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E j should be a blackbody times 2 however the actual

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Unformatted text preview: derations that the equilibrium temperature of the dust scales weakly with the intensity of the ambient radiation; for example, if the € radiation field normalization is G0, then Td~G01/(4+β). For silicate grains, if we model the dielectric constant by a superposition of damped harmonic oscillators, 1 χ (ω ) ∝ 2 , ω 0 − ω 2 − iγω then we have β=2 and we expect Td~G01/6. For an a=0.1 μm grain, and parameters εDC=11 and ν0~1 THz the above € numbers give L ≈ 8×10−20(Td/K)6 erg/s. The flux of starlight in the far UV is 1.2×10−4G0 erg/cm2/s/sr, where G0 is a normalization (of order ~1.7 in the diffuse ISM).1 Assuming a geometric cross section for absorption (good to an order of magnitude in the FUV), we find that the absorbed power by the above grain is 5✕10−13 erg/s. This suggests Td = 14G01/6 K. This is roughly correct, although values of ~18 K are more typical. Note that this is far greater than what one would obtain for a blackbody in the ISM due to the steep fall ­off of emission with frequency. For graphite grains, which are conductors, the expected behavior at low frequencies is that Imε ρω → ∝ ω, 2 |ε + 2 | 4π so once again we expect the behavior that the total grain luminosity scales as L~Td6. The thermal emission spectrum from the dust peaks at ~150 μm. At lower € frequencies (longer wavelengths) we expect to see a modified blackbody, i.e. jν should be a blackbody times ν2. However, the actual spectrum observed by COBE/FIRAS2 deviates from a modified blackbody at ν<500 GHz, with excess emission observed. The FIRAS team suggested the fit: 1 Tielens, Ch. 1. 2 Wright et al, ApJ 381, 200 (1991) 5 jν (dust ) ∝ ν 2 [ Bν (20.4 K) + 6.7 Bν ( 4.77K)]. This is suggestive of an additional “very cold dust” component. This component has attracted much attention, by the FIRAS team3 and others. € Explanations have fallen into two major categories. One is that there really is very cold dust, e.g. due to material with low optical/UV absorption or very high millimeter wave emissivity, or due to a population of very large grains (although the expected dependence of the second blackbody temperature on G0 is not observed). The other is that the emissivity law (equivalently, the frequency dependence of the susceptibility) we have used is wrong, and an enhancement of Im ε above the ν1 dependence occurs for ν < 500 GHz. This explanation is most commonly invoked today but the case is not closed....
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