Modeling optical properties of cosmic dust grains using a distribution of hollow spheres

In this paper we study the combined effects of size and shape of small solid state particles on the absorption, emission and scattering characteristics. We use the statistical approach to calculate these optical properties. In this approach the average optical properties of an ensemble of particles in random orientation are represented by the average optical properties of an ensemble of simple shapes. The validity of this approach is studied in detail for a uniform distribution of hollow spheres where the fractional volume of the central inclusion is varied. We apply the results to two different areas of interest, i) infrared spectroscopy; and ii) polarization of scattered light. The effects of particle size and shape on the optical characteristics are discussed. We compare the results using the distribution of hollow spheres with those obtained by using randomly oriented spheroids. Also we compare the results with observations and laboratory measurements. The distribution of hollow spheres is very successful in reproducing laboratory measurements of the scattering angle distribution of the degree of linear polarization for incident unpolarized light of randomly oriented irregular quartz particles. Furthermore, we show that we are able to derive the size distribution of dust grains by fitting the measured degree of linear polarization using computational result for hollow spheres. It is shown that the distribution of hollow spheres is a powerful tool for studying light scattering, absorption and emission by cosmic dust grains and in particular when large numbers of particle parameters need to be considered since the computational demand of the distribution of hollow spheres is small.