Carbon Stars I - the nature of the silicon carbide around C-rich AGB stars

`Whether we are based on carbon or silicon makes no fundamental difference.
We should each be treated with appropriate respect.''
Chandra, 2010 (1984)

Introduction

It has been known for more than two decades that dust particles form in the atmospheres of cool stars and are ejected into the interstellar medium c.f. Gilra (1971), Woolf (1973), Stephens (1980), Mathis (1990) and Evans (1994). In this context there has been a great deal of work published on silicon carbide (SiC). From equilibrium condensation models, Friedemann (1969) and Gilman (1969) showed that silicon carbide should condense in the atmospheres of carbon stars. Following the work of Gilra & Code (1971), Hackwell (1972) and Treffers & Cohen (1974), a broad infrared emission feature seen in the spectra of many carbon stars, peaking between about 11.0 and 11.5µm, has been attributed to solid SiC particles. SiC is therefore believed to be a significant constituent of the dust around carbon stars. There are in fact about 70 different forms of silicon carbide, known as polytypes, and a large number of papers have been published discussing which form most closely fits the observed feature near 11µm. All these polytypes are variants of the same basic structure, based on a tetrahedral group of silicon and carbon atoms (Taylor & Jones, 1960). These seventy different forms of silicon carbide can be divided into 2 basic groups - alpha- and beta- silicon carbide (Bechstedt et al. 1997). The alpha-SiC form has a hexagonal or rhombohedric crystal structure and is very stable up to approximately 2700°C. The beta-SiC form has a cubic structure and, at T < 2100°C, is the favoured type when condensation takes place in a vacuum. Beta-SiC will transform into alpha-SiC at temperatures above about 2100°C but it is thermodynamically unlikely that this process will work in reverse. Very little (a few percent at best) alpha-SiC will transform into beta-SiC (I.P.Parkin; private communication). The difference between these two forms is small, both structurally and thermodynamically (below 2100°C), but they can be distinguished by crystallographic techniques and by their infrared spectra (See chapter 4). One of the aims of the current work was to determine whether either type predominates in the circumstellar outflows around carbon stars, via observations of the 11µm spectra of a significant sample of carbon stars.

Background

Alpha-SiC vs beta-SiC in astronomical environments

In the literature concerning the 11µm SiC feature in carbon star spectra, much of the work already published is somewhat contradictory, and certainly needs some introduction. In order to address this problem, I therefore begin with a review of some of the existing work on this topic.

Gilman (1969) and Friedemann (1969) predicted that SiC could condense in the atmospheres of cool carbon stars. Gilra & Code (1971) used this information, together with calculations published by Gilra (1972), to predict that SiC should re-emit absorbed visible radiation as a feature in the 10-13µm region. Hackwell (1972) found an emission feature in two carbon stars in this spectral region that was quite similar to Gilra's calculated emission feature. Treffers & Cohen (1974) published high resolution spectra of the SiC feature in several carbon stars and made use of unpublished calculations by Gilra, based on alpha-SiC optical constants, to interpret these spectra. It was shown that small particles of a single shape produce several narrow emission features situated between the longitudinal and transverse vibrational wavelengths of alpha-SiC at 10.2µm and 12.8µm and that particles of different shapes would produce features at different wavelengths between these limits (see also Kozasa et al. 1996). It was also shown that a continuous distribution of shapes should give a smooth feature with cut-on and cut-off wavelengths corresponding to the longitudinal and transverse vibrational modes of SiC.

Stephens (1980) investigated various dust species (silicates, carbon and SiC) with a view to explaining the visible and ultraviolet extinction in the interstellar medium (ISM). He chose to use beta-SiC for his experiments, as it is the most stable structural form of SiC below about 2000 K. He found that in order to fit the interstellar extinction curve, the SiC particles needed to be very much smaller (radius <0.005µm) than the particles he used to produce spectra. He also used the fact that no 11.5µm SiC feature is seen in the extinction curve of the ISM to constrain the SiC abundance. He concluded that ``SiC is probably not the major contributor to the observed visible and ultraviolet extinction'', contradicting the conclusion of Gilra (1971) that SiC was one of the constituents needed to explain the entire extinction curve of the ISM.

Whittet, Duley & Martin (1990) also investigated the presence of SiC in the ISM. They concurred with Stephens (1980) that SiC is not a major contributor to the ISM extinction curve, estimating that less than 5% of silicon atoms in the ISM can reside in SiC dust. To reconcile this lack of interstellar SiC with the fact that SiC is found in the circumstellar shells of carbon stars, they suggested that SiC is rare in carbon stars, citing the lack of SiC absorption in stars with optically thick circumstellar shells as evidence. However, as will be seen in section 6.7, SiC has now been seen in absorption in the spectra of several carbon stars. Another explanation for the lack of observed SiC in the ISM is the grain size. Many of the presolar SiC grains found in meteorites are large (>1µm) and may not be observable by their IR spectrum (see section 3.2.2)

Laboratory spectra

Several papers have used laboratory analyses of SiC samples to simulate the SiC emission feature at 11-13µm, with a view to identifying observed astronomical features. Friedemann et al. (1981) used two forms of commercially available alpha-SiC. They used five samples with various size distributions, made up of measured mixtures of the two types of alpha-SiC. They found that the bandwidth of the absorption feature was not affected by the size distribution or by impurities, but that the absorption peak (i.e. where the ratio of the feature intensity to the continuum intensity reaches a minimum) was affected, so that when comparing different grain-size distributions, the larger grain-sizes give rise to reduced absorption peaks. They found a peak wavelength of 11.8µm before correcting for their experimental substrate, and a wavelength peak of 11.4µm after correction. Use of the correction factor is discussed in chapter 4. They also fitted one of their sample spectra to the spectrum of Y CVn. Goebel et al. (1995) describe the unusual J-type carbon star Y CVn as having a ``somewhat different SiC band profile than normally found in other visible carbon stars''. However, our CGS3 spectrum of Y CVn is not particularly unusual in the shape and peak wavelength of its SiC feature (see Fig. 6.1 and Table 6.2 below).
 
