Stratified dust grains in the interstellar medium -: I.: An accurate computational method for calculating their optical properties

We present an accurate method of computing the optical properties of layered spherical grains in which the grain core and the layers may each have different refractive indices. We show how the results of this method differ from effective medium approximations commonly in use. We use the method to compute the optical properties of spherical dust grains composed of silicate cores coated with two carbonaceous layers, the inner layer of sp(2) carbon and the outer layer of sp(3) carbon, and explore the consequences of varying the core-grain size distribution and the thicknesses of the carbonaceous layers. Guided by these results, we compute a family of interstellar extinction curves in which the underlying extinction is caused by a size distribution of silicate cores coated with two carbonaceous layers; the well-known extinction bump at 217.5 nm is attributed to a large population of polycyclic aromatic hydrocarbon (PAH) molecules for which a data base of computed optical properties exists. The family of curves is created by varying the extents of the sp(2) and the sp(3) layers. The so-called 'standard' observed interstellar extinction curve is well matched by one of this family of computed curves. The total amount of carbon required in this model is within the carbon budget for the interstellar medium. We also show that thin carbon mantles tend to suppress 10 and 20 mu m emission from very small silicate cores that are heated by the absorption of a single photon.