5 Discussion and summary

We have decomposed the ISO-SWS spectra of a number of objects covering a wide range of excitation conditions in order to study the individual profiles of the Aromatic Infrared Bands (AIBs) between 3 and 13 $\mu$m. All spectra have been decomposed coherently into Lorentz profiles and a broadband continuum. We find that the individual profiles of the main AIBs at 3.3, 6.2, 8.6 and 11.3 $\mu$m are well represented with at most two Lorentzians. The 7.7 $\mu$m-AIB has a more complex shape and requires at least three Lorentz profiles. We find that the AIB positions and widths are stable to within a few cm_1 (see Table 2) over a range of radiation field hardness ( $T_{\rm eff}=23\,000$ to 45000 K) thus confirming results gathered with data at lower spectral resolution (Boulanger et al. 1998a; Uchida et al. 2000; Chan et al. 2000). This spectral decomposition with a small number of Lorentz profiles implicitly assumes that, (i) the AIBs arise from a few vibrational bands common to many carriers and, (ii) that most of the bandwidth arises from a single carrier. Boulanger et al. (1998b) recently proposed that the AIBs are the intrinsic profiles of resonances in small carbon clusters containing more than 50 C-atoms. This interpretation can be tested by comparing the AIB profile parameters (band position and width) given in this work to laboratory data on relevant species when it becomes available.

This spectral decomposition, which separates the AIB emission from the underlying continuum, allowed us to do a detailed comparison of the observed AIB spectrum with the predictions of the PAH model where the AIB carriers are free-flying aromatic molecules emitting during temperature fluctuations. This model uses recent laboratory data and assumes that PAHs are predominantly in cationic form as is expected from theoretical work (Bakes & Tielens 1994; Dartois & d'Hendecourt 1997). Within this framework, the position and width of the AIBs are rather explained by a redshift and a broadening of the PAH vibrational bands as the temperature of the molecule increases (Joblin et al. 1995). The observed similarity in the AIB profiles thus requires that some process renders the temperature distribution of PAHs rather constant in the interstellar regions considered here. We first derived the temperature distribution for a population of interstellar PAHs. In particular, we show that the hot tail of the temperature distribution of PAHs (which determines the AIB spectrum) depends sensitively on $N_{\min}$ and $T_{\rm eff}$ which are respectively the size of the smallest PAH (in terms of the number of C-atoms in the molecule) and the effective temperature of the exciting radiation field. The size of the largest PAH, $N_{\max}$ (by number of C-atoms), and the index of the power law size distribution (expressed in terms of the number of C-atoms per molecule), $\beta$, were found to have little impact on the overall AIB emission.

We compared our model results to the data in the two extreme cases of our sample: NGC 2023 ( $T_{\rm eff}=23\,000$ K) and M17-SW ( $T_{\rm eff}=45\,000$ K). We are able to reproduce the spectral distribution of the AIB emission with $N_{\min} = 20$ in NGC 2023 and $N_{\min} = 30$ in M17-SW and a PAH abundance amounting to 10 and 8% of the interstellar carbon (these latter values are in good agreement with the constraints set by the extinction curve, Joblin et al. 1992; Verstraete et al. 1992; and the infrared emission, Désert et al.  1990. An abundance twice as high is required in the case of the cold interstellar medium, Dwek et al. 1997). The minimum PAH size $N_{\min}$ was found from the requirement that the observed 3.3/11.3 $\mu$m-band be well matched. This change in $N_{\min}$ may reflect the enhanced photodestruction rate of small PAHs in regions with harder radiation fields (small PAHs reach higher temperatures and evaporate efficiently). Using the same $N_{\min}$-values, we find that all AIB profile shapes, except for the 8.6 $\mu$m-band, can be explained with the temperature dependence of the band position and width measured in the laboratory. We also show that the PAH size distribution must be very steep ( $\beta =-3.5$) in order to account for the observed bandwidths: in our model representation, the AIB profiles are thus mostly contributed to by small PAH species. The case of the 8.6 $\mu$m-band is anomalous: first, the laboratory cross-section is 3 times too weak to explain the observed AIB ratios; in addition, we find that the broadening of this band with the temperature should be 5.5 times faster in order to match the profile width seen in the SWS data. More laboratory work is required to explain this issue.

In summary, using the present best knowledge of PAH spectroscopy, it is possible to account for the AIB spectrum towards bright interstellar objects where the fraction of singly-ionized PAHs is high. We emphasize that both the spectral shape of the AIB spectrum as well as the individual AIB shapes are explained consistently with a single set of parameter ($N_{\min}$ and $\beta$) values. In this context, the remarkable stability of the AIB profiles arises if the hot tail of the PAH temperature distribution remains essentially the same, whatever the exciting radiation field (the low-temperature side corresponding to the larger molecules is practically unaffected by changes in the radiation field). This requirement is naturally met while considering the photodestruction of PAHs: when the energy per bond (which is directly proportional to the molecular temperature) is sufficient the molecule efficiently loses its atoms. A consequence of this is that interstellar PAHs would predominantly be destroyed by thermal evaporation (photo-thermo-dissociation, see Léger et al. 1989a) rather than non-equilibrium processes like direct photodissociation (Buch 1989) or Coulomb explosion (Leach 1989).

These results must however be placed in the broader context of ISO observations which include less irradiated regions ($\chi = 1$ to 1000). Indeed, ISOCAM-CVF and ISOPHOT-S spectra of faint AIB emission highlight the pre-requisites of this work. Namely, two strong assumptions have been made in the present model:

1.

the behaviour of the band profiles with the temperature (measured on small molecules only, $N_{\rm C}\leq 50$) is the same for all PAH sizes. This assumption applies for all the AIBs except the 3.3 $\mu$m: in that case the band profile is actually dominated by the contribution of small species (see Fig. 8b);

2.

all PAHs have the infrared emissivity of singly ionized cations.

Assumption 1 is questionable because the intrinsic bandwidth ( $\Delta\nu_0$, see Sect. 4.4.2) depends on the density of states and on the rate of internal conversion processes (e.g. , Léger et al. 1989a). In particular, at a given internal energy of the molecule, the density of vibrational states is known to increase steeply for larger and larger molecules (e.g. , Cook & Saykally 1998). Many isoenergetic molecular levels may then couple together and eventually lead to a decrease of the level lifetime (Smalley 1983). Hence, relaxing the first assumption will probably result in a significant broadening of the model band profiles; this will require a larger minimum PAH size in order to reproduce the observed width of AIBs. Increasing $N_{\min}$, the 3.3 $\mu$m-band emission will decrease rapidly because larger (colder) molecules emit more at longer wavelengths and we will then fail to match the intensity of the observed 3.3 $\mu$m-band. This problem will not be alleviated by assuming a PAH ionized fraction of less than 1, (i.e. , not all PAHs are cations): neutral PAHs, which have strong C-H/C-C band ratios, (typically 10 times larger than in cations, Langhoff 1996; Pauzat et al. 1997; Hudgins & Sandford 1998), will not reproduce the observed 11.3/7.7 $\mu$m-band ratio. This relates to the second assumption of the present model.

We have assumed that PAHs are all singly ionized (cations) throughout our data sample. Such a choice is required to reproduce the observed band ratios, in particular the C-H/C-C ratio (Langhoff 1996; Allamandola et al. 1999). Yet, this requirement is not fully consistent with theoretical predictions (Dartois et al.  1997) of the PAH ionized fraction along our lines of sight, namely, 0.5 (50% of PAHs are cations). Furthermore, this problem becomes even more acute in the context of other observations spanning a broader range of physical conditions: ISOCAM-CVF and ISOPHOT-S data (Boulanger et al. 1998a, 1999; Chan et al. 2000; Miville-Deschênes et al. 1999; Onaka et al. 1999, 2000, Onaka 2000; Uchida et al. 1998, 2000) obtained towards regions with $\chi$ = 1 to 10⁵ (from the diffuse interstellar medium to H II  region interfaces and reflection nebulae) show that the C-H/C-C ratio of the AIBs is roughly constant and always corresponds to that of PAH cations. Over such a large range of UV radiation flux, the state of PAHs is actually expected to change from fully neutral to fully ionized. The ionized fraction of PAHs is determined by the value of $\gamma=\chi\,\sqrt{T}/n_{\rm e}$ with T the gas temperature and $n_{\rm e}$ the electron density (this parameter is proportional to the ratio of the ionization rate to the recombination rate of PAHs, Bakes & Tielens 1994). To keep the AIB band ratios constant, and hence the ionized fraction of PAHs, requires that the ratio $\sqrt{T}/n_{\rm e}$ can vary over five orders of magnitude in order to compensate the variation of $\chi$. In reality, T probably does not change by more than 2 orders of magnitudes: then $n_{\rm e}$, which reflects the density variations mostly, would have to vary by three orders of magnitude across the regions observed to keep $\gamma$ constant. Such large density contrasts at large scale are at odds with what is currently known of the structure of these interstellar regions.

More generally, the predicted strong variability of the physico-chemical state (ionization, dehydrogenation) of PAHs in space is not reflected in the recent ISO spectroscopy database which covers a variety of astrophysical conditions. This prediction was based on studies of small PAHs ( $N_{\rm C}\leq 50$), the only species currently accessible for investigation either in the laboratory or with quantum chemistry. As shown by Schutte et al. (1993), the 6 to 16 $\mu$m-AIB spectrum is also contributed to by large PAHs ( $N_{\rm C}\geq 100$) while the 3.3 $\mu$m-AIB is dominated by the smallest species ( $N_{\rm C}\leq 35$, see Fig. 8): this other solution (large "PAHs'' or carbon clusters) to the 6 to 16 $\mu$m-AIB spectrum may alleviate the present difficulties. However, the spectroscopical and structural properties of carbon clusters are poorly known at present: the ISO spectroscopic database is ideally suited to identify plausible candidates and stimulate future work on the physics and chemistry of carbon clusters.

Acknowledgements

We are grateful to François Boulanger, Alain Abergel, Christine Joblin and Anthony Jones for many stimulating discussions and our referee for helpful comments. We also thank the MPE-SDC (Garching) and the DIDAC (Groningen) for their constant support in the data reduction phase and with the use of SWS-IA3. SWS-IA3 is a joint developement of the SWS consortium. Contributing institutes are SRON, MPE, KUL and the ESA Astrophysics division. K. S. gratefully acknowledges support from a NATO collaborative Research Grant nr. 951347.