On graphite and the 2175 Å extinction profile

Classical electromagnetic theory is used to study the constraints placed on interstellar graphite grains by the observations of Fitzpatrick & Massa (who found large variations in FWHM γ of the bump with minimal, and uncorrelated, variations in the central wavelength λ₀). Accurate calculations using the discrete dipole approximation are used to test the accuracy of the commonly used "1/3-2/3 approximation" for graphite spheres. We show that the 1/3-2/3 approximation is sufficiently accurate for use in studying variations in the extinction profile due to changes in graphite grain size or coatings on the grains. We investigate the effect on the 2175 Å extinction profile of (1) changes in size distribution, (2) changes in grain shape, and (3) coatings of ice or other material. We show that all of the above effects produce correlated changes in both γ and λ₀. The calculated shifts in λ₀ are such that the observed near-constancy of λ₀ appears to limit variations in the size, shape, or coatings of small graphite grains. We also investigate the consequences of coagulation with other grains. We find that in the Rayleigh limit, only quite small shifts in λ^-1₀ result when a spherical graphite grain is in contact with one or two silicate grains. These shifts are small enough that such coagulation is not ruled out by the observed constancy of λ^-1₀. However, such coagulation does not appear able to account for the observed variations in profile width. We conclude that the observed variations in width of the 2175 Å profile cannot be explained by changes in graphite grain size, shape, clumping, or coating, but must instead be due to variations in the dielectric properties of the graphite, due either to impurities, degree of crystallinity, or to surface effects.