Figure 6.1: 8-13µm flux-calibrated spectra of carbon stars (x-axis: wavelength in µm; y-axis: flux in Wm^-2 µm^-1)

Borghesi et al. (1985) performed a comparative laboratory study of several samples of both alpha- and beta-SiC. Their samples were ground and sedimented to various degrees in order to determine the effects of the size distribution. They found the feature to peak in wavelength at about 11.8µm for alpha-SiC, and at about 11.4µm for beta-SiC, before correction for the KBr-dispersion technique, and at 11.4µm and 11.0µm after correction. This agrees well with the results of Friedemann et al. (1981). Borghesi et al. (1985) also found that, for their less pure alpha-SiC samples (i.e. 89% SiC rather than 99% SiC, with carbon, silicon, metallic iron and SiO₂ impurities), the peak wavelength shifted towards longer wavelengths as the particle size increased. This did not occur for their purest alpha-SiC nor for their beta-SiC samples. Comparing this with the results of Friedemann et al. (1981), there are some obvious discrepancies as Friedemann et al. found no changes in the emission feature due to impurities. The data published by Borghesi et al. (1985) is not corrected for the use of the KBr matrix method, although they did state that it was necessary to apply a correction factor to their data. As discussed in chapter 4, the KBr correction is unnecessary. The result of applying the correction is to shift the peak wavelength of the feature. How this affects the attribution of the 11.3µm feature to a certain type of SiC is discussed later in this chapter.

Pégourié (1988) set out to derive a synthetic dielectric function for SiC, from which spectral features could be predicted. He argued that the work of Baron et al. (1987) showed alpha-SiC to be the best candidate to reproduce the 11-11.5µm feature in the IRAS LRS spectra of carbon stars. However, what Baron et al. (1987) actually concluded was that ``The shape of the strongest feature is quite similar to the mass absorption of alpha-SiC'' (whether this was KBr corrected or uncorrected data is unclear). Taken together with their statement that ``the feature becomes stronger and narrower as the temperature of the underlying continuum increases'', this implies that their alpha-SiC spectrum probably gives a good fit to features in the spectra of the carbon stars with the most optically thin dust shells. However, the same conclusion might not necessarily be applicable to cooler stars and to features produced by optically thick shells. Having decided to use alpha-SiC, Pégourié (1988) derived a comprehensive dielectric function by compiling partial data from a number of different authors and using a Kramers-Kronig analysis. He found that slight changes in impurities or morphology have a huge impact on the shape of the feature. This is consistent with the findings of Borghesi et al. (1985) and contradicts the work of Friedemann et al. (1981) discussed above. This conclusion that morphology has a big influence is also consistent with the work of Gilra presented by Treffers & Cohen (1974), regarding the sensitivity of the feature wavelength to particle shape for single-shape particles. Pégourié (1988) found that the `synthetic' alpha-SiC feature he had created had a peak wavelength of 11.33±0.5µm. This is quite similar to the results of both Friedemann et al. (1981) and Borghesi et al. (1985; after KBr-correction). However, Pégourié (1988) used the KBr-corrected data of Borghesi et al. (1985). Following the finding in chapter 4, it is my belief that the use of KBr-corrected optical constants has given rise to a synthetic spectrum with an unnecessarily shifted absorption peak.

Previous studies of the mid-infrared spectra of carbon stars

Hackwell (1972) presented spectra and photometry of eleven M-, S- and C- type stars, only two of which are classed as carbon stars: V Hya and CIT 6. The spectra of both these stars showed a broad feature between 10 and 12µm, similar to the emission feature calculated by Gilra (1972). This is one of the first published observations of the 11µm feature, although it was not attributed to SiC by Hackwell (1972). Earlier, however, Hackwell (1971) had concluded on the grounds of condensation sequence studies that SiC was likely to be a major contributor to the circumstellar dust around carbon stars.

In 1974, Treffers & Cohen published the mid-infrared spectra of two carbon stars - IRC+10216 and CIT 6. They found that both stars showed a broad emission band peaking at about 11.5µm which could be fitted very well using model spectra calculated by Gilra for small alpha-SiC particles having a distribution of shapes. Forrest, Gillett & Stein's (1975) sample of 8-13µm spectra of cool stars included seven carbon stars, four of which overlap with the present sample. They noted that the SiC feature in the spectra of the carbon stars varied in morphology from star to star. Merrill & Stein (1976) investigated the evolution of the infrared spectra of late-type stars. Their sample consisted of 23 oxygen-rich stars and 9 carbon-rich stars (four of which are also included in the present sample). They discussed the 11.5µm emission feature, attributed to SiC, which had been seen in the spectra of all carbon stars surveyed at that time and noted that it was unique to carbon stars.

Jones et al. (1978) investigated the infrared source AFGL 3068, which had been suggested by Lebofsky & Rieke (1977) to be the most heavily obscured carbon star known at that time. From its infrared spectrum from 2 to 4µm and 8 to 13µm, Jones et al. (1978) found that: 1) there was an absorption feature at 3.1µm 2) there was an absence of a silicate feature at 9.7µm; 3) there was a spectral break near 10.5µm. The first two findings confirmed that AFGL 3068 is indeed a heavily dust-enshrouded carbon star. The third discovery was attributed to absorption by SiC grains, the first time that this had been observed. The large optical depth indicated by this implies a large mass-loss rate. Jones et al. (1978) therefore suggested that if there are many sources like AFGL 3068, they could be major contributors of material to the ISM.

Cohen (1984) presented the mid-IR spectra of 10 carbon stars. He divided the spectra by appropriate blackbodies to normalise them, in order to see the SiC features more clearly. By doing this he found that there appeared to be two types of features: triangular (narrow and peaked) and rectangular (broader and flatter-topped). The triangular feature could be fitted by a laboratory spectrum of alpha-SiC from Friedemann et al. (1981). The rectangular feature could not be fitted by any of Friedemann et al. (1981)'s laboratory spectra. He suggested that these two distinct features were indicative of different mechanisms of grain formation in different stars, controlled by the mass-loss rates. Alternatively, he suggested that the different feature shapes could arise as a result of different SiC optical depths.

Baron et al. (1987) studied the IRAS Low Resolution Spectrometer (LRS) spectra of 542 carbon stars and came to the following conclusions: 1) The strength of the circumstellar SiC feature is positively correlated with the temperature characterising the underlying continuum; 2) The shape of the feature varies regularly with its strength and becomes narrower as the strength increases; 3) Weak SiC features are accompanied by an additional bump which peaks at about 8.75µm. The strongest SiC features are accompanied by a steep rise in the continuum towards 8µm.

Papoular (1988) studied the IRAS LRS spectra of about 3000 carbon stars. Using various smoothing and averaging techniques he found that the 11µm features can be divided into three types, which he denoted - SiC(a), (b), and (c). Comparing these separate groups of features to laboratory spectra taken from Borghesi et al. (1985), he found that the different types could be attributed to different laboratory samples. SiC(a) could be fitted by the purest alpha-SiC with the smallest grains, while SiC(c) was fitted by the least pure alpha-SiC with the largest grains.

