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Interstellar dust grains are heated primarily by absorption of starlight photons. A small fraction of the absorbed starlight energy goes into luminescence or ejection of a photoelectron, but the major part of the absorbed starlight energy goes into heating (i.e., vibrationally exciting) the interstellar grain material. Figure 5 shows grain temperature vs. time simulated for four sizes of carbonaceous grains exposed to the average interstellar radiation field. For grain radii a gtapprox 100 Å, individual photon absorptions are relatively frequent, and the grain heat capacity is large enough that the temperature excursions following individual photon absorptions are relatively small; it is reasonable to approximate the grain temperature as approximately constant in time. For a ltapprox50 Å grains, however, the grain is able to cool appreciably in the time between photon absorptions; as a result, individual photon absorption events raise the grain temperature to well above the mean value. To calculate the time-averaged infrared emission spectrum for these grains, one requires the temperature distribution function (see, e.g., Draine & Li 2001).

Figure 5

Figure 5. A day in the life of 4 carbonaceous grains, exposed to the average starlight background. tauabs is the mean time between photon absorptions.

Figure 6 shows the average emission spectrum of interstellar dust, based on observations of the FIR emission at high galactic latitudes, plus observations of a section of the galactic plane where the surface brightness is high enough to permit spectroscopy by the IRTS satellite (Onaka et al. 1996; Tanaka et al. 1996).

Figure 6

Figure 6. Observed emission spectrum of diffuse interstellar dust in the Milky Way. Crosses: IRAS (Boulanger & Perault 1988); squares: COBE-FIRAS (Finkbeiner et al. 1999); diamonds: COBE-DIRBE (Arendt et al. 1998); heavy curve for 3-4.5 µm and 5 - 11.5µm: IRTS (Onaka et al. 1996, Tanaka et al. 1996). The total power ~ 5.1 × 10-24 ergs s-1 / H is estimated from the interpolated broken line.

The similarity of the 5-15 µm spectrum with that of reflection nebulae is evident (see Figure 3). Approximately 21% of the total power is radiated between 3 and 12 µm, with another ~ 14% between 12 and 50 µm. This emission is from dust grains that are so small that single-photon heating (see Figure 5) is important. The remaining ~ 65 % of the power is radiated in the far-infrared, with lambda Ilambda peaking at ~ 130 µm. At far-infrared wavelengths, the grain opacity varies as ~ lambda-2, and lambda Ilambda propto lambda-6 / (ehc / lambda k Td - 1) peaks at lambda = hc / 5.985 k Td = 134 µm (18 K / Td). The emission spectrum for 18 K dust with opacity propto lambda-2 shown in Figure 6, provides a good fit to the observed spectrum for lambda geq 80 µm, but falls far below the observed emission at lambda leq 50 µm. From Figure 6 it is apparent that ~ 60% of the radiated power appears to originate from grains which are sufficiently large (radii a gtapprox 100 Å ) so that individual photon absorption events do not appreciably raise the grain temperature.

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