cm-1, and +100,-130 cm-1 at q = 1800 cm-1. (Note that in the PAH model, a Gaussian profile with a FWHM of 30 cm-1 is added to each measured absorption line (Allamandola et al. 1999)).

In Figs. 3 and 4 a comparison with two spectra (type A and B respectively) also used by Allamandola et al. (1999) is shown. (Note that the upper scale in the figure in Allamandola et al. is erroneous: the largest peak in Fig. 3 in Buss et al. (1993) is at 12 µm or 830 cm-1, not at 900 cm-1 or 11.1 µm as given by Allamandola et al.). The observations are from Buss et al. (1993) and Bregman et al. (1989). The main transitions included are given in the figure captions. The only transitions included in Fig. 4 are such that they correspond to a two-electron process as described by Eq. (2), using intermediate values of RM excitation state (upper level) around 70, increasing with higher n levels for the lower state. The only range where the fit could have been improved substantially is at 8.3 µm, where lower RM states seem to contribute. In Fig. 3 also processes corresponding to electron capture as in Eq. (1) are included in a few sharp peaks, but their total contribution to the signal is very small. Otherwise, just a few transitions are needed to explain the spectrum well. To improve the fits in two band shoulders, small contributions from lower RM states are included in Fig. 3, namely at 8.0 and 12.8 µm.

[FIGURE] Fig. 3. The best fit of the RM emission model (narrow curve) to the observed data from Orion ionization ridge (broad curve) (Bregman et al. 1989, taken from Allamandola et al. 1999) of spectral type A. The width parameter is t = 35 for most transitions. A width of t = 120 is used for the electron capture process, which is barely significant at n = 16 and 22 ([FORMULA] 2%). The contributions for transitions to the various lower states n is given in percent in parentheses: 14 (29.5), 15 (3.0), 16 (15.9), 17 (5.3), 18 (17.7) and 19 (10.6). Two other contributions are included to take into account transitions to lower RM states (see Table 1) at 8.0 (5.9) and 12.8 [FORMULA]m (5.9). Note that the observed signal is lower than the interpolated background around 10 µm, probably due to foreground absorption.

[FIGURE] Fig. 4. The best fit of the RM emission model (narrow curve) to the observed data from IRAS 22272+5435 (broad curve) (Buss et al. 1993, taken from Allamandola et al. 1999) of type B. The width parameter is t = 20. The contributions for transitions to the various lower states n is given in percent in parentheses: 14 (10.5), 15 (7.8), 16 (9.2), 17 (11.8), 18 (17.0), 19 (13.9), 21 (7.8), 22 (15.7), 23 (7.8), 24 (5.9) and 25 (2.0).

To compare the goodness of fits between two different models is certainly not trivial. However, the RM model has the added benefit that it is does not use a large a priori information content like the PAH model with its large number of complex spectra. Instead, the RM model assumes only the Bohr formula for the energy levels of Rydberg states. If the PAH spectra could be reduced to a (presumably large) set of parameters, the comparison of the two models could be made on an equal basis. However, in most cases the simplest model, that is the one with the lowest information content, should prevail. The number of simple parameters actually used for the fits of the spectra in Figs. 3 and 4 is 10-12 intensity parameters (contributions above 2%), plus two width parameters. This should be compared to the fits to the PAH model by Allamandola et al. (1999), where 24 intensity parameters (contributions above 2%) are used. The RM model in total comprises 22 parameters in the spectral range in Figs. 3 and 4, while the PAH model (the whole database) comprises 44 parameters (different molecules and ion states). A comparison of the quality of the fits between Allamandola et al. (1999) and the present study shows that the RM model gives considerably better fits to the two observed spectra chosen by Allamandola et al. Thus, both the number of parameters and the required information content in the RM model is considerably smaller than in the PAH model, with better fits.

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Online publication: June 26, 2000
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