Skinner & Whitmore (1988b) discussed the mass-loss rates of carbon stars. They had previously shown that the mass-loss rates of oxygen-rich stars can be determined using the strength of the 9.7µm silicate dust emission feature (Skinner & Whitmore 1988a). They attempted to use the same method for carbon stars, using the 11µm SiC feature, and concluded that the method is reliable. From a sample of 29 carbon stars, they suggested that it is likely that the mass-loss rates increase with the carbon star's age. They also suggested that the amorphous carbon to SiC grain abundance ratio increases with mass-loss rate.

In 1988 Willems published two papers on the IRAS LRS spectra of carbon stars (Willems 1988a & b). He found that, for 72 relatively hot carbon stars (T_NIR > 2000K), the SiC feature peaked near 11.7µm in most cases and was accompanied by an unidentified 8.6µm emission feature, possibly similar to the feature seen by Baron et al. (1987). For 15 cooler carbon stars (T_NIR < 2000K) he found that the SiC feature peaked near to 11.3µm and concluded that, for these cooler stars, amorphous carbon dust is the main constituent of the circumstellar dust shells.

Goebel et al. (1995) have used SiC and other dust species to create a new classification system for carbon stars. Like Chan & Kwok (1990), they proposed a model explaining the variations in dust types as related to the evolutionary status of the star. They chose to use the alpha-SiC data of Pégourié (1988) for their model. They proposed that SiC is the first species to condense (because it is very refractory). So, when the star is still relatively hot the contrast of the SiC feature should be very strong. Then, as the star cools and evolves to higher mass-loss rates, newly-formed SiC particles form nucleation sites for amorphous hydrogenated carbon (a:C-H). As the star evolves still further and more SiC grains are coated with a:C-H, the SiC feature weakens and a feature appears at about 8.5µm due to a:C-H. Features in circumstellar spectra due to a:C-H have been discussed before (Baron et al. 1987, Skinner & Whitmore 1988, Puget et al. 1985). Baron et al. (1987) suggested that, together with the 8.5µm feature, there is a feature at 11.7µm also attributable to a:C-H. If this is true both features should appear in spectra when a:C-H is present.

Meteoritic SiC

Silicon carbide grains are also found in meteorites. From isotopic studies, many of these grains are believed to have formed around carbon-rich AGB stars. Meteoritic SiC and its implications are discussed in chapter 3 (section 3.2.2) . The most notable information from meteoritic work is that all meteoritic SiC is of the beta-SiC polymorph, whereas nearly all previous work based on astronomical observations, discussed in section 6.2.3, finds that all carbon star spectra with the 11.3µm feature are best fitted by laboratory alpha-SiC.

Target Selection

We selected our carbon star targets from a number of source lists. Groenewegen et al. (1992) extended the carbon star infrared classification scheme of Willems & de Jong (1988) by defining five groups of carbon stars. Group I consisted of a small number of J-type carbon stars that exhibit a silicate emission feature. These are not considered further here. Group II sources are those with near-IR colour temperatures, T_NIR, exceeding 2000 K, while Group III sources have T_NIR between 1000 K and 2000 K. Group II and III sources have optical counterparts. Group IV sources have T_NIR values below 1000 K. Group V sources have the reddest IR colour temperatures. This sequence was interpreted as one of increasing dust mass loss rate. Twenty-five of the objects in our sample were amongst the carbon stars having 12µm IRAS fluxes larger than 100 Jy that were classified into these groups by Groenewegen et al. (1992), while Groenewegen (1995) classified another star in our sample AFGL 5076 (IRAS 02345+5422) as a Group V source. The Group classifications of the sources are listed in column 5 of Table 6.1

Jura and Kleinmann (1989, 1990) tabulated sources which they classified as very dusty asymptotic giant branch stars. Nine stars in our sample were included in their 1989 listing of sources estimated to be nearer than 1 kpc to the Sun, while eight of our sources were included in their 1990 listing of very dusty carbon-rich sources estimated to be between 1 and 2.5 kpc from the Sun.

Volk, Kwok & Langill (1990) used the IRAS LRS database to identify a group of 32 known or candidate extreme carbon stars. They asserted that these extreme carbon stars have very weak or no SiC features and have a relatively low temperature blackbody-like continuum and so can be distinguished from `normal' carbon stars. Ten stars from their sample are included in the present survey. IRAS 02408+5458 was selected from Volk, Kwok and Woodsworth's (1993) list of candidate carbon-rich AGB and post-AGB stars. OH maser emission has been searched for from this source, but not detected (e.g. Blommaert, Van Der Veen & Habing 1993, Wouterloot, Brand & Fiegle 1993). Our 8-13µm spectrum of it exhibits an 11µm SiC feature in absorption (see section 6.7), confirming its carbon-rich nature.

