4. The models
4.1. Mkn 496, Mkn 1116 and NGC 6000
We first apply the radiative transfer code to the nuclei of Mkn 496, Mkn 1116 and NGC 6000. We attempt to reproduce in the models the infrared measurements which we obtained with ISOPHT, as well as IRAS and submm/mm data. Galactic nuclei have a diameter of only a few kpc, the active region being usually considerably smaller. Given the distance to our objects, the angular diameter of their nuclei on the sky is of order 10 arcsec, whereas the whole galaxies including their disks are some ten times bigger.
The luminosity in starburst galaxies is likely to be dominated by the nucleus. Therefore, when comparing theoretical fluxes of the nucleus with actual observations that were obtained with a beam larger than the nucleus, we assume that the contribution of the galactic disk is moderate. Qualitatively, one expects the disk to be more influential at submm wavelength because there must be plenty of interstellar matter in the disk. However, the star formation rate in the disk is probably relatively low.
The IR spectra are shown in Fig. 1 together with the fit results. The model fluxes refer to a uniform aperture (beam size) of 24", about equal to the resolution of the P-40 detector of ISO. The full lines in the right boxes of Fig. 1 show the overall fits. At far IR wavelengths, they are somewhat below our ISOPHT as well as the IRAS 100 µm points, but this is the way it should be for extended galaxies. The 1.3 mm fluxes of the two Markarians were obtained with an 11" beam and lie therefore below the theoretical line.
In the left boxes, the P-40 spectra comprising the silicate absorption feature at 9.7 µm and the mid IR emission bands 6.2, 7.7, 8.6 and 11.3 µm are zoomed for easier read off. Overall, the models are not bad. However, the P-40 fluxes at 12 µm are generally smaller than the IRAS photometry at that wavelength. Assuming that IRAS is basically right, this may be due to a combination of several effects. For Mkn 496, the difference is marginal and may be fully explained by the broadness of the IRAS filter which includes part of the steeply rising spectrum beyond 12 µm. For NGC 6000, the difference is a bit larger. This galaxy is the nearest (29 Mpc) and its mid infrared emission may be extended beyond the ISO beam (24"). Such radiation would still be picked up by IRAS which has a larger beam.
In Mkn 1116, the discrepancy amounts to a factor 2.5. Both previous effects may contribute. Moreover, the IRAS flux is close to the detection limit where there is always the tendency to overestimate the flux. But the most likely explanation lies in our observing position. We used IRAS coordinates, partly to be in line with the previous 1.3 mm continuum measurement, partly because it would not matter in the broad-beam P-22 observations. The IRAS position is 14" off from the optical center. We therefore conclude that the P-40 and 1.3 mm fluxes towards the center of Mkn 1116 may be twice as large than those which we measured. The affect on the model parameters of Table 2 is, however, not dramatic. For example, to double the mid IR fluxes of the model, one may just double the PAH abundance.
In all three galaxies, the 3.3 µm feature slipped detection because of ISOPHT's insufficient sensitivity. However, the model fluxes of this feature lie always within the observed noise. Unfortunately, there are no data to compare with our predictions for the 11.95 and 13.3 µm resonance.
The structure of the three nuclei is described in Table 2. All nuclei are powered by a starburst of 1011 luminosity and there are about 106 OB stars within the central few hundred parsec. The nuclei are also similar otherwise: they have comparable total dust mass ( ), comparable extinction (27 mag), size of the starburst region (200 pc), and ratio of starburst to total luminosity (2/3). The OB stars created in the burst have a strong central peak, their density increase is steeper than that of the giants (, whereas ). The OB star region, which is the place where the PAHs are excited and the mid IR radiation originates, has a moderate visual optical depth of 5 mag. Therefore most of the extinction occurs in the envelope of the galactic nucleus.
For illustration, the temperature profiles within the galactic nucleus of the large grains are plotted in Fig. 2. As the grains have a size distribution, there is at every radius r for each chemical component a range of temperatures. It is not a strict, but nevertheless quite general rule that if one has in a radiation field two grains of the same material and shape but different size, the smaller one is warmer. The upper boundary curve represents the smallest, the lower the biggest particles. The spread in temperature is much smaller in the outer parts of the galaxies because there the radiation field becomes very soft.
4.2. Arp 220
To further illustrate the potential of modeling the IR spectra, we compute the radiative transfer for the nucleus of Arp 220. This is a famous ultraluminous object ( ) which belongs to the local universe and is an order of magnitude brighter in the IR than the three galaxies discussed before.
Arp 220 is probably also powered by a starburst as, for example, Sturm et al. (1996) observe fine structure lines only of low excitation. These authors derive an optical depth mag. Their value is compatible with our model, also described in Table 2, which has a dust mass within pc.
Our model fits the IR emission quite satisfactorily (see Fig. 3). It correctly reproduces the 10 µm silicate absorption feature as well as the PAH resonances. The model fluxes are calculated for a 10" beam; they therefore underestimate the submillimeter emission as Arp 220 is known to be more extended. The temperature profiles are shown in Fig. 4. They are flat within the starburst region as it should be for a constant density of the OB-stars (see Table 2). For comparison with another radiative transfer model which assumes a somewhat different geometry and includes optical emission from unobscured stars, one may consult Silva et al. (1998). As far as we can make out, except for this presence of stars outside the heavily veiled nucleus, there is no qualitative disagreement between their model and ours.
© European Southern Observatory (ESO) 1999
Online publication: November 2, 1999