The discrete-dipole approximation and its application to interstellar graphite grains

The discrete dipole approximation (DDA), a flexible method for computing scattering of radiation by particles of arbitrary shape, is extended to incorporate the effects of radiative reaction and to allow for possible anisotropy of the dielectric tensor of the material. Formulas are given for the evaluation of extinction, absorption, scattering, and polarization cross sections. A simple numerical algorithm based on the method of conjugate gradients is found to provide an efficient and robust method for obtaining accurate solutions to the scattering problem. The method works well for absorptive, as well as dielectric, grain materials. Two validity criteria for the DDA are presented. The DDA is then used to compute extinction cross sections for spherical graphite grains and to calculate extinction cross sections for nonspherical graphite grains with three different geometries. It is concluded that the interstellar 2175 A extinction feature could be produced by small graphite grains which should have aspect ratios not far from unity.