Observations

Table 6.1: Sources Observed

Source IRAS names Other names Spec. Type^a Group^b Observation Date Calibrator

IRAS 02152+2822 02152+2822 ... ... IV 2/11/93 beta Peg

R For 02270-2619 AFGL 337 C3,4e III 1/11/93 alpha Lyr

AFGL 341 02293+5748 ... ... IV 1&2/11/93 beta Peg

AFGL 5076 02345+5422 ... ... V 1/11/93 alpha Tau

IRAS 02408+5458 02408+5458 ... ... ... 1/11/93 alpha Tau

IRC+50096 03229+4721 V384 Per/AFGL 489 ... III 30/10/93 alpha Tau

AFGL 5102 03448+4432 ... ... IV 1&2/11/93 alpha Tau

V414 Per 03488+3943 AFGL 527 ... III 1/11/93 beta Peg

R Lep 04573-1452 AFGL 667 C7,4e III 30/10/93 alpha Tau

UV Aur 05185+3227 AFGL 735 ... ... 31/10/93 alpha Tau

TU Tau 05421+2424 AFGL 812 C5,4 ... 31/10/93 alpha Tau

UU Aur 06331+3829 AFGL 966 C6,4 II 31/10/93 alpha Tau

CS 776 07270-1921 AFGL 1131 C8,1e ... 1/11/93 alpha CMa

IRC+10216 09452+1330 CW Leo/AFGL 1381 C IV 17/3/95 beta Gem

CIT 6 10131+3049 RW LMi/AFGL 1403 C4,3 III 23/5/91 alpha Boo

V Hya 10491-2059 AFGL 1439 C7,5e III 25/5/91 alpha Boo

Y CVn 12427+4542 AFGL 1576 C7,1e II 23/5/91 alpha Boo

AFGL 2155 18240+2326 ... C IV 23/5/91 alpha Boo

IRC+00365 18398-0220 AFGL 2233 ... III 31/5/91 alpha Boo

V Aql 19017-0545 AFGL 2314 C5,4 II 1/11/93 alpha Lyr

AFGL 2333 19075+0921 ... ... V 1/11/93 alpha Lyr

AFGL 2368 19175-0807 ... C5,4 III 31/5/91 alpha Lyr

AFGL 2477 19548+3035 ... ... ... 31/10/93 alpha Tau

AFGL 2494 19594+4047 ... ... IV 31/11/93 alpha Lyr

V Cyg 20396+4757 AFGL 2632 C7,4e III 30/10/93 alpha Lyr

AFGL 2699 21027+5309 V1899 Cyg C8,3 ... 30/10/93 beta Peg

AFGL 5625 21318+5631 ... ... V 2/11/93 alpha Tau

IRAS 21489+5301 21489+5301 ... ... IV 2/11/93 alpha Lyr

AFGL 3068 23166+1655 ... ... V 4/10/90 beta Peg

AFGL 3099 23257+1038 IZ Peg C IV 1/11/93 beta Peg

IRC+40540 23320+4316 LP And/AFGL 3116 C8,3.4 III 30/10 & 2/11/93 beta Peg

TX Psc 23438+0312 AFGL 3147 C ... 1/11/93 beta Peg

^a from Willems (1988a&b), Lorenz-Martin & Lefèvre (1993 & 1994), Blanco et al. (1994), Cohen (1979)

^b from Groenewegen et al. (1992) and Groenewegen (1995)

Most of the stars in this sample were observed on the nights of October 30 - November 2 1993. The sources CIT 6, V Hya, Y Cvn, AFGL 2155, AFGL 2233 and AFGL 2368 were observed on the nights of May 23-31 1991 while AFGL 3068, whose CGS3 spectrum has also been presented by Justtanont et al. (1996), was observed on the night of October 4 1990. The spectrum of IRC+10216 was obtained on the night of March 17 1995 and was kindly made available to us by Dr. T.R. Geballe. Table 1 provides some details of the observations. All observations were made using the 3.8m United Kingdom Infrared Telescope (UKIRT) with the common-user spectrometer CGS3, a liquid helium cooled, 10- and 20- µm grating spectrometer built at University College London. CGS3 contains an array of 32 discrete As:Si photoconductive detectors, and three interchangeable, permanently mounted gratings covering the 7.5-13.5 and 16.0-24.5  µm wavebands. Two settings of a grating give a fully sampled 64-point spectrum of the chosen waveband (in the case of IRC+10216, three setting of the grating gave a 96-point spectrum). We obtained 7.4-13.5µm spectra with a 5.5-arcsec circular beam, and a spectral resolution of 0.17µm. Further details about CGS3 can be found in Cohen & Davies (1995). Six stars, alpha Boo, alpha CMa, alpha Tau, alpha Lyr, Beta Peg and beta Gem, were used as flux standards. Table 6.1 lists the calibrator used for each source. The spectra of sources taken using alpha Tau as the standard star were flux-calibrated using the absolutely calibrated spectrum of alpha Tau constructed by Cohen et al. (1992a), whilst several sources were calibrated using a similarly constructed spectrum of beta Peg provided by Dr. M. Cohen (see Cohen and Davies 1995). A number of sources were calibrated with respect to the A-type stars alpha Lyr and alpha CMa, for which Kurucz model atmosphere calibrations, described by Cohen et al. (1992a), were adopted. Several spectra were calibrated with respect to beta Gem and alpha Boo, which were assumed to emit as blackbodies in the 10µm region (see Cohen & Davies 1995), with effective temperatures of 4750K and 4450K respectively. The deep telluric ozone feature at 9.7µm could not always be completely cancelled, hence in some cases spurious spectral structure could be present in the 9.3-9.8µm region. The flux-calibrated spectra of all the sources are shown in Fig. 6.1. The error bars represent 1 sigma standard errors on the fluxes.

The most prominent characteristic of the flux-calibrated spectra shown in Figs. 6.1 is the silicon carbide feature, which typically extends from just shortwards of 10µm to about 12.5µm. For 26 of the sources the SiC feature is in emission but for four sources the SiC feature appears to be in absorption. One of these, AFGL 3068, was the only source previously known to exhibit the SiC feature in absorption (Jones et al. 1978), while the other three sources were found to exhibit SiC absorption during the current survey, namely IRAS 02408+5458, AFGL 2477 and AFGL 5625. All four of these sources are discussed in more detail in section 6.7.

About half of the spectra plotted in Fig.6.1 show a marked downturn shortward of 8µm. This effect was first noticed by Forrest et al. (1975) and, making use of complete spectrophotometry from 0.75-13µm for the carbon star V CrB, Goebel et al. (1981) were able to attribute this turndown to the long wavelength wing of a band centred at 7.1µm due to HCN and C₂H₂. Note that the carbon stars in our sample with optical counterparts tend not to exhibit a downturn shortwards of 8µm, whereas the sources lacking optical counterparts do tend to exhibit the downturn. Since the latter sources are likely to correspond to those with higher mass loss rates, this indicates that the HCN and C₂H₂ molecules apparently responsible for the downturn reside in the outflows.

In the normalised spectra shown in Fig.6.2 (see section 6.5), in addition to the obvious SiC feature between 10 and 12.5µm, a weaker emission feature between 8 and 9.5µm can be discerned in several of the plots, e.g. those of V Aql and Y CVn. This is presumably the same as the feature found in IRAS LRS spectra of carbon stars by Baron et al. (1987) and Skinner and Whitmore (1988b), and attributed by Papoular (1988) and Goebel et al. (1995) to amorphous hydrogenated carbon. Note that the uncertainty in the true level of the continuum in the 8µm region, caused by the presence of the HCN/C₂H₂ absorption band shortwards of 8µm in about half of the sources, may lead to artificial amplification of some of the 8-9.5µm features during the normalisation process. Another additional feature that is discernable in the spectra of two stars: TU Tau and UV Aur. This is a narrow peak at ~11.3µm, superimposed on the SiC feature. This 11.3µm narrow peak will be discussed further in chapter 7.

