Beyond Mie Theory: The Transition Matrix Approach in Interstellar Dust Modeling

Abstract

We model cosmic dust grains as aggregates (clusters) of spheres of appropriate geometry, whose optical properties we calculate in the framework of the transition matrix method. The calculation is performed without resorting to any approximation and with a computational effort that is noticeably lighter than the one required by other methods. Whatever the geometry chosen to model the cosmic grains, the orientational averages that are necessary to describe the propagation of the electromagnetic radiation through a dispersion of clusters are easily handled by exploiting the transformation properties of the transition matrix elements under rotation of the coordinate frame. In this paper we focus on the potentialities of the cluster model by comparing the extinction spectrum of a sphere of astronomical silicates with those of aggregates containing the same mass of silicates and composed of up to 12 spheres. Our main result is that, when a given mass of silicates is subdivided into clustering spheres, the extinction increases in regions of the spectrum determined by the degree of subdivision. We also show to what extent the substitution of the material of some of the clustering spheres with the same volume of carbon changes the extinction signature of the clusters. Finally we show to what extent modification of the geometry of the clusters produces detectable changes in their optical signatures. Detailed analysis of our results leads us to the conclusion that modeling the dust grains as clusters of a single morphology is not sufficient to describe the extinction in the whole wavelength range of astrophysical interest. The cluster model may help emphasize the decisive role of morphology in the identification of sustainable structures for dust grains in the typical physical and chemical conditions of the diffuse interstellar medium.