## 4. ResultsThere 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
The energy changes following the deexcitation from the RM to a
relatively low The possible transitions from RM levels down to states in
M A few special features can be observed directly from Table 1.
Peaks have been detected for all the bands with lower 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 which means that the integral over
from zero to infinity is normalized
to unity. Here, is used in wave
numbers. The peak of this distribution is at 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
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. © European Southern Observatory (ESO) 2000 Online publication: June 26, 2000 |