 
Figure 6.2: 8-13µm normalised spectra of carbon stars with ~11µm emission feature with chi² fits;
dashed lines = pure emission fits; solid lines = self absorption fits.
(x-axis: wavelength in µm; y-axis: flux in Wm^-2 µm^-1)

Properties of the spectral features

Table 6.2: Properties of the SiC features measured on the normalised spectra

Source Peak/Cont.^a T_BB^b FWHM FWZI -EW^c

Ratio (K) (µm) (µm) (µm) (µm)

IRAS 02408+5458 0.87 320 10.87 1.28 3.23 -0.367

AFGL 5625 0.89 337 10.67 1.96 3.42 -0.055

AFGL 2477 0.85 340 10.56 2.05 3.51 -0.279

AFGL 3068 0.93 377 10.81 1.58 2.54 -0.097

AFGL 341 1.12 410 11.88 1.38 2.76 0.163

IRAS 21489+5301 1.17 455 11.28 1.75 2.69 0.299

IRC+10216 1.24 520 11.45 2.08 4.55 0.557

AFGL 5076 1.14 525 11.45 1.93 2.95 0.275

AFGL 2494 1.15 525 11.29 1.93 3.22 0.296

AFGL 2699 1.32 530 11.27 1.75 3.03 0.553

AFGL 3099 1.21 600 11.64 2.13 3.48 0.404

AFGL 5102 1.18 600 11.50 1.74 3.31 0.329

AFGL 2155 1.19 615 11.72 1.87 2.99 0.386

IRAS 02152+2822 1.23 675 11.33 1.44 3.45 0.459

IRC+40540 1.23 680 11.33 1.93 2.93 0.446

AFGL 2368 1.50 800 11.25 1.85 3.48 0.866

V Hya 1.33 865 11.24 1.74 3.48 0.649

IRC+00365 1.39 975 11.38 1.93 3.24 0.713

CIT6 1.47 1100 11.35 1.84 3.48 0.933

TU Tau 1.39 1100 11.50 2.18 3.58 0.597

IRC+50096 1.47 1200 11.20 1.83 3.06 0.869

Y CVn 1.33 1350 11.55 1.64 2.05 0.573

R For 1.43 1400 11.12 1.74 3.43 0.704

R Lep 1.74 1500 11.13 1.75 4.90 1.609

UU Aur 1.42 1500 11.22 1.65 2.97 0.703

UV Aur 1.46 1500 11.23 1.83 3.85 0.917

V Cyg 1.75 1500 11.29 1.76 4.87 1.508

CS 776 1.58 1600 11.15 1.74 3.32 0.857

V414 Per 1.25 1600 11.24 1.74 3.41 0.423

V Aql 1.40 2250 11.29 1.73 3.49 0.725

Each of the flux-calibrated spectra was divided by a suitable blackbody, in order to more easily discern the spectral features against the underlying continuum. The blackbodies were chosen by fitting them to the flux calibrated spectra typically at around 8µm and around 13µm. In most cases, the blackbodies used in the normalisation process are of approximately the same temperature as those fitted by the chi²-minimisation routine described in the next section. Table 6.2 gives temperatures of the blackbodies used to normalise the spectra, together with some properties of the 11µm feature measured on the normalised spectra. The sources are listed in Table 6.2 in order of increasing 8-13µm blackbody temperature, which is usually interpreted as a sequence of decreasing mass loss rate, since stars with very low mass loss rates ought to show a photospheric continuum, while stars with high mass loss rates and optically thick dust emission ought to exhibit lower (dust) colour temperatures in the 8-13µm region. The listed properties of the 11µm feature are: the feature peak to continuum flux ratio, the wavelength of the peak of the feature (_peak), its full width at half maximum (FWHM), full width at zero intensity (FWZI), and equivalent width. The peak to continuum ratio is the maximum value of the ratio of the intensity in the feature to the underlying continuum intensity. The peak wavelength of the feature is the wavelength at which this peak to continuum ratio is measured. Some of the flattened spectra have obvious features at about 8-8.5µm - possibly due to hydrogenated amorphous carbon (Papoular 1988; Goebel et al. 1995). Stars displaying this feature are: AFGL 341, TU Tau, Y CVn, V Aql and AFGL 2699. Fig.6.2 shows all the normalised spectra, excluding TX Psc, AFGL 2333 and the spectra with absorption features, which are dealt with later. The five stars mentioned above can be seen to exhibit prominently the 8-8.5µm features.

Fitting the Spectra

We have fitted our observed spectra using a chi²-minimization routine based on one developed for the 10µm region by Aitken et al. (1979) and Aitken & Roche (1982). The program has been extended by R.J. Sylvester to include the optical constants for six forms of silicon carbide. These are: alpha-SiC from Friedemann et al. (1981); Pég-SiC, a ``synthetic'' alpha-SiC from Pégourié (1988); three different forms of alpha-SiC: SiC-1200, SiC-600 and SiC-N, from Borghesi et al. (1985); and beta-SiC, also from Borghesi et al. (1985). The program is also equipped with the optical constants of silicates from observations of the Orion Trapezium and µ   Cep (see Roche & Aitken 1984). The sources of these optical data are discussed in section 6.2.2. Following the findings in chapter 4, some of this data is felt to be erroneous due to the unnecessary application of a KBr correction to the raw laboratory data. In the original fitting of this sample of carbon star spectra we used the KBr corrected laboratory data, the details and results of which can be found in Speck et al. (1997a,b). However, following the work on optical constants of solids and the effects of small particles, presented in chapter 4, it was felt that this and previous work was irretrievably flawed and the whole fitting process was repeated using non-KBr corrected laboratory data.

The chi²-fitting program is equipped with a mechanism which sets minimum errors on the fluxes to be 3% of the flux. For the higher quality spectra used here, all spectra have errors <3% of the flux (except at the extremes of the wavelength window and in the ozone region), and therefore the 1sigma errorbars shown in the figures are smaller than the errors used for the chi² calculation. Even the noisiest spectra (i.e. those for IRC+00365 and V   Hya) have errors of only ~2%, while the lowest errors on any carbon star spectrum are those for IRC+10216, which has errors of ~0.0003%. The fixing of the minimum errors explains why the reduced chi² values reported in the results tables do not always correspond to the real flux errors shown on the figures.

Table 6.3: Results of the pure emission chi²-fitting for the 7.5--13.5µm region of flux-calibrated spectra.

