Annu. Rev. Astron. Astrophys. 1990. 28: 37-70
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2.3 Mean Extinction Laws

Table 1 is an estimate of the extinction law for the observable range of wavelengths, normalized to J (approx 1.25 µm) because the extinction law is assumed to be independent of environment for lambda > 0.9 µm. The reader can convert to A(lambda) / A(V) by means of the tabulated A(V) / A(J). There are two columns for lambda < 0.9 µm, representing the mean for diffuse dust (RV = 3.1) and outer-cloud dust (RV = 5), both calculated from CCM89. The difference between the two laws is striking. The 9.7- and 18-µm feature profiles, as given by ``astronomical silicate'' (DL84), have been added to a power-law interpolation of an underlying continuum fitted between 250 and 7 µm. The profile of the silicate band was truncated at 25 µm, as is appropriate for circumstellar dust (128), but perhaps not for interstellar dust. The FIR opacity should be extrapolated to longer wavelengths with a lambda-2 dependence (see Section 3.2.3); the value in the table is determined by the estimate of Hildebrand (70). The ionizing-UV cross sections are from Martin and Rouleau (107), adjusted by a factor of 1.15 to make them continuous with the extinction value of CCM89 at 0.12 µm. Both the ``astronomical silicate'' and ionizing-UV opacities are based upon the bare-silicate/graphite grain model (see Section 8) and depend (through the Kramers-Krönig relations) upon the assumption that interstellar grains have densities of ~ 3 gm cm-3.

Table 1. Interstellar extinction and A(lambda) / A(J), where J approx 1.25 µm a
Table 1
a A(lambda) / A(J) is the same for lambda > 0.9 µm for all lines of sight, to within present errors. To estimate A(lambda) / N(H), multiply tabulated entry for RV = 3.1 by 1.51 x 10-22 cm2 (H atom)-1. Except as noted below, entries are calculated from CCM89. Other values of RV can be determined from that paper.
b For lambda > 250 µm, multiply entry for 250 µm by (250 µm / lambda)2.
c For lambda < 0.1 µm, entries are from (107), increased by 1.15 for continuity with the CCM89 extinction value at 0.12 µm.

The entries in the table for lambda > 15 µm are uncertain by at least a factor of two. There are as yet very few observational constraints upon the extinction law between the longer wavelengths of the silicate feature (which probably varies from one line of sight to another) and wavelengths lambda > 100 µm, for which the energy is produced by steady-state emission from large grains. The opacity at lambda > 100 µm is somewhat constrained by the emission from isolated clouds warmed by the interstellar radiation field, which can be estimated.

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