4.1. Choice of intrinsic distributions of stars and dust

The old stellar disk and associated dust

The obvious starting point in identifying a spatial distribution of stars and dust that can account for the entire optical/FIR/submm SED is to test whether the distributions which are consistent with the observed optical SEDs can also account for the FIR/submm SEDs. We will use the model of Xilouris et al. [58] to address this question as it is the only model that fits the geometry of stars and dust as seen in the optical, and so should provide the best representation of the intrinsic distributions of the stars and dust in spiral galaxies that can be probed by optical extinction measurements.

To provide a benchmark, we will in the first instance ignore the heating of dust by UV photons, since these could not be included in the analysis of the edge-on systems considered by Xilouris et al. For the FIR emission calculation we use the standard dust model of graphite/silicate from Draine & Lee [16] (and with optical constants specified by Laor & Draine [32]). This is consistent with the Milky Way type extinction law derived for these galaxies. The results are shown in Fig. 3. It is clear that the prediction for the FIR/submm SED falls well short of the observed measurements. In terms of luminosity the shortfall is by a factor of 5. This shows that, according to these models, the old stellar population alone cannot account for the dust emission.

Figure 3. The FIR/submm SED of NGC 891 predicted for the old stellar population and associated dust (taken from Misiriotis et al. [38]). It is clear that the prediction (solid line) for the FIR/submm SED falls well short of the observed measurements (symbols).

Lets now add the UV emitting stellar population, but keep the amount and distribution of dust the same. This was considered as a new geometrical component in the model of Popescu et al. [46]. The UV emissivity was assumed to be distributed in a thin disk with the same scalelength as the B band disk, but with an assumed scale height of 90 pc, close to that of the Milky Way ([36]). This is smaller than the scale heights for the optically emitting stars and for the dust distribution derived in the model of Xilouris. The spectral distribution of the UV emission was fixed according to the predictions of a population synthesis model, and its amplitude parameterised in terms of a SFR. Now it is easy to raise the level of the predicted FIR emission to the observed level by simply adjusting the SFR. (see Fig. 4).

Figure 4. The FIR/submm SED of NGC 891 predicted for the old stellar population and associated dust, supplemented by the young stellar disk (taken from Popescu et al. [46]). It is obvious that the model prediction (solid line) for the submm emission falls short of the observed measurements (symbols).

It is obvious from Fig. 4 that the FIR-submm colours are not fitted, in the sense that the model prediction for the submm emission falls short of the observed emission. This suggests either that a further component of dust is present which is not constrained by the optical data, or that the ratio of the submm emissivity to the FIR emissivity is higher than that predicted by the standard Draine & Lee [16] dust model. The latter possibility was recently investigated by Alton et al. [1] and Xilouris [57], who found a submm emissivity enhanced by a factor of 4. This result was obtained by comparing the visual optical depth derived from Xilouris's model with the submm emission, assuming that the same grains emitting in the submm are responsible for the optical extinction. However, this assumption is only true if self-shielding effects of grains are not present. In fact, real galaxies do contain optically thick components, which makes it inevitable that the submm emission will always be higher than predicted on the basis of optical extinction alone. Therefore the solutions obtained by Alton et al. [1] and Xilouris [57] for the submm emissivity can only be treated as upper limits. We should also note that there is no direct observational evidence of enhanced submm emissivity in the diffuse ISM. It has only been possible to investigate submm emissivities of grains in discrete clouds, where the brightness of the dust emission from the clouds can be compared with the extinction of background stars. Although enhanced submm emissivities have been found in these investigations, this is not unexpected since the clouds shield the grains from the diffuse UV radiation field, allowing ice mantles to form. Thus, such grains are probably not typical of grains in the bulk of the volume of the galaxy, and, as already noted, are in any case not probed by global extinction studies due to the low filling factor of the clouds. We also note that there are other constraints on the wavelength dependence of grain emissivity (see Li [33]) which would tend to favour a steep decline of emissivity with increasing wavelength in the submm. A steep decline in emissivity would not however lead to the enhanced ratio of the submm to the FIR emissivity needed to explain the FIR/submm colours of galaxies in the absence of a further dust component.

In conclusion, there is no independent observational evidence that an interstellar medium composed entirely of diffuse dust, as probed by the optical extinction studies, could have enhanced submm emissivity.

By contrast, there is strong independent observational evidence for a further dust component to explain the observed FIR-submm colours of galaxies. The geometrical model that we presented previously has no dust component associated with the young stellar population, yet we know that such a component exists. We know that dust is associated with the CO emitting layer and we know that this dust is associated with the spiral arms where most of the young stars are formed. The only question is how to prescribe the distribution of this dust. In order to mimic the effect of this component of dust associated with the young stellar population, and in the absence of direct observational constraints, Popescu et al. [46] introduced a second dust disk, having the same scale height as the young stellar disk. A second disk of dust associated with the molecular layer was also considered by Bianchi et al. [6] for the modelling of NGC 6946. Of course, in reality the dust distribution is much more complex due to the spiral arm structure and the (at least in part) clumpy nature of the dust associated with the young stellar population. Because of the presence of clumps, some fraction of the additional dust will be subject to strong self-shielding, and will hardly be seen at all even in the K band images. This may be one reason why the dust lanes observed on K-band images of edge-on galaxies are not much more prominent than the dust lanes predicted from the single dust disk model of Xilouris et al. (see the comparison of Dasyra et al. [12]). Nevertheless, the dust lane seen on the K-band images (Fig. 5) is, particularly in the central regions, too strong to be accounted for by the single dust disk model. This provides a hint that the additional dust layer is more concentrated towards the centre of the galaxy, following the distribution of molecular gas.