Source	Tcolour	SiC type	TBB(K)	T (K)	chi2R*
AFGL 341	385	...	...	...	...
IRAS 21489+5301	455	beta-SiC	449	293	0.515
IRC+10216	520	beta-SiC	511	230	1.260
AFGL 5076	525	beta-SiC	521	183	0.480
AFGL 2494	525	beta-SiC	508	293	0.515
AFGL 2699	530	...	...	...	...
AFGL 3099	600	beta-SiC	588	253	2.323
AFGL 5102	600	beta-SiC	599	211	0.561
AFGL 2155	615	beta-SiC	566	170	1.186
IRAS 02152+2822	675	beta-SiC	640	287	1.068
IRC+40540	680	beta-SiC	704	216	0.861
AFGL 2368	800	beta-SiC	727	321	1.772
V Hya	865	beta-SiC	874	275	1.524
IRC+00365	975	beta-SiC	1033	164	2.464
CIT 6	1100	beta-SiC	760	269	2.229
TU Tau	1100	...	...	...	...
IRC+50096	1200	beta-SiC	940	455	2.166
Y CVn	1350	...	...	...	...
R For	1400	beta-SiC	906	800	1.237
R Lep	1500	beta-SiC	1284	573	5.274
UU Aur	1500	beta-SiC	1620	345	1.597
UV Aur	1500	beta-SiC	1115	485	2.924
V Cyg	1500	beta-SiC	1008	501	3.676
CS 776	1600	beta-SiC	993	576	1.879
V414 Per	1600	beta-SiC	1508	358	0.810
V Aql	2250	...	...	...	...

* The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. The errors shown in Fig. 6.2 are 1sigma. In all these spectra, the majority of points have errors that are <3% of the flux, the exceptions being for those points at the edges of each spectra and in the ozone region (9.4-9.9µm). Thus the 1sigma error bars shown in the fits are not necessarily the errorbars used by the fitting program.

Table 6.4: Results of the emission chi²-fitting for the 9.5--13.5µm region of flux-calibrated spectra.

Source	Tcolour	SiC type	TBB (K)	TSiC (K)	chi2R*
AFGL 341	385	beta-SiC	405	126	0.788
AFGL 2699	530	beta-SiC	469	258	2.568
TU Tau	1100	beta-SiC	1095	195	1.245
Y Cvn	1350	beta-SiC	2307	149	1.153
V Aql	2250	beta-SiC	3467	342	1.283

* The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. The errors shown in Fig. 6.2 are 1sigma. In all these spectra, the majority of points have errors that are <3% of the flux, the exceptions being for those points at the edges of each spectra and in the ozone region (9.4-9.9µm). Thus the 1sigma error bars shown in the fits are not necessarily the errorbars used by the fitting program.

Table 6.5: Results of the self-absorbed emission chi²-fitting for the 7.5--13.5µm region of the flux-calibrated spectra.

Source	Tcolour	SiC type	TBB (K)	TSiC (K)	opt depth	chi2R#
AFGL 341*	385	beta-SiC	726	329	0.242	1.370
IRAS 21489+5301	455	-No fits-	...	...	...	...
IRC+10216	520	-No fits-	...	...	...	...
AFGL 5076	525	beta-SiC	557	298	0.137	0.369
AFGL 2494	525	beta-SiC	516	383	0.167	0.306
AFGL 2699*	530	beta-SiC	402	354	0.238	1.334
AFGL 3099	600	beta-SiC	726	329	0.242	1.370
AFGL 5102	600	beta-SiC	650	355	0.161	0.345
AFGL 2155	615	beta-SiC	734	288	0.235	0.418
IRAS 02152+2822	675	beta-SiC	548	519	0.223	0.504
IRC+40540	680	beta-SiC	859	313	0.173	0.508
AFGL 2368	800	-No fits-	...	...	...	...
V Hya	865	beta-SiC	1129	393	0.211	0.761
IRC+00365	975	beta-SiC	1788	215	0.114	2.316
CIT 6	1100	beta-SiC	960	363	0.217	1.294
TU Tau*	1100	-No fits-	...	...	...	...
IRC+50096	1200	-No fits-	...	...	...	...
Y Cvn*	1350	beta-SiC	5239	305	0.200	0.387
R For	1400	-No fits-	...	...	...	...
R Lep	1500	-No fits-	...	...	...	...
UU Aur	1500	beta-SiC	2505	446	0.165	1.105
UV Aur	1500	beta-SiC	920	745	0.187	2.343
V Cyg	1500	beta-SiC	2556	568	0.139	1.014
CS 776	1600	-No fits-	...	...	...	...
V414 Per	1600	beta-SiC	1102	920	0.177	0.579
V Aql*	2250	beta-SiC	2556	568	0.139	1.014

* These spectra were fitted over the 9.5-13.5µm wavelength region

^# The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. The errors shown in Fig. 6.2 are 1sigma. In all these spectra, the majority of points have errors that are <3% of the flux, the exceptions being for those points at the edges of each spectra and in the ozone region (9.4-9.9µm). Thus the 1sigma error bars shown in the fits are not necessarily the errorbars used by the fitting program.

Table 6.6:Summary of the best chi²-fits for emission features

Source	SiC type	TBB (K)	TSiC (K)	opt. depthSiC$	chi2R*
AFGL 3411	beta-SiC	405	126	...	0.788
IRAS 21489+53011	beta-SiC	449	293	...	0.515
IRC+102161	beta-SiC	511	230	...	1.260
AFGL 50762	beta-SiC	557	298	0.137	0.369
AFGL 24942	beta-SiC	516	383	0.167	0.306
AFGL 26992	beta-SiC	402	354	0.238	1.334
AFGL 30992	beta-SiC	726	329	0.242	1.370
AFGL 51022	beta-SiC	650	355	0.161	0.345
AFGL 21552	beta-SiC	734	288	0.235	0.418
IRAS 02152+28222	beta-SiC	548	519	0.223	0.504
IRC+405402	beta-SiC	859	313	0.173	0.508
AFGL 23681	beta-SiC	727	321	...	1.772
V Hya2	beta-SiC	1129	393	0.211	0.761
IRC+003652	beta-SiC	1788	215	0.114	2.316
CIT 62	beta-SiC	960	363	0.217	1.294
TU Tau1	beta-SiC	1095	195	...	1.245
IRC+500961	beta-SiC	940	455	...	2.166
Y Cvn2	beta-SiC	5239	305	0.200	0.387
R For1	beta-SiC	906	800	...	1.237
R Lep1	beta-SiC	1284	573	...	...
UU Aur2	beta-SiC	2505	446	0.165	1.105
UV Aur2	beta-SiC	920	745	0.187	2.343
V Cyg2	beta-SiC	2556	568	0.139	1.014
CS 7761	beta-SiC	993	576	...	1.879
V414 Per2	beta-SiC	1102	920	0.177	0.579
V Aql2	beta-SiC	2556	568	0.139	1.014
\hline

¹ Fits with pure emission only

² Fits with self-absorbed net emission

* The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. The errors shown in Fig. 6.2 are 1sigma. In all these spectra, the majority of points have errors that are <3% of the flux, the exceptions being for those points at the edges of each spectra and in the ozone region (9.4-9.9µm). Thus the 1sigma error bars shown in the fits are not necessarily the errorbars used by the fitting program.

