Hildebrand (1983)
gave a prescription for deriving dust masses in galaxies from far
infrared data which has been widely used.
Young et al (1989)
have used the
Hildebrand prescription to conclude that the average gas-to-dust ratio
in galaxies is 1200.
Draine (1990)
has given a discussion of the derivation of dust masses which
emphasizes some of the difficulties. He emphasizes that here is considerable
disagreement about the grain opacity at long wavelengths, though this
disagreement is
somewhat exaggerated by illustrating the most extreme of the models
discussed by
Rowan-Robinson
(1986)
in which Q
all the way to 1 mm. Draine shows
that if
only IRAS observations are available of galaxies, then the derivation of
dust mass is
very uncertain, since several rather different models could in principle
be fitted to
the same observations. However provided a significant proportion of the
12-100 µm
emission from a galaxy is due to cirrus, and fluxes are available in all
four IRAS
bands, a good separation into cirrus and starburst components can be
made, and
reasonable estimates of dust mass derived. Observations at long
wavelength (> 300
µm) are very valuable in tying down the value of X , the radiation
field intensity, and
are essential if the 12-100 µm spectrum is dominated by a starburst.
Table 2 gives dust masses derived from the study of Hughes et al (1989) based on the grain model of Rowan-Robinson (1989) described in section 5 above. Comparison of the dust mass in the cirrus component with the neutral hydrogen masses given by Young et al (1989) shows normal gas-to-dust ratios for this model in most cases. However since in many cases the neutral hydrogen in a galaxy extends well beyond the optical image, whereas the bulk of the infrared emission is generally located within the optical image, there may be a tendency to underestimate the total dust mass from far infrared observations. Dust in the outer parts of a galaxy, illuminated with a starlight intensity much lower than in the central regions, may contribute only a very small fraction of the total infrared flux. Sensitive observations at long wavelengths with large beam-throws will be needed to characterize such dust.
| galaxy | distance | ________ | cirrus model | ___________ | starburst model | |
| (Mpc) | X | depletion | log Md(C) | log M(HI) | log Md(SB) | |
| (H=50) | of 5 Å grains | |||||
| NGC520 | 45.4 | 30 | 90% | 7.25 | 10.10 | 5.94 |
| NGC1614 | 92.9 | 30 | 90% | 7.57 | 9.88 | 6.83 |
| NGC2076 | 48.4 | 10 | 50% | 7.73 | ||
| NGC2339 | 46.7 | 10 | 90% | 7.50 | 10.05 | 5.75 |
| NGC3690 | 62.1 | 1 | - | 8.34 | <9.73 | 6.97 |
| NGC4102 | 19.7 | 10 | 90% | 6.97 | 9.02 | 5.60 |
| NGC7469 | 102.0 | 30 | 90% | 7.63 | 9.90 | 6.80 |
It is important when modeling the far infrared emission from dust in
galaxies to take
account of the fact that several grain components are present, at different
temperatures. Calculations based on the assumption of a single composite
grain model
and a single temperature are unlikely to yield accurate results. However
the cirrus
models of Fig 10 can be
approximately fitted at long wavelengths with a
2B (T) curve, with the values of T as given in
Table 3 for different X. The validity of this fit
is for 
> 1700/T
µm. Also given for these models are the values of
log{S(100) / S(60)} and log {Md / S(100µm)
D2}, log {Md / S(800µm) D2}. Note that
whereas Md/S100 D2
approximately proportional to X, Md / S800
D2 approximately proportional to X0.3, so much
more accurate dust
masses can be obtained if long wavelength observations are available.
| X= | 1 | 3 | 5 | 10 | 20 | 30 | 50 | 100 | 200 | 500 | SB |
| log{S(100) / S(60)} | 0.69 | 0.70 | 0.64 | 0.54 | 0.44 | 0.34 | 0.24 | 0.13 | 0.03 | -0.11 | 0.0 |
| T(
2B) a
| 16 | 19 | 21 | 24 | 27 | 29 | 31 | 34 | 37 | 43 | 40 |
| log(Md/s100 D2) b | 4.08 | 3.42 | 3.16 | 2.83 | 2.60 | 2.37 | 2.17 | 1.93 | 1.67 | 1.44 | 1.33 |
| log (Md/S800 D2) b | 4.99 | 4.84 | 4.78 | 4.70 | 4.62 | 4.57 | 4.52 | 4.43 | 4.34 | 4.19 | |
| a valid for
> 1700/T µm
| |||||||||||
| b solar masses/(Jy Mpc2) | |||||||||||