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# In the presence of a multicomponent model for the

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Unformatted text preview: , so it is common to normalize extinction to the hydrogen column density NH (units: cm−2). (In theory this is the total hydrogen density, atomic, ionized, or molecular; although often only NHI is known directly.) Then the extinction curve is given by: Aλ 1 dn gr = 1.086 ∫ [σ abs (a) + σ sc ( a)]da. NH n H da Here dngr/da is the grain size distribution, and we have normalized it to the H density. In the presence of a multi ­component model for the grain composition, we € should include a summation over the components. The total amont of element X in dust grains is given by n X,dust 1 dn gr 4 3 f X,mass =∫ πa ρ da , nH n H da 3 mX where ρ is the grain density and fX,mass is the fraction by mass of the grain material in X. This represents an important constraint on grain models, since otherwise one € 2 could place most of the dust in “boulders” (a >> 1 μm) that have no observable effect on extinction or thermal emission. B. FEATURES We now consider the basic features of the extinction curve and their uses. The model shown below indicates the major features of an extinction curve. 1.00E ­20 Milky Way, R_V=3.1 (Model) A_lambda/N_H (cm^2) 1.00E ­21 1.00E ­22 1.00E ­23 1.00E ­01 1.00E+00 Wavelength (microns) The two most prominent aspects of this curve are (i) the broadband slope (Aλ decreases as something between λ−1 and λ−2), and (ii) the bump at 2200Å. The rollover of the broadband slope across the optical bands (i.e. where there are no features in the dielectric constant) is suggestive of a break in the grain size distribution at a few tenths of a micron. As described in the previous lecture, the 2200Å bump is believed to be due to an electronic absorption band in the carbonaceous grains. Thus its strength is indicative of the amount of carbonaceous material. As we found in the last lecture, the strength of absorption (assuming grain sizes a<<λ) is proportional to a3 (i.e. to grain volume), whereas for a>>λ the absorption scales as ~a2 and the strength of spectral features is even weaker. Therefore one might naively guess that the 2200Å bump is telling us about the amount of carbon in small grains (radius of a few × 0.01μm or smaller). The amount of such carbon required is (by number) C:H~6✕10−5, or roughly a quarter of the solar abundance (with weak dependence on how this is distributed among the range of sizes from PAH to several tens of nm). A further ~30% of solar abundance (C:H~10−4) can be found in the gas phase (as 3 traced by...
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