Infrared extinction by homogeneous particle aggregates of SiC, FeO and SiO2: comparison of different theoretical approaches

Particle shape and aggregation have a strong influence on the spectral profiles of infrared phonon bands of solid dust grains. Calculating these effects is difficult due to the often extreme refractive index values in these bands. In this paper, we use the Discrete Dipole Approximation (DDA) and the T-matrix method to compute the absorption band profiles for simple clusters of touching spherical grains. We invest reasonable amounts of computation time in order to reach high dipole grid resolutions and take high multi-polar orders into account, respectively. The infrared phonon bands of three different refractory materials of astrophysical relevance are considered Silicon Carbide (SiC), Wustite (FeO) and Silicon Dioxide (SiO2). We demonstrate that even though these materials display a range of material properties and therefore different strengths of the surface resonances, a complete convergence is obtained with none of the approaches. For the DDA, we find a strong dependence of the calculated band profiles on the exact dipole distribution within the aggregates, especially in the vicinity of the contact points between their spherical constituents. By applying a recently developed method to separate the material optical constants from the geometrical parameters in the DDA approach, we are able to demonstrate that the most critical material properties are those where the real part of the refractive index is much smaller than unity. 1 phone: (+45) 3532 5229, fax: (+45) 3538 9157 , e-mail: [email protected] Preprint submitted to Elsevier Science 5 February 2008 Fig. 1. The clusters we study; a linear cluster of five particles lin5, a seven particle cluster frac7 and a eight particle cluster sc8. Grain growth by aggregation is an important process in dense cosmic environments as well as in the Earth’s atmosphere. Besides influencing dynamic properties it also changes the absorption and scattering properties of the solid dust particles for electromagnetic radiation (e.g. [1,2]). This is especially true in spectral regions where resonant absorption occurs, such as the phonon bands in the infrared (IR). It is quite well known that shape and aggregation effects actually determine the band profiles of such absorption and emission bands, which hinders e.g. the identification of particulate materials by their IR bands. Despite many detailed investigations the full understanding of the influence of grain aggregation is still lacking, due to the complicated nature of the problem (e.g. [3,4]). We have investigated different simplified cluster shapes, as a means to compare how the numerical codes which are often used in astrophysical calculations manage to converge. The clusters consist of 5, 7 and 8 particles and are of significantly different shapes. For the material properties we have considered three astrophysically relevant materials differing in their optical properties; Silicon Carbide (SiC), Wustite (FeO) and Silicon Dioxide (SiO2). The paper is structured such that Sect. 1 presents a description of the cluster shapes, Sect. 2 provides a description of the different materials considered and their optical properties. In Sect. 3 the numerical methods used for determining the extinction of the clusters are described. Sections 4 and 5 describe our results for the cluster-of-spheres method and the DDA calculations, respectively, and describe the convergence problems encountered by the different methods. Sect. 6 offers our conclusions. 1 Cluster Structures We consider clusters of identical touching spherical particles arranged in three different geometries: fractal, cubic, and linear. For a high precision of the calculations, we restrict the number of particles per cluster to less than 10.