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Astron. Astrophys. 324, 32-40 (1997)

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5. Discussion and conclusion

5.1. Dust-to-gas ratio

The result presented in Sect. 3 (in particular Fig. 4) suggests that in the inner part of the galaxies disks where most of the extinction occurs (Paper II), the dust-to-gas ratio is on average about the same as the Solar Neighbourhood value. On the other hand one should be aware of the large uncertainties of this result, given the crudeness of the method with which we estimate the gas column density (in particular the constant N(H2 /I(CO)) conversion factor). For example changing by a factor of 1.4 the assumed disk size of the molecular gas, which dominates the gas column density for most of galaxies in our sample, the dust-to-gas ratio will be changed by about a factor of 2. Moreover, the extinction estimated from the gas column density depends not only on the dust-to-gas ratio, but also on the radiative transfer model adopted. For example, as shown in Fig. 3, when the slab model for the radiative transfer is used, the assumption of a Solar Neighbourhood dust-to-gas ratio results in estimates for extinction from the gas column density significantly higher than the values from the frequency converter model. An average dust-to-gas ratio of a factor of 2 lower than the Solar Neighbourhood value is indicated by our data when the slab model is used.

Nevertheless, it is fair to say that galaxies in our sample do show dust-to-gas ratios similar (within a factor of few) to the Solar Neighbourhood value. This is consistent with the results for M31 (Van den Berg 1975; Bajaja & Gergely 1977), the only spiral galaxy outside the Milky Way with extinction (reddening) directly measured over the entire galaxy disk.

5.2. The effects of the clumpiness of dust distribution

Apparently the dust associated with the molecular gas dominates the extinction in most of galaxies in our sample (Sect. 4). This result may be general for spiral galaxies, for which the gas in the inner disk is often predominantly molecular (Young & Scoville 1991). The molecular gas at all observable scales appears to be clumpy, perhaps fractal (Falgarone, et al. 1992), hence the CO emission of unresolved external galaxies is related to molecular clouds of different dimension and gas density. If the physical conditions characterizing the interstellar medium of our sample galaxies (UV radiation field and metallicity) are similar to the one of the Solar Neighbourhood, this suggests that, as in the Milky Way, a significant contribution to the large-scale CO emission of the target galaxies is made by low optical depth diffuse molecular gas (Polk et al. 1988, Boselli et al. 1996). So the dust associated with this gas may also be diffuse and our model which assumes a uniform distribution of the dust may be valid at large scales.

The effects of clumpiness on the extinction are expected to be strong only when individual fragments are optically thick (Boissé 1990). Sofue & Yoshida (1993) have found only a moderate extinction for a dark molecular cloud in the central region of M31. Furthermore, Boissé & Thoraval (1996) find very small extinction fluctuations in front of some molecular clouds at the subparsec scale and conclude that these clouds can be considered as a uniform absorbing medium. Therefore, we argue that the total extinction on the scale of an entire galaxy is not sensitive to the opaque dust structures, although locally these structures may be very prominent (see e.g. the images by Block et al. 1994). Generally speaking, these structures occupy only a small part of the disk, i.e with a small filling factor. Therefore the contribution from them to the extinction of the total emission from a galaxy is not significant except for some special cases, for example when a galaxy is seen very edge-on so that the filling factor of the dust lanes is relatively high.

Furthermore, as far as the dust-to-gas ratio is concerned, there is another reason for the insensitiveness to the effect of very opaque clumps: the gas in these clumps, as well as the dust, may be missing, too. Allen (1996) argues that dense molecular clouds, especially when far away from UV sources, can be very cold and therefore with very high CO-to-H2 conversion factor. Since both the CO and the FIR emissions are small from these clouds, their existence yields little effect in our results.

However, it should be noted that giant molecular clouds (GMC's) associated with active star formation regions represent a different case from the dark dense clouds discussed above. A significant fraction of total extinction (and dust emission) in a galaxy occurs in these clouds (see, e.g. Boulanger & Pérault 1988; Scoville & Good 1989). The radiative transfer problem in these regions can be very complicated (Leisawitz 1991) and is obviously quite different from that in the diffuse interstellar space depicted in our model. However first, as indicated by the FIR emission, the dust in these clouds is generally not the dominant component in the absorption-reradiation process in a galaxy: Sodroski et al. (1989) concluded that less than 30% of the FIR emission of the Milky Way is from dust associated with star forming GMC's. Second, with the present data set we don't have enough contraint to separate the contribution from this component to the total extinction. Finally, as claimed in Sect. 3, our results are basically determined by the FIR/UV-optical luminosity ratio and not very sensitive to the radiative transfer model and therefore even for the dust in GMC's our result may provide a reasonable approximation to the real extinction.

5.3. Conclusion

In this paper we test the classical method for the extinction correction based on the gas column density. A positive correlation is found between total gas column density and the extinction estimated using a model based on energy conservation (`frequency-converter model'). Assuming a Solar Neighbourhood optical-depth-to-gas ratio, extinction predicted from gas surface density using a radiative transfer model which adopts a `Sandwich' configuration for the stellar and dust distributions, and which takes also into account the effect of scattering, agrees well with the extinction estimated from the energy conservation consideration. This indicates that (1) the method for the extinction correction based on the gas column density is a reasonably robust one; (2) in the inner part of galaxy disks where most of the extinction occurs (Paper II), the dust-to-gas ratio is on average about the same as the Solar Neighbourhood value.

Our results also suggest that dust grains associated with both gas phases (HI and H2) participate in the extinction, with a relative importance depending on the abundance of the gas phase in the inner disk. For most of galaxies in our sample the extinction is mainly due to the dust associated with the molecular gas as indicated by the good correlation between the extinction and the column density of the molecular gas, and by the high molecular to atomic gas column density ratio in the inner part of these galaxies. On the other hand, for galaxies whose gas column density is dominated by the atomic gas, the extinction is mainly caused by the dust associated with atomic gas.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998