We attempted to fit all of the spectra taken. AFGL 3068, IRAS 02408+5458, AFGL 2477 and AFGL 5625 all appear to be sources with SiC in absorption and are dealt with in section 6.7. All attempted fits involved either a pure blackbody or a blackbody with a ^-1 emissivity, together with some form of silicon carbide. For some spectra (AFGL 341, AFGL 2699, TU Tau Y CVn and V Aql) the emission fitting routine was unable to provide a satisfactory fit. The spectra cover the 7.5-13.5µm waveband. There are at least two problems with using the fitting routine over this range. (1) There may be problems produced by the atmospheric ozone feature at 9.7µm. Anomalies at this point may produce erroneous solutions from the fitting program. (2) Goebel et al. (1995) have hypothesised that some carbon stars may have amorphous hydrogenated carbon dust in their circumstellar shells, which apparently is the cause of a feature seen in some spectra at about 8.5µm. At this time the fitting program is not capable of including such a feature in its minimisation routine, due to a lack of suitable laboratory data. Spectra which show this feature can mislead the fitting program into asserting that the spectrum in fact has a higher temperature blackbody part, rather than a feature. Thus, the fitting program was used several times and in several ways for each spectrum in the sample.

First of all, the routine was used on the flux-calibrated spectra, over the whole range (7.5-13.5µm) with no alterations. The results are listed in Table 6.3 The chi²_R values are the reduced chi² values given by dividing the chi² value by the number of degrees of freedom. The second attempt at using the fitting routine was restricted to wavelengths longward of 9.5µm. The reason for this was to minimise the effects of any features shortward of 9.5µm that might confuse the fitting program (e.g. the 8.5µm feature). It was not practicable to do the same for the ozone feature at 9.7µm as this would have resulted in the loss of part of some of the features. This restricted wavelength fitting was only applied to the five spectra for which no fits could be found over the entire wavelength range, all of which appear to have the 8.5µm feature. The results are listed in Table 6.4 and, for these five stars, these are the fits seen in Fig. 6.2

Cohen (1984) suggested that the shape of some of the features in carbon stars may arise as a result of different SiC optical depths. With this in mind a third fitting attempt was made, using silicon carbide in both emission and absorption simultaneously, i.e. self-absorbed SiC emission. This self-absorption comprises a warm emitting component and a colder outer component, so that some of the warm 11.3µm SiC emission is re-absorbed by the cooler dust component. In the case of the five stars with the 8.5µm feature, the self-absorption fitting only yielded results over the 9.5--13.5µm range. The results of the self-absorption fitting can be seen in Table 6.5

The results for the overall best fits for emission features are listed together in Table 6.6 and shown in Fig. 6.2 Where both the pure emission and self-absorption fits yielded good results, both are shown, with the pure emission fits as dashed lines and the self-absorption fits as solid lines.

Sources with Absorption Features

There are four carbon star spectra in our sample which exhibit net absorption features. AFGL   3068 and IRAS 02408+5458 both show evidence of a broad absorption band in the 10-12.5µm region. AFGL   3068 was originally investigated by Jones et al.   (1978), who concluded that this feature was due to SiC in absorption. IRAS 02408+5458 has a very similar, but much stronger feature than AFGL 3068, as seen from a comparison of Figs. 6.3(a)&(d).

AFGL 2477 and AFGL 5625 also show evidence of absorption features, only this time they appear to have a double absorption peak (see Figs. 6.3(b)&(c)). The longer wavelength feature is very similar to that seen in the spectra of AFGL   3068 and IRAS 02408+5458. The shorter wavelength feature is centred at about 9.7µm. Incomplete cancellation of telluric ozone absorption may contribute to this peak but the absorption appears to extend, on both sides, well beyond the 9.3-9.9µm region affected by ozone. Both these stars had their spectra calibrated using several different standard stars which were observed on the same night and the short wavelength extended absorption was found to persist. For this reason we believe that this feature is real. One possibility is that it is due to interstellar silicate absorption.

We applied the chi²-minimisation routine to the flux-calibrated spectra in a variety of different ways. In addition to fitting the spectra with a single form of SiC pure absorption, fitting was also attempted using a combination of one silicon carbide variant and an interstellar silicate. Following the success of fitting the emission features using self-absorbed SiC, the absorption features were also fitted using self-absorbed silicon carbide both with and without an interstellar silicate absorption. The results of these fits are listed in Table   \ref{absfit}. The fits obtained using self-absorbed SiC proved to be very good with plausible optical depths. Fitting using both SiC and interstellar silicate only yields fits for AFGL 2477 and AFGL 5625. We have already mentioned the possibility that the spectra of these two stars are affected by interstellar silicate absorption. Self-absorption fits using SiC only for AFGL 3068 and IRAS 02408+5458 together with fits using self-absorbed SiC and interstellar silicate absorption for AFGL 2477 and AFGL 5625 are shown in Fig. 6.4

Table 6.7: Results of the self-absorption chi²-fitting for the 7.5--13.5µm region of flux-calibrated spectra

Source	Tcolour	SiC type	TBB (K)	TSiC (K)	opt. deptSiC	opt. deptsil	chi2R*
AFGL 3068	377	beta-SiC	394	62	0.030	...	0.092
IRAS 02408+5458	320	beta-SiC	388	96	0.152	...	1.686
AFGL 2477	340	beta-SiC	377	114	0.073	0.104	0.419
AFGL 5625	333	beta-SiC	358	185	0.097	0.113	0.306

AFGL 2477 is fit with Trapezium interstellar silicate

AFGL 5625 is fit with µ Cep interstellar silicate

* The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. The errors shown in Fig. 6.2 are 1sigma. In all these spectra, the majority of points have errors that are <3% of the flux, the exceptions being for those points at the edges of each spectra and in the ozone region (9.4-9.9µm). Thus the 1sigma error bars shown in the fits are not necessarily the errorbars used by the fitting program.

 
Figure 6.3: 8-13µm flux-calibrated spectra of carbon stars with ~11µm absorption features. The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. Thus the 1sigma error bars shown here are not necessarily the errorbars used by the fitting program

 
Figure 6.4: 8-13µm normalised spectra of carbon stars with ~11µm absorption feature with self absorption fits. The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. Thus the 1sigma error bars shown here are not necessarily the errorbars used by the fitting program.

