Observational tracers of grain coagulation

Another important complication is that dust opacities are calculated from the dielectric properties of the bulk material in combination with the particle size/shape model. While the opacities of dust particles are very sensitive to their detailed shapes and sizes, these effects are difficult to separate from the underlying dielectric properties of the grain material (see Chapter 6). 

Expressing the size distributions in this way is analogous to the way a spectral energy distribution vFv presents equal energy radiated in equal logarithmic frequency bins. 

Examples of the dust cross-section distributions for astronomical silicate at different wavelengths and for different power-law particle size distributions are shown in Fig. 7.1. The 9.7 pm absorption cross-section distribution for particles with p = — 3.5 actually peaks at 1 pm, but is otherwise dominated by particles 3 pm. Thus, for this distribution, observations at 9.7 pm are not very sensitive to large particles and their presence cannot be ruled out. For only a slightly shallower size distribution with p = —3.0, the absorption cross-section suddenly becomes dominated by large particles, and particles smaller than 1 pm will not contribute much to the total opacity. At 1 mm, the picture is different. Here, the absorption 

The spectral profiles of solid-state resonances from small particles depends on both the shape and the size of the particles. This is particular true for the strong mid-infrared Si-0 stretching and O-Si-O bending modes, characteristic of circumstellar silicate dust. In the dielectric spectrum, the stretching mode is roughly centered on 10 pm, while the bending mode is centered on 18 pm. Both resonances are very broad and strongly dependent on the structure of the molecules in which the SiO  

2 Up to a certain point very large (meter-sized or larger) particles will no longer contribute to the opacity. 

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