Figure 5. Left upper panel: The 2MASS K-band image of NGC 891 (folded). Left lower panel: The simulated K-band image produced using the solution of Xilouris et al. [59], containing a single dust disk associated with the old stellar population. Especially in the central region, the dust lane seen in the 2MASS image is too strong to be accounted for by the single dust disk in this model. This is quantified in the right hand panel, which shows the average brightness of the data and of the model (in arbitrary units) within 50 arcsec of the centre, plotted versus vertical position.

Finally, we note that the prevalence of clumps in the dust associated with the young stellar population may reduce the dust mass required to account for the submm data, since, as we have already mentioned, dust in optically thick clumps may have an enhanced submm emissivity compared to dust in the diffuse inter-clump medium. Thus, the dust mass derived by Popescu et al. [46] for the additional dust component should be treated only as an upper limit. In this sense, elements of both the enhanced emissivity hypothesis and the additional dust hypothesis may be needed for a realistic description of the SEDs of normal galaxies.

Despite the complex structure of the dust associated with the young stellar population, the simplification of placing it in a common thin disk with the young stars is a reasonable approximation to predict the optical appearance of galaxies (Misiriotis et al. [39]), as well as the overall energy balance and FIR and submm radial profiles of spiral galaxies (as will be shown here). The effect on the predicted FIR/submm SEDs of including the second disk of dust in the radiative transfer calculation is shown in Fig. 6. Although the longer wavelengths points are now well fitted, the predicted SED is not broad enough to fit the short wavelengths as well. We are clearly missing a warmer component of emission.

Figure 6. The FIR/submm SED of NGC 891 predicted for the old stellar population and associated dust, supplemented by the young stellar disk and associated dust (adapted from Popescu et al. [46]). It is obvious that the model prediction (solid line) for the shorter FIR wavelengths falls short of the observed measurements (symbols), indicating the need for a warmer component of emission.

Ideally one would like to have radiation transfer calculations on scales ranging from pc to kpc, to properly understand the propagation of photons on both short and large scales. The closest that has been achieved is the radiative transfer calculation of Sauty et al. [49]. They calculated the transfer of UV radiation in a interstellar medium consisting of star-forming molecular clouds, visualised at a resolution of 12 pc, as well as a diffuse atomic medium extending up to 12 kpc. They derived the distribution of the distance travelled by UV photons before absorption. Fig. 7 shows that half of the radiation is absorbed within the first ~ 10 resolution elements out to a radius of ~ 120 pc. This calculation cannot tell us, though, what happens within the first cell, which is larger than the size of most HII regions and their immediate surroundings. From an infrared point of view this means that the calculation is not sensitive to the absorption on the shortest scales, and therefore is not sensitive to the warmest grains. It is thus preferable to consider the local absorption and re-emission of UV photons separately from these processes on galactic scales. This approach was adopted both by Silva et al. [50] and by Popescu et al. [46] (see also Charlot & Fall [11]).

Figure 7. Distribution of the distance travelled by UV photons from their parent OB association, before absorption, taken from Sauty et al. [49]. The median distance is 120 pc, and the mean distance is 440 pc.

The basic idea is to consider that some fraction F of the non-ionising UV is locally absorbed in star-forming complexes and only a fraction (1 - F) will go in the diffuse young stellar disk. If this clumpy component is added, the whole FIR/submm SED can indeed be fitted. This can be seen for both the model of Silva et al. [50] in Fig. 8 and for the model of Popescu et al. [46] in Fig. 9. Both figures show the contribution of the diffuse and localised components of the FIR emission. We note that in the model of Silva et al. [50] the diffuse and localised components peak at similar wavelengths, whereas in the model of Popescu et al. [46] they do not. This difference is due to the different treatment of the localised component. The model of Popescu et al. [46] has a fixed empirically determined template for the FIR emission from star-forming complexes, specified by just one parameter (its amplitude - the factor F). The model of Silva et al. [50] incorporates a separate radiative transfer calculation for an idealised star-forming complex, visualised as a molecular cloud with a central embedded source and parameterised by the radius and lifetime of the clouds. Thus, whereas the model of Silva et al. allows for the possible presence of cold dust emission from the optically thick parts of their localised component, the model of Popescu et al. considers only the warm dust emission from this component, and instead includes the cold dust in the second disk of dust which mimics the distribution of molecular material. This conceptual difference will however not have a major effect on the results obtained by the two techniques. The major difference is that one model (Popescu et al.) constrains the geometries of stars and dust from fitting the optical images, and has therefore only a few (in fact just three) free parameters needed to fit the FIR SED, while the other model (Silva et al.) has more free parameters, partly because it also makes a calculation for the photometric evolution of a galaxy, but also because it has to define the geometries with further free parameters.

Figure 8. Fit to the SED of NGC 6946, taken from Silva et al. [50].

Figure 9. The final fit to the FIR/submm SED of NGC 891, taken from Popescu et al. [46]. The total predicted SED is given with the solid line, the diffuse component with the dashed line and the clumpy component with the dotted line. The observed data are given as symbols.