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The $\lambda$ 2175Å feature

Laboratory and theoretical modelling of the UV bump on the interstellar extinction curve is a very popular topic in dusty investigations. Since the discovery of the bump by Stecher ([1965]) and its first explanations (Wickramasinghe and Guillaume, [1965]; Stecher and Donn, [1965]), consideration proceeded in the following directions: search for carrier candidates, improvement of the optical constants (mainly for graphite being the most likely candidate) and application of more progressive light scattering theories which give the possibility of including the particle shape and material anisotropy effects. Among possible candidates, silicate (enstatite), irradiated quartz, oxides (MgO, CaO), organic molecules were considered too. However, carbonaceous species and especially graphite are the favourite material. The number of different explanations of the UV bump (both successful and failed) using carbon-based materials is rather large. They include consideration of both ordered and disordered forms of carbon: graphite, amorphous and graphitic carbons, coals, quenched carbonaceous composites, PAHs, carbonaceous (amorphous/glassy) particles (see Mennella et al., [1998] and references therein). The use of well-ordered carbon like graphite is preferable because of smaller amount of carbon required although perfectly ordered, true graphite is unlikely to be present in the interstellar medium¹.

The problem is to interpret simultaneously the central position of the peak and its width². Unfortunately, this problem does not have unique solution: the observations can be explained, for example, by the effects of coating (Mathis, [1994]), clumping (Rouleau et al., [1997]) or clustering (Schnaiter et al., [1998]) of the isolated carbon particles.

The contradictoriness of identification of the $\lambda$ 2175 Å feature is illustrated by Fig. 10 where the profiles were calculated using the model of graphite spheres.

Figure 10: Normalized extinction efficiencies for graphite spheres. The calculations were made for homogeneous particles (upper panel) and hollow particles with a different fraction of vacuum (middle panel). The curve marked as ``observations'' corresponds to the wavelength dependence of the UV bump given by the mean galactic extinction curve (see,e.g., Sect. 3.1.2 in Voshchinnikov [2002]). The central position of the observed UV bump and its range of variations are marked. The lower panel shows the summary extinction of two graphite spheres with radii $r_{\rm s} = 0.005 \,{\mu}\rm{m}$ and $r_{\rm s} = 0.03 \,{\mu}\rm{m}$ (from upper panel) taken in equal proportions. All calculations were made in the ``2/3-1/3'' approximation (Eq. (7)).

The anisotropic dielectric functions for graphite were taken from Laor and Draine ([1993]) and so-called ``2/3-1/3'' approximation for the averaged extinction factors was employed

$$Q_{\rm ext} = \frac{2}{3}\, Q_{\rm ext}(\varepsilon_{\bot}) + \frac{1}{3}\, Q_{\rm ext}(\varepsilon_{\vert\vert}),$$ (7)

where $\varepsilon_{\bot}$ and $\varepsilon_{\vert\vert}$ are the dielectric functions for two cases of orientation of the electric field relative to the basal plane of graphite and the efficiencies $Q_{\rm ext}(\varepsilon_{\bot})$ and $Q_{\rm ext}(\varepsilon_{\vert\vert})$ are calculated with the Mie theory. Using the DDA, Draine and Malhotra ([1994]) showed that the ``2/3-1/3'' approximation is sufficiently accurate in studying the extinction profile of the $\lambda$ 2175 Å feature: in the range $\lambda^{-1} =$3.5-5.0 $\,{\mu}\rm {m}^{-1}$ the maximum error is approximately $6(r_{\rm s}/0.04\,{\mu}\rm {m})$%, for .

As follows from Fig. 10, the profiles with the central position near $\lambda_0^{-1} = 4.6 \,{\mu}\rm {m}^{-1}$ can be obtained if we take the compact spheres with radius $r_{\rm s} = 0.015\,{\mu}\rm {m}$ (upper panel) or hollow spheres with $r_{\rm s} = 0.010\,{\mu}\rm {m}$ and $V_{\rm vac}/V = 0.1$ (middle panel). Although for single-size particles the width of the calculated profiles is smaller than the observed one, a simple bi-modal size distribution allows one to fit both the position and the width of the mean galactic profile (Fig. 10, lower panel).

Note that the shape effects cannot be identified from extinction measurements (see, e.g., Draine and Malhotra, [1994], Mathis, [1994]). Duley and Seahra ([1998]) investigated extinction produced by small carbon particles consisting of aromatic rings in configurations similar to those of PAH molecules. They found that the changes of the bump position and width can be attributed to the variations of the degrees of hydrogenation, ionization and defects.

So, we can conclude that identification of the $\lambda$ 2175 Å feature is still a problem without a single solution, especially if only the extinction profile is considered.