The anomalous extinction law

In this paper we present the results of the calculations of anomalous extinction laws characterized by different values of the ratio of the total to selective extinctionR=A _v/E(B-V). As far as we are aware, no such theoretical extinction laws have been published before. The calculation is based on the Mie theory of light scattering by small particles assuming a two-grain dust model of Mathiset al. (1977) and by adopting theri particle size (a) distribution, given byn(a)=a ^–3.5, in which the minimum and maximum size is taken to be 0.005 and 0.22 m, respectively. Furthermore, we use the dielectric functions for the two types of grains, graphite and astronomical silicate, as derived by Draine and Lee (1984), published in tabular form by Draine (1985). Following Mathis and Wallenhorst (1981), we then obtained the anomalous extinction laws by changing the upper size cutoff of the particles.A comparison shows that the calculated anomalous extinction laws agree quite well with the corresponding laws derived observationally using the colour-difference method. Finally, a trial and error method for the determination of the anomalous extinction law based on a comparison of the observed extinction-free spectral energy distribution with the corresponding theoretical Kurucz (1979) model, is explained.