4. Temperature distribution model: results and discussion
4.1. FIR dust masses
The dust masses computed by adopting a single temperature and a temperature distribution are compared in Fig. 1. Both methods lead to a temperature dependence, as expected when the dust amount is derived by using thermal emission. In fact, the colder the dust grains, the larger should be their total number in order to produce a given FIR emission.
The dust masses obtained with a temperature distribution are larger than those derived from a single-temperature model. This confirms that IRAS measurements allow to determine the warm (30-54 K) dust amount only, while the contribution of the cold dust is neglected. Moreover, it turns out that, in the present sample, the FIR luminosity does not depend on the color temperature, thus confirming that the FIR emission is a result of different contributions and cannot be properly explained by a source with a single equilibrium temperature. The two models give masses differing by factors from 2 to 6. This wide range is due either to the shape of the temperature distribution and/or to the uncertainties in the dust parameters. On the other hand, the ratio between the two dust mass evaluations (Fig. 2) shows a general temperature dependence which suggests that colder galaxies have a larger amount of missed dust.
4.2. Dust "mass discrepancy"
The temperature distribution model enhances the dust "mass discrepancy". In order to explain that discrepancy, it has to be noticed that the dust mass evaluated from optical observations critically depends on the spatial distribution of the dust with respect to the stars. Usually the extinction is thought to be due to an overlying absorbing screen of dust grains. That is the geometry where a given amount of dust has the strongest effect on the starlight. In order to test how a peculiar and oversimplified spatial distribution affects the dust mass evaluation from optical data, I compared the optical dust masses in Table 1 to those derived by assuming a more realistic spatial distribution (e.g. Witt et al. 1992) and by using the optical data by Goudfrooij et al. (1994a, b). The new optical masses turn out to be enhanced by a factor 2-4, cutting the "mass discrepancy" down. However, even if the "mass discrepancy" is reduced by assuming a more realistic spatial distribution, the optical absorption can only account for the dust in the obscured galaxy regions, while the distributed dust component is always neglected.
A similar case concerns the "extra" dust component suggested by Tsai & Mathews (1996) to explain the 60-100 µm flux ratio: due to its low temperature, it is not detected by IRAS. Following their model, it is possible to estimate the contribution of the "extra" dust in the sample. Taking into account the "extra" dust amount, the dust masses derived by a single temperature model are slightly enhanced, but the large uncertainties due to the observations and, then, to the temperature evaluation do not allow to judge this enhancement as significative. One can argue that, with a model of temperature distribution, it is possible to overestimate the dust amount. Actually, this cannot happen because of the severe constraints which are chosen, whether two different flux ratios are available or when a flux ratio and the relative color temperature are used as it is here suggested. In this respect, the last method is also the more conservative, since the warm dust observed at 60 µm affects the dust mass evaluation in the sense of underestimating the cold dust amount.
Therefore, since these computations are very sensitive to the assumed dust temperature, the model by Kwan & Xie (1992) greatly improves the mass evaluation by taking into account a wide temperature range, and can be applied to a wide range of galaxy morphological types when, because of lack of the data, it is no possible to adopt and to develop a suitable radiation model.
© European Southern Observatory (ESO) 1998
Online publication: September 17, 1998