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2 m the peak in the silicate size distribution cannot

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Unformatted text preview: C I and C II UV absorption lines – see later lectures). The rest of the carbon must be found in large dust grains. Their specific size distribution is related to the extinction curve in the optical/NIR; however silicate grains also contribute here so modeling is necessary. For the silicate grains, we know from UV absorption line spectroscopy that Si, Mg, and Fe are heavily depleted in the ISM gas phase so that they must be mostly locked up in dust. This suggests a dust mass in silicates comparable to that in carbon (volume ~3✕10−27 cm3 per H atom). One would therefore expect both to be of comparable importance in the optical/NIR. Weingartner & Draine (2001) performed χ2 fits of dust models to the observed interstellar extinction curves. Their key findings for diffuse Milky Way ISM dust are: The silicate size distribution can be fit with a peak at a ~ 0.2 μm. The peak in the silicate size distribution cannot be made too wide without putting more mass in larger grains and underproducing the UV extinction. (This UV extinction could be compensated by increasing the small carbonaceous grains, but this would overproduce the 2200Å feature.) A variety of carbonaceous grain size distributions are possible, but they are needed to contribute to the NIR extinction, so a substantial portion of the mass must be placed at a ~ few × 10−1 μm. The tail to small sizes is not constrained by the extinction curve. It is clear that the extinction curve fits are underconstrained, as one might expect. Therefore we turn to the emission from dust. 3. Infrared Emission The thermal emission from dust is a powerful diagnostic of its properties, including the grain size distribution. A. EQUILIBRIUM TEMPERATURE The equilibrium temperature of a dust grain can be derived by balancing the emitted and absorbed radiation. Specifically, we recall the luminosity per unit frequency of a grain: 192π 3 ha 3ν 4 1 Imε Lν = . 3 hν / kTd c e − 1 | ε + 2 |2 If we assume that the dielectric constant at low frequencies (where the grain emits; far below the main vibrational resonances of the material) is given by Re ε εDC = constant, while € imaginary part is given by Im ε = (ν/ν0)β−1, then we find an the emitted spectrum 4 The total luminosity is € 192π 3 ha 3 ν 3+ β Lν = 3 β −1 . c ν 0 (εDC + 2) 2 e hν / kTd − 1 4 +β 192π 3 hΓ( 4 + β )ζ ( 4 + β ) a 3 ȹ kTd ȹ L= ȹ ȹ . β ȹ h Ⱥ c 3ν 0 −1 (εDC + 2) 2 This must balance the absorbed flux: € ∞ L = 4 πc ∫ Jν σ abs (ν ) dν . 0 It is clear from these consi...
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This document was uploaded on 03/08/2014 for the course AY 102 at Caltech.

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