Modeling Porous Dust Grains with Ballistic Aggregates I: Geometry and   Optical Properties
  We investigate the scattering and absorption of light by random ballistic aggregates of spherical monomers. We present a general measure for the porosity of an irregular particle. Three different classes of ballistic aggregates are considered, with different degrees of porosity. Scattering and absorption cross sections are calculated, using the discrete dipole approximation (DDA), for grains of three compositions (50% silicate and 50% graphite; 50% silicate and 50% amorphous carbon; and 100% silicate), for wavelengths from 0.1 micron to 4 micron. For fixed particle mass, increased porosity increases the extinction at short wavelengths, but decreases the extinction at wavelengths long compared to the overall aggregate size. Scattering and absorption cross sections are insensitive to monomer size as long as the constituent monomers are small compared with the incident wavelength. We compare our accurate DDA results with two other approximations: the analytical multi-layer sphere (MLS) model and effective medium theory (EMT). For high porosity and/or absorptive materials, the MLS model does not provide a good approximation for scattering and absorption by ballistic aggregates. The EMT method provides a much better approximation than the MLS model for these aggregates, with a typical difference less than 20% in extinction and scattering cross sections compared with DDA results, for all types, compositions and wavelengths probed in this study. 
Yue Shen, B. T. Draine, Eric T. Johnson (Princeton)