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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 Qnu propto nu 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 lambda > 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(nu 2Bnu) 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 lambda > 1700/T µm
b solar masses/(Jy Mpc2)

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