Silicon carbide (SiC) is universally considered as the carrier of the emission band which is seen around 11.3 µm towards the circumstellar shells (CS) of many C-rich stars. This assignment may seem strange in view of the fact that 1) the measured vibrational spectrum of bulk crystalline SiC can be described by a single Lorentzian oscillator tuned at 12.6 µm (Spitzer et al. (1959), and 2) most published laboratory data on SiC powders (e.g. Friedman et al., 1981; Borghesi et al. 1985; Orofino et al. 1991) exhibit an absorption peak at a wavelength distinctly longer than 11.3 m and different for different samples.
Moreover, the analysis, by Baron et al.(1987), of the survey data provided by the Low Resolution Spectrometers (LRS) of the IRAS satellite (IRAS Science Team, 1986) showed that, of the 535 features assigned to the SiC class (class 4n) of the LRS Catalog, only about 5% peaked at 11.3 µm. Those are the features with the highest contrast (ratio of feature peak to underlying continuum). With decreasing contrast, another peak progressively grows around 11.7 µm, which ultimately dominates the feature, leaving only a shoulder near 11.3 µm. Nearly 40% of the features peak at 11.75 µm. A hint to such a dichotomy of peak wavelengths is already apparent in the dozen features previously observed by Cohen (1984) from the ground.
As early as 1974, Treffers and Cohen invoked calculations by Gilra and Code (1971) based on Mie's theory, to explain a wide feature observed in IRC 10216, around 11 µm. Indeed, this theory predicts that the appearence of the feature is strongly dependent on the size and shape of the carrier grains. However, in spite of sparse references to the extensive work of Bohren and Huffman (1983) on shape effects, this line of attack does not seem to have been carried much further in the interpretation of laboratory or celestial SiC spectra by astrophysicists. Rather, they explain away the discrepancies by invoking the red shift due to the electromagnetic influence of the potassium bromide (KBr) matrix in which SiC powders are usually embedded for IR measurements (op. cit.; Papoular, 1988; Pegourie, 1988). Some more recent works do not even mention the problem, and take it for granted that the celestial "SiC feature" is emitted by simple small spheres of crystalline SiC, with most of the discussion bearing on the effects of structural differences (e.g. Kaito et al., 1995; Speck et al., 1996).
Lately, however, Kozasa et al. (1995) considered alternative schemes, namely core-mantle spherical grains with SiC in the core and amorphous carbon in the mantle, and vice versa. They suggest that the former is "the most plausible candidate to reproduce the 11.3 µm feature". But, although, this model reproduces the observed trend of increasing red shift of the peak with decreasing contrast of the feature, it too has its problems: in the range of observed peak positions (11.3 to 11.8 µm) the carbon mantle volume fraction is unreasonably tightly constrained ( 0.5 to 0.7); the model feature is too narrow and too asymmetric as compared with observations; for small bare SiC spheres (which cannot be excluded) the feature peaks at 10.75 µm and is about 0.1 µm wide at half-maximum, at complete variance with observations. Therefore, while it is quite plausible, on thermodynamic grounds, as shown by the authors, that carbon condenses on pre-existing SiC grains, it seems necessary to pursue the search for a better model.
The difficulty lies in disentangling the combination of several effects due to size, shape and physical state (amorphous or crystalline) of SiC grains, as well as embedding matrix. Understanding laboratory measurements and using them to model celestial spectra requires at least an estimation of the individual effects. With this purpose in mind, in the present work, we study SiC particles produced by two relatively new techniques: laser pyrolysis and mechanical synthesis (briefly described in Sect. 3). The particles are small enough to minimize scattering effects, which plague many previous measurements.
Instead of trying to infer the optical properties of bulk SiC from these (or other) measurements, we consistently use those given by Spitzer et al. (1959) who showed that, for all practical purposes, they apply to both - and -SiC, and to both principal polarizations as well. Fortunately, the fact that these properties are quite accurately described by a single electron oscillator makes it easy to deduce the optical cross-section of any given ellipsoidal grain embedded in a given dielectric matrix. We show that the matrix does not shift the resonance feature as a whole but, rather, slants the profile. The necessary formulae are assembled in Sect. 2. Inversion of these formulae allows us to infer unambiguously a distribution of depolarization factors, L, for any given extinction spectrum(Sect. 3). It is then possible to compute the expected spectrum from the same particles, but in vacuum. This is done in Sect. 4 for our two powders, embedded in KBr or CsI (Cesium Iodide). Finally, it is shown that the LRS spectra of the SiC feature can be fitted with a linear combination of the two spectra expected from our powders in vacuum.
© European Southern Observatory (ESO) 1998
Online publication: December 16, 1997