4. A lower limit to grain temperature
We found very cold dust in all inactive spirals of our sample. One may wonder whether still colder dust might exist that has escaped detection. To partially answer this question, we compute under reasonable assumptions a lower limit, , to the temperature of a grain in a disk galaxy. Very cold dust must be well protected from direct starlight, mag, and can only be found inside clouds. Such clouds are nevertheless transparent to FIR emission of the galaxy itself, at least for wavelengths above 25 µm. In this range, the optical depth is according to most dust models over 50 times smaller than in the visual (e.g. Draine 1985, Zubko et al. 1996). To minimize the FIR heating, which is rather inefficient anyway because of small absorption cross sections, we adopt the source of FIR radiation to reside in the galactic nucleus of say the central 500 pc. Heating by radiation at shorter wavelengths and/or spatially spread-out energy sources, like stars in the disk, would increase the estimate for .
As is appropriate for most inactive spirals, we assume a spectral shape for the FIR radiation with K. Fig. 16 gives a flavor of the minimum dust temperature as a function of galactocentric radius. If the total FIR luminosity is , as in the Milky Way, the dust in the disk within a radius of 15 kpc, which is a typical optical radius of a galaxy, cannot become colder than K. In addition, one may use this figure to get an impression on where to find the bulk of the very cold component of the ISM. Fig. 16 also shows the variation of with .
Fig. 16 is almost independent of the size or composition of grains. Only a -variation of the absorption efficiency at long wavelengths is required because for the deeply buried dust both absorption and emission occur in the FIR and it is just the slope, not the absolute value of the absorption efficiency that determines . The grain model, however, has an influence on the derived dust mass. If the very cold dust is fluffy and icy, or has an elongated form, its millimeter absorption coefficient is enhanced relative to that of the standard dust by some factor (Krügel & Siebenmorgen 1994, Ossenkopf & Henning 1994) and the mass will be overestimated by exactly this amount.
© European Southern Observatory (ESO) 1999
Online publication: November 3, 1999