TX Psc

 
Figure 6.5: 8-13µm spectrum of unusual carbon stars TX Psc

TX Psc is the only carbon star in the sample for which the chi²-fitting routine consistently had problems finding fits to the spectrum. For this reason the spectrum of TX Psc needed further investigation. Its flux-calibrated spectrum is shown in Fig. 6.5. The best-fitting 8-13µm blackbody has a temperature of 3500 K. Dividing by this blackbody yields a normalised spectrum which does not show an obvious 11µm feature (Fig.6.5 (b)). It does, however, exhibit a prominent feature at 8.8µm. This could be the usual feature found in this region, attributed to alpha:C-H. The 3500 K blackbody does not fit perfectly, so that the ``normalised'' spectrum in Fig. 6.5 (b) does not have a flat underlying continuum. The resulting spectrum has peaks at 8.8µm and 11.3µm (Fig. 6.5(b)). It would appear that the spectrum of TX Psc may have contributions from three sources: 1) a hot 3500K photospheric continuum; 2) a feature at 8.8µm possibly due to alpha:C-H; and 3) a weak feature at 11.3µm possibly due to SiC. Whatever the explanation, it is clear that the mid-IR spectrum of TX Psc is markedly different from those of other carbon stars in our sample.

AFGL 2333

 
Figure 6.6: The 8-13µm flux-calibrated spectrum of AFGL 2333, fit by self-absorbed silicate. The errors used to calculate the reduced chi² are set to 3% of the flux if the 1sigma error on the flux is less than this value. Thus the 1sigma error bars shown here are not necessarily the errorbars used by the fitting program.

AFGL 2333 was originally included in our sample as it had been classified as a carbon star based on its IRAS LRS spectrum and HCN emission (Groenewegen et al. 1992, Loup et al. 1993, Volk, Kwok & Woodsworth 1993, Volk Kwok & Langill 1992). However, on the basis of its OH maser emission (see David et al. 1993, Le Squeren et al. 1992), we believe that it is an OH/IR star. The flux-calibrated spectrum of AFGL 2333 is included with those of the rest of the sample in Fig. 6.6 and shows that the spectrum in fact exhibits an absorption feature centred at about 9.6µm rather than an emission feature at about 11.5µm. AFGL 2333 can therefore be interpreted as an oxygen rich OH/IR star that exhibits silicate self-absorption. The spectrum of AFGL 2333 can be fitted very well using self-absorbed silicate. The minimisation routine gave a reduced chi² value of 0.265 using a Trapezium silicate profile, with an optical depth of 1.51. The fit is shown in Fig. 6.6

Discussion

The original fitting of the carbon star spectra was performed using KBr-corrected optical constants. This led to nearly all the sources being best fit by alpha-SiC. However, as discussed in chapter 4, it is now believed that the KBr-correction is unnecessary and leads to erroneous optical constants. The original results, using corrected optical constants can be found in Speck et al. (1997a,b). The current work uses raw (uncorrected) SiC data.

Fig. 6.7 uses some of the SiC feature parameters listed in Table 6.2 with a view to finding trends in the SiC features. In each plot (a-c), the solid line represents a linear regression fit to the plotted data.

 
Figure 6.7: Plots of the 8-13µm colour temperature versus various parameters: (a) colour temperature vs. the mass-loss rate (from Loup et al. 1993); (b) colour temperature vs. the peak wavelength of the SiC feature; (c) colour temperature vs. the peak to continuum ratio of the SiC feature.

We found no correlation between the full width at half maximum (FWHM) of the SiC profile and the 8-13µm colour temperature (the formal linear correlation coefficient is -0.241) or between the full width at zero intensity (FWZI) of the SiC profile and the colour temperature (the linear correlation coefficient is 0.312) An attempt was made to find correlations between the stellar mass-loss rates and the properties of the 8-13µm spectra.

The mass-loss data were taken from Jura (1986), Jura & Kleinmann (1989), Volk, Kwok and Woodsworth (1993) and Loup et al. (1993). Published mass-loss rates were found for 25 of our sources. The only combination of data that yielded any correlation was that of the mass-loss rates of Loup et al. (1993) versus the 8-13µm colour temperature. The plot excludes the mass-loss rates for the four stars whose spectra exhibit absorption features, as well as TX Psc. The resulting correlation can be seen in Fig. 6.7(a). The linear correlation coefficient is -0.605. It can be seen that as the mass-loss rate increases, the underlying continuum colour temperature decreases. This is as expected for dust shells that becomes increasingly optically thick as the mass loss rate increases. Fig. 6.7(b). shows the SiC peak wavelength (i.e. the wavelength at which the ratio of the flux of the feature to the flux of the underlying continuum is highest) versus the colour temperature of the underlying 8-13µm continuum. There is no correlation (the formal linear correlation coefficient for the best straight line fit through the data is 0.11). This lack of correlation between the peak wavelength of the feature and the 8-13µm colour temperature disagrees with the findings of Willems (1988a,b). Fig. 6.7(c) shows a plot of the SiC peak to continuum ratio versus the underlying 8-13µm colour temperature. There is an obvious trend, whereby the spectra with the hotter underlying colour temperatures have higher peak to continuum ratios. The linear correlation coefficient is 0.73 This trend is not surprising, since Baron et al. (1987) had already found that the SiC feature tends to get stronger as the temperature of the underlying continuum increases. The decrease in the peak to continuum ratio of the SiC feature with decreasing 8-13µm colour temperature (i.e. increasing mass-loss rates; Fig. 6.7(a) can be attributed to two effects: (a) for low mass-loss rates there is no dilution of the SiC feature by dust continuum emission originating in the outflow but as the mass-loss increases the continuum emission produced by an increasingly optically thick dust shell dilutes the SiC emission to an increasing degree; (b) as the mass-loss rate increases (causing the 8-13µm continuum colour temperature to decrease) the SiC feature itself begins to become optically thick. This causes self-absorption also which reduces the peak to continuum ratio of the SiC emission band and for large enough mass-loss rates, the feature ultimately goes into net absorption. While many of the sources in this sample are best fit by self-absorbed SiC, it is not necessary to use self absorption, as good fits can be achieved using SiC pure emission. There is no tendency for self absorption to become necessary as the colour temperature decreases. Radiative transfer modeling is now desirable, in order to ascertain how much SiC is required for self-absorption to occur. Previous radiative transfer analyses of the SiC feature have neglected self-absorption and have therefore probably underestimated the quantities of SiC in the outflows. The use by previous authors of the KBr-correction for laboratory data will also affect radiative transfer models, which