Extinction and dust properties in a clumpy medium

The dust content of the universe is primarily explored via its interaction with stellar photons, which are absorbed or scattered by the dust, producing the effect known as interstellar extinction. However, owing to the physical extension of the observing beam, real observations may detect a significant number of dust-scattered photons. This may result in a change in the observed (or effective) extinction with a dependence on the spatial distribution of the dust and the spatial resolution of the instrument. We investigate the influence of clumpy dust distributions on the effective extinction toward both embedded sources and those seen through the diffuse interstellar medium (ISM). We use a Monte Carlo radiative transfer code to examine the effective extinction for various geometries. By varying the number, optical depth and volume-filling factor of clumps inside the model for spherical shells and the diffuse interstellar medium (ISM), we explore the evolution of the extinction curve and effective optical depth. Depending on the number of scattering events in the beam, the extinction curve is observed to steepen in homogeneous media and flatten in clumpy media. As a result, clumpy dust distributions are able to reproduce extinction curves with arbitrary R-V,R-eff, the effective ratio of total-to-selective extinction. The flattening is also able to wash out the 2175 angstrom bump and results in a shift of the peak to shorter wavelengths. The mean R-V,R-eff of a shell is shown to correlate with the optical depth of an individual clump and the wavelength at which a clump becomes optically thick. Similar behaviour is seen for edge-on discs or tori. However, at grazing inclinations the combination of extinction and strong forward scattering results in chaotic behaviour. Caution is therefore advised when attempting to measure extinction in AGN tori for example or toward SNIa or GRB afterglows. In face-on discs, the shape of the scattered continuum is observed to change significantly with clumpiness, however, unlike absorption features, individual features in the scattering cross-sections are preserved. Finally, we show that diffuse interstellar extinction is not significantly modified by scattering on distance scales of a few kpc.