On Graphite Particles as Interstellar Grains, II

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Abstract
A closer examination of interstellar reddening on the basis of graphite grains has been undertaken. The Mie formulae have been computed for values of the complex refractive index corresponding to graphite and accurate extinction curves constructed for graphite spheres of various radii. The reddening law is found to be essentially the same as that given by Hoyle and Wickramasinghe provided the radii are less than ∼ 5 × 10 −6 cm. For slightly larger particles, with radii ∼ 8 × 10 −6 cm, the reddening law already begins to deviate markedly from this curve. Particles of radii 8 × 10 −6 cm are found to have an albedo y ≅ 0.4 at a wavelength λ = 0.4 μ , whereas smaller particles, which fit the reddening law better, possess somewhat lower albedos. Grains of radius ∼ 5 × 10 −6 cm have an albedo of ∼ 0.3 at a wavelength of 0.4 μ . Albedo considerations lead us to examine the possibility that graphite grains, in certain circumstances, may become coated with ice. Rigorous computations have also been done to obtain extinction and scattering cross-sections for graphite spheres covered with concentric spherical shells of ice. It is found that graphite cores, which themselves come near to satisfying the reddening law, do not lose this property when they become coated with ice. The outer radius of a grain may increase to as much as thrice the core radius. The effect of the ice is to produce as light steepening of the extinction curve in the blue, whilst also enhancing the blue albedo. In a typical case the albedo at λ = 0.4 μ is raised to about 0.8. Expressions have been derived for the extinction cross-sections of graphite grains in the form of small oblate spheroids with anisotropic conductivity. It is shown that provided 2 πa / λ ≪ 1, the extinction cross-section for light with electric vector perpendicular to the axis of symmetry is ∼ 10 2 times that for light with electric vector parallel to the axis of symmetry. For larger grains with 2 πa / λ ∼ 1, this ratio may not be much smaller than ∼ 10 at visual wavelengths. These results do not appear to depend strongly on the ratio of axes of the spheroid, and are essentially due to the anisotropic conductivity of graphite. Normalized reddening curves have been constructed for small oblate spheroidal grains which are aligned by a magnetic field. It is shown that the variability of the reddening law observed by Wampler cannot be produced by fluctuations in the alignment of graphite grains. Such an effect may, however, be caused by variations in the amount of ice round graphite grains.

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