Extinction calculations of multi-sphere polycrystalline graphitic clusters - A comparison with the 2175 Å peak and between a rigorous solution and discrete-dipole approximations

Certain dust particles in space are expected to appear as clusters of individual grains. The morphology of these clusters could be fractal or compact. In this paper we study the extinction by compact and fractal polycrystalline graphitic clusters consisting of touching identical spheres, based on the dielectric function of graphite from Draine & Lee (1984). We compare three general methods for computing the extinction of the clusters in the wavelength range 0:1 100 m, namely, a rigorous solution (G erardy & Ausloos 1982) and two dierent discrete-dipole approximation methods { MarCODES (Markel 1998) and DDSCAT (Draine & Flatau 1994). We consider clusters of N = 4, 7, 8, 27, 32, 49, 108 and 343 particles of radii either 10 nm or 50 nm, arranged in three dierent geometries: open fractal (dimension D =1 :77), simple cubic and face-centred cubic. The rigorous solution shows that the extinction of the fractal clusters, with N 50 and particle radii 10 nm, displays a peak within 2% of the location of the observed interstellar extinction peak at4.6 m 1 ; the smaller the cluster, the closer its peak gets to this value. By contrast, the peak in the extinction of the more compact clusters lie more than 4% from 4:6 m 1 . At short wavelengths (0:1 0:5 m), all the methods show that fractal clusters have markedly dierent extinction from those of non-fractal clusters. At wavelengths >5 m, the rigorous solution indicates that the extinction from fractal and compact clusters are of the same order of magnitude. It was only possible to compute fully converged results of the rigorous solution for the smaller clusters, due to computational limitations, however, we nd that both discrete-dipole approximation methods overestimate the computed extinction of the smaller fractal clusters.