Free Access
Volume 528, April 2011
Article Number A96
Number of page(s) 9
Section Interstellar and circumstellar matter
Published online 08 March 2011

Online material

Appendix A: Coated monomers

thumbnail Fig. A.1

Core-mantle particles constructed of dipoles together with their projections are shown. Each dipole is represented by one cube, green dipoles indicate astronomical silicate and black dipoles indicate amorphous carbon. . The projection shows the distribution of dipoles with different materials in the centre of the aggregate. a) single sphere of core material, b) a single core-mantle particle, c) two separated spheres of core material, d) two separated core-mantle particles, e) two connected spheres of core material, , f) two core-mantle monomers connected, .

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We calculate Qabs for core-mantle particles where we assume that the core consists of astronomical silicate and the mantle consists of either amorphous carbon or water ice. We also calculate Qabs for particles consisting of only astronomical silicate. The absorption coefficient is calculated with DDA, where we use monomers with . We consider N = 51 for all monomers (mantled and bare) so as to exclude any deviations due to surface effects. For core-mantle monomers we assume a mantle thickness of 3 dipoles so that the number of dipoles across the core is N = 45. A smaller mantle thickness gives divergent results due to the limitations of DDA. The radius of the core is assumed to 0.1 μm. A core-mantle particle has a radius of 0.113 μm so that the mantle has a thickness of 0.013 μm. For an amorphous-carbon mantle this thickness is larger than 3 nm assumed by Jones et al. (1990) and for water-ice mantles it is slightly smaller than 14.7 nm assumed by Guillet et al. (2007). For aggregates we calculate the radius of a volume-equivalent sphere to 0.126 μm for the bare cores and 0.143 μm for the core-mantle monomers.

We consider the following aggregates: a) a single core, b) a single core surrounded by a mantle, c) two cores separated by one dipole (approximating the TMM case), d) two core-mantle particles separated by one dipole (approximating the TMM case), e) two connected cores , f) two connected core-mantle particles . All of these cases are illustrated in Fig. A.1.

We calculate the absorption cross section Cabs of the particle and divide by the total volume Vcore of the cores. We then normalize to , where is either determined for the core or for a core-mantle monomer. is the volume of a core.

The results for are summarised in Tables A.1 and A.2. Table A.1 shows the increase in due to the accretion of a mantle onto a core. The results are normalized to for a core. We assume that the mantle is “free” material accreted from that gas that therefore leads to a change in the particles optical propteries. For a mantle of amorphous carbon the increase in Cabs/V is a factor of 1.86 while for water ice the increase is a factor of 1.31. Clearly, adding a carbon mantle for “free” leads to a large increase in the particle emissivity.

In Table A.2 we show the increase in due to coagulation effects for aggregates of core-mantle monomers (upper case) and pure cores (lower case).

We showed before that a single grain shows the same results as two well-separated monomers. Approaching two monomers (which is comparable with TMM calculations) results in an increase of 1.2 for grains with a mantle of amorphous carbon and for grains consisting of pure astronomical silicate.

Aggregates with a mantle of water ice show only an increase of 1.13. In the case of connected monomers the increase is largest for astronomical-silicate cores with 1.36. Astronomical silicate shows the largest n at λ = 250   μm compared to the other materials. The increase assuming a mantle of amorphous carbon is also large with 1.33. With a mantle of water ice the increase is only by a factor of 1.17. Essentially, the accretion of carbon mantles before accretion will not affect the enhanced emissivity. However, if ice mantle accrete before coagulation the “available” enhancement in emissivity is reduced by about a factor of 2.

Table A.1

Absorption cross section divided by the volume of the core Cabs/Vcore normalized to Cabs/Vcore of a single astronomical-silicate core.

Table A.2

Absorption cross section divided by the volume of the core Cabs/Vcore normalized to Cabs/Vcore of a single core-mantle grain (upper) or core of astronomical silicate (lower).

© ESO, 2011

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