Astron. Astrophys. 337, 85-95 (1998)

4. Application: the starburst galaxy NGC 6090

The starburst galaxy NGC 6090 is located at a distance of about 117 Mpc (). Observations in the optical by Mazzarella & Boroson (1993) show that NGC 6090 is an interacting pair of galaxies in the process of being merged. The two nuclei are separated by a distance of pc and have comparable luminosities. First ISO results, recently reported by Acosta-Pulido et al. (1996), show strong PAH emission lines. Therefore, any modeling of NGC 6090 has to take into account emission from quantum heated particles.

4.1. Energy sources

To model NGC 6090 we used an association of OB-type stars (K) in combination with red-giant stars (K). Both kinds of stars are assumed to have the same total luminosity of , which results in a total luminosity of for the central source. The source itself is surrounded by a molecular dusty torus. To account for starbursts, additional radiative sources ("starburst sources") located inside the dust torus were added. These "starburst sources" are treated in a similar way as the so-called "hot spots" of Krügel & Siebenmorgen (1994):
Each of the "starburst sources" consists of a B-star (, K) surrounded by a homogeneous, optically thin dust envelope (). For the sake of computational simplicity, the "starburst sources" are assumed to form distinct concentric shells of starburst activity inside the dust torus. For our best-fit model (Fig. 7), we used 27 shells of starburst activity. Each of them has a luminosity of . They are located each at 20 pc distance starting at a distance of 10 pc from the central source. However, the exact positions of the starburst sources have only very little effect on the results of the radiative transfer calculations.

Fig. 7. Best fit model SED for NGC 6090, illustrating the effect of quantum heating. The numerical results are compared to IRAS and recent ISO data (Acosta-Pulido et al. 1996). Filled circles: ISOPHOT-P aperture measurements, filled squares ISOPHOT-C measurements, open diamonds: IRAS values. The fluxes obtained from our models are multiplied by a factor of two, to account for the bi-nuclear structure of NGC 6090.

4.2. The dusty torus

4.2.1. Dust models

In a detailed modeling, one might have to use dust mixtures consisting of amorphous carbon and silicate grains as well as grains with ice mantles (Men'shchikov & Henning 1997). These should correspond to the physical conditions in the objects which are studied, e.g., dense molecular cloud cores (Ossenkopf & Henning 1994, Preibisch et al. 1993, Henning et al. 1995), protostellar envelopes (Lenzuni et al. 1995) or protoplanetary accretion disks (Henning & Stognienko 1996). For silicates, recent optical data measured for cosmic dust analogues (Jäger et al. 1994, Dorschner et al. 1995) are available.

Applying Mie theory, we calculated the coefficients of absorption and scattering for compact spherical grains.

The power-law index q of the grain size distribution

is set to 4.

The dust used in this work is composed of silicate, graphite, and amorphous carbon grains with the optical data from Dorschner et al. (1995), Draine (1985), and Preibisch et al. (1993), respectively, as well as of PAHs. According to chemical composition and heating mechanism, we have six distinct dust components:

1. Big silicate grains with radii between 0.05 µm and 1µm.

2. Big graphite grains (0.05 µm to 1µm).

3. Big amorphous carbon grains (0.05 µm to 1µm).

4. Small silicate grains
   (0.001 µm (10 Å) to 0.01 µm (100 Å))

5. Small graphite grains
   (0.001 µm (10 Å) to 0.01 µm (100 Å))

6. Compact PAH molecules, composed of 30 to 500 carbon atoms, with the absorption cross sections from Schutte et al. (1993).

The silicate to carbon mass-ratio is 1:2 and the mass ratio of graphite to amorpous carbon is 2:1. To simplify matters, we have chosen the same sublimation temperature of 1500 K for all dust grains, whereas the PAHs may exist up to temperatures of 2500 K.

To calculate the quantum heating of the small silicate and graphite grains, the internal energy of the grains as a function of temperature is required. In agreement with GD89, for the graphite particles we used the analytic fit to the graphite enthalpy data of Chase et al. (1985).

where E(T) is in erg per atom. These enthalpies were also used for the PAHs. Léger et al. (1989) pointed out that the specific heat of PAHs is comparable to the one of carbon, especially if the PAHs are in a dehydrogenated state.

For the silicate grains we used a fit to experimental results for and obsidian (Léger et al. 1985).

where is the specific heat in erg per per K, which is related to the enthalpy by

To account for the fact that the enthalpies described above were determined for bulk material, whereas we apply them to clusters of N atoms, the enthalpies had to be multiplied by a correction factor of .

According to the grain size distribution, for the dust model containing big and small dust grains, the ratio of masses of small dust grains to big grains is . The amount of PAHs is assumed to be 3% of the mass of the total carbon content of the dust torus, being fairly in agreement with estimates by Pendleton et al. (1994). To reduce the strength of the C-H lines we choose a degree of dehydrogenation of 90%.

4.2.2. The model torus

The dust torus used to model NGC 6090 is assumed to have a radius of 900 pc and an opening angle of . The observations of Mazzarella & Boroson (1993) indicate that NGC 6090 is viewed almost face-on. Therefore, the line of sight was chosen to have a viewing angle of above the torus midplane. The value for the opening angle of the torus is somewhat constrained by the required optical depth (see below).

The density distribution used for the model torus is given by

The dust mass is resulting in an optical depth along the line of sight, in direction to the central source, of . For this value of optical depth the strength of the silicate absorption feature (m) obtained from the model matches the observed data (Fig. 7).

4.3. Results

As shown in Fig. 7, even this simple model gives a reasonable fit to the ISOPHOT-data. It reproduces the main spectral characteristics of NGC 6090. The calculated spectral energy distribution (SED) fits well to the observed 10 µm silicate absorption feature and produces similar fluxes at longer wavelengths. The somewhat plateau-like structure around 15 µm is also reproduced. On the other hand, the model SED shows too few emission in the far infrared region (m). But the far-infrared emission can be explained by emission from cool (23 K) dust located outside the nuclei of NGC 6090. This emission from the host galaxy is included in the observed data but not covered by our torus model. In Fig. 8, we compare our results with the ISOPHOT-SL data obtained by Acosta-Pulido et al. (1996). ISOPHOT-SS data were not taken into account because according to Acosta-Pulido et al. (1996) theses data are too noisy to be used in a detailed analysis. All calculated PAH line intensities are roughly in agreement with the observed ones. However, the line-widths are somewhat different. Additionally, the observed 6 µm, 7.6 µm, and 11 µm feature seem to have slightly different center-wavelengths as the corresponding features in our model but this is mainly red-shift caused (). However, a more detailed fit of the SED of NGC 6090 seems not desirable, at the moment: First, even for the most recent ISOPHOT observations (Acosta-Pulido et al. 1996) the area covered at the distance of NGC 6090 is much larger than 2000 pc in radius (torus diameter), especially at wavelengths larger than 10 µm. Therefore, the emission at infrared wavelengths is systematically somewhat underestimated by the model. However, Acosta-Pulido et al. (1996) pointed out that the observed emission at wavelengths above 100 µm can be explained by emission from diffuse interstellar dust. Second, a detailed fit of the observed PAH emission lines is extremely challenging because of the many free parameters which are necessary to parameterize the dust model: size limits for the small grains, mass ratio of small to big grains, grain size power law exponent, sizes of the PAHs, degree of ionisation and hydrogenation of PAHs. Especially the ionisation and dehydrogenation of PAHs have significant influence on line widths and relative line intensities. Moreover, astrophysical PAH models contain mainly compact PAHs (i.e. Léger et al. 1989, Schutte et al. 1993), whereas also non-compact PAHs may be present in space. Each of these parameters, or even all together, may be responsible for the differences between the observed and calculated PAH emission fluxes. However, a detailed fit of the infrared lines is not the basic intention of this paper. The PAH model is basically used to demonstrate the capabilities of the new combined radiative transfer code. Further investigations may show that other materials, i.e. very small hydrogenated amorphous carbon (HAC) grains, are necessary to explain some aspects of the observed infrared features. As soon as the specific heat data of these materials are available, their emission can be calculated with the code developed by us.

Fig. 8. Comparison of observed and calculated PAH emission. The astrisks represents the fluxes from our model SED, the vertical bars are the ISOPHOT-SL data published by Acosta-Pulido et al. (1996).

4.3.1. Effect of quantum heating

Apart from the appearance of the PAH emission lines, the main effect of including quantum heated particles on the SEDs can be nicely seen in Fig. 7. It is the increase of emission at wavelengths shortwards of 10 µm, balanced by the decrease of emission in the FIR (m).

Not only the total emission is affected by quantum heating, it also changes the temperature structure of the dust torus and, therefore, the intensity maps. In Fig. 9 we present intensity maps for our best-fit torus model for both kinds of dust models. Due to the orientation of the dust torus relative to the line of sight, the horizontal (east-west direction in observations) intensity profiles are symmetrical with respect to their center. In the vertical (north-south direction) intensity profiles the asymmetry of the projection of the torus surface onto the plane of sky can be seen. Here, the majority of intensity asymmetry originates from dust around the polar cones of the torus.

Fig. 9. Horizontal (left column) and vertical (right column) intensity profiles of the model torus for various wavelengths. In each panel we compare the results obtained for the dust model containing quantum heated particles (full line) with those obtained using the dust model consisting only of big grains (dashed line). The abscissa is always in fractions of the torus radius. The ordinates show logarithms of intensities in arbitrary units.

As already indicated by the SED (Fig. 7), the flux in the FIR is dominated by emission of big dust grains. For m the intensity maps show comparable levels of emission at most points in the torus, whether quantum heated particles are present or not. The higher total emission seen in Fig. 7 originates from higher intensities at the inner torus points. At shorter wavelengths, the picture changes. In the inner hot parts of the torus, where most of the UV radiation emitted by the central source is converted to the IR, the emission of small quantum heated grains is, in general, higher than those of the big grains. This results in the somewhat plateau-like structures seen in the maps for 30, 18, and 7.6 µm. In the outer cooler parts of the torus, where the thermal emission of dust peaks at wavelengths above 10 µm ( K and lower), the quantum heating "shifts" emission to shorter wavelengths. This effect can be seen by the inspection of the maps for 10 µm. In the inner regions (about 10 % of the torus radius) the emission from big grains is comparable to the emission from dust including small particles. But as the distance to the central source increases, the emission from big grains dominates more and more. Moreover, the maps for 2, 3.3, and 7.6 µm illustrate that at shorter wavelengths quantum heating is the dominant source of dust emission, all over the dust torus. For and m this effect is strengthened by the fact that PAH emission lines are located at these wavelengths. Hence, the PAH emission increases the continuum emission of big grains up to an order of magnitude, independently of their location in the dust torus.

© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998
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