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Astron. Astrophys. 325, 450-456 (1997)

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5. Model fits

5.1. Observed spectrum

The target overall spectral energy distribution used for testing the models is that shown by Moorwood & Glass (1984) and which comprises ground-based and IRAS photometry and CVF low resolution spectroscopy covering the 3.28µm PAH and 9.7µm silicate absorption features. Additional CVF spectroscopy of the 3.28µm feature yielded identical fluxes in 7.5 and 10" diameter apertures but a slightly larger equivalent width in the smaller aperture implying that the feature is associated with the nuclear source while the continuum may include some extended stellar contribution (Moorwood, 1986). The recent ISO spectra in a larger aperture of 14 x 20" show a larger 3.28µm equivalent width which may be due to additional PAH emission from the 10" radius starburst ring. The ISO spectra also show prominent 6.2, 7.7, 8.6 and 11.3 µm PAH features which may be associated with the nucleus and/or starburst ring and were not visible in the CVF spectrum due to atmospheric absorption and inadequate spectral sampling.

5.2. Predicted spectrum

The observational constraints on the basic model parameters have already been discussed in Sect. 4. Unless otherwise mentioned, all models have been calculated with a total luminosity L [FORMULA] L [FORMULA] ; power law heating source with an index of [FORMULA] ; distance [FORMULA] Mpc and a gas mass of [FORMULA] M [FORMULA]. Parameters which were varied to investigate their influence on the predicted spectrum are the size of the emitting region, luminosity, gas mass, dust density distribution and the amount and composition of the small grains (PAHs). The best fit parameters are listed in Table 2 and the corresponding predicted SED is shown in Fig. 2 together with the observational data. Agreement between the model and the observations is excellent at all wavelengths except around 100 µm where the small excess flux observed may originate in the starburst region. To test the uniqueness of the fit we have run a large number of models with different parameters.

[FIGURE] Fig. 2. The SED of the Circinus galaxy. Broad band observations are represented by circles, CVF measurements by triangles and the best fit model (solid line) with parameters as given in Table 2

Small variations of [FORMULA] 20% in [FORMULA] have a large effect on the predicted SED because [FORMULA] is directly related to the optical depth. The models with an outer shell radius [FORMULA] underestimate the J, H, K colors. By changing the abundance of the silicates with respect to the large carbon grains in our standard model it is possible to improve the near IR fit although such changes are somewhat arbitrary given the information available and the uncertain stellar contribution. One has also to consider that extinction at these wavelengths becomes important so deviations from spherical geometry are no longer negligible (Efstathiou & Rowan-Robinson, 1990). A fully realistic standard Seyfert model would also have to include a torus like structure which requires an axial-symmetric radiative transfer code (Efstathiou & Rowan-Robinson, 1995, Piere & Krolik, 1992). It should be noted that the Si-O absorption is not a good discriminator between star-burst and AGN activity if a spherically symmetric dusty halo is assumed.

Models with constant density distribution ([FORMULA]) show a similarly strong dependence of the SED on [FORMULA] and the Si-O absorption. In these models there are more dust grains in the inner cloud regions than for models with [FORMULA]. More of the large grains are found at higher temperatures and the predicted equivalent widths of the PAH features become too small compared with those observed. Overall the best fit is found for models with [FORMULA] computed using Eq. 2-4.

Reducing the total luminosity by e.g. [FORMULA] 30% results in a similar SED shape but lowers the flux by the same factor.

The influence of the gas mass on the SED is shown in Fig. 3. For ease of comparison, all other model parameters are as specified in Table 2. One sees that models with a factor of two higher (lower) gas mass will indeed overestimate (underestimate) the 1.3mm flux by the same and the infrared spectrum by a larger amount. As discussed by Chini et al. (1987), the proportionality, [FORMULA], holds as long as the dust temperature is not a strong parameter in Eq. (1). This is the case for cold dust temperatures [FORMULA] 30K.

[FIGURE] Fig. 3. Influence of the gas mas on the SED of the Circinus galaxy. Results are shown for: [FORMULA] (dotted line), [FORMULA] (solid line), [FORMULA] (dashed line); other parameters remain as for our standard model (see Table 2).

Although the parameters of the small grains are not well constrained we find that large PAH clusters with [FORMULA] C atoms provide a good fit. Adopting an extreme cluster abundance of [FORMULA] the total fluxes in the PAH bands are [FORMULA] Jy, [FORMULA] Jy, [FORMULA] Jy, [FORMULA] Jy and [FORMULA] Jy which are consistent with the ISO SWS spectrum M96. However, after extensive searches in our parameter space we have not found a solution where both the CVF spectra in a small aperture and the ISO SWS in the large aperture can be fit simultaneously. One possible explanation is that the PAH features in the large aperture spectra are dominated by the emission from the starburst ring.

5.3. Sizes

Although the central heating source in our model is a point source the predicted size of the infrared dust emitting region increases with wavelength. Fig. 4 shows the model predictions together with the various observed sizes and upper limits discussed earlier. The best fit model to the SED (solid line) also proves to be consistent with the estimated 10 µm size and the longer wavelength upper limits. It predicts a somewhat larger value than observed at 3 - 5 µm but only by [FORMULA] 60% at 3.8 µm which is probably within the uncertainties. The observed 3.8 µm size of [FORMULA] 6pc in fact makes it tempting to identify this emission with the torus proposed in Seyfert unification models (Antonucci, 1993) in which case exact agreement with a spherically symmetrical model cannot be expected.

[FIGURE] Fig. 4. Size (FWHM) of the emitting region in Circinus as a function of wavelength. The observations are shown as symbols; the solid line represents the model which best fits the SED and whose parameters are given in Table 2.
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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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