2. Current theoretical models
Detailed theoretical comparisons between electromagnetic scattering models involving small graphite grains and the interstellar UV feature are complicated by the fact that graphite is a highly anisotropic material. In particular, an approximation must be used when computations involving Mie theory (valid only for isotropic spheres) are carried out. The MRN model (Mathis et al. 1977) and its variants, using a size distribution of spherical grains of silicate and graphite, can explain the mean extinction curve, but fail to satisfy the above observational constraints. Draine (1988) has studied the UV feature produced by graphite particles using the discrete dipole approximation (DDA). This method is ideally suited for handling the anisotropic dielectric tensor of graphite. He found that only particles of small elongation with equivalent radii in the range 100-200 could provide a reasonable fit to typical interstellar UV features.
Draine & Malhotra (1993) studied the variations in peak position, width, and strength of the bump for various models based on a size distribution of graphite grains to see whether they were compatible with the observational constraints. DDA calculations included spherical graphite grains with an ice coating, spheroidal graphite grains, and graphite spheres in contact with silicate spheres. All models using variations in shape or coating produced correlations between the peak position and width. Therefore, they concluded that the variations observed must be due to changes in the dielectric properties of the grains either through impurities or surface effects, rather than purely "geometric" effects.
Mathis (1994) considered a model consisting of a graphite oblate spheroidal core and a coating of material represented by an appropriately chosen single Lorentz oscillator. The weakness of this model lies in the fact that the shape of the grain had to be unreasonably fine-tuned in order to reproduce the stability in peak position of the UV feature. Having a coating to broaden the bump and eliminate correlations between its width and its peak position can be considered a second order effect, the overall shape of the grain being the first order effect. Therefore, implicit in this model is the unlikely assumption that all interstellar grains along every possible line of sight have exactly the same shape. Any deviation in shape shifts the peak position outside the observed range. Furthermore, variations in shape introduce a correlation between the strength, the width, and the peak position of the feature. Since the width and peak position of the narrowest interstellar UV features are narrower and shifted to smaller wavenumbers, respectively, compared to those of Rayleigh graphite grains, Mathis had to "tinker" with the dielectric function of graphite tabulated by Draine (1985). This is somewhat justified in view of the lack of agreement between laboratory measurements carried out by various authors in that spectral region (see e.g., Draine & Lee 1984), but it introduces additional free parameters. Note that virtually all of these graphite optical constant measurements yield a plasmon resonance for Rayleigh spheres at wavenumbers significantly larger than .
Henrard et al. (1993) considered a model in which the bump carrier was assumed to consist of small spherical onion shells of graphite. Again, an unreasonable fine-tuning in the number of shells was required to reproduce the peak position of the interstellar UV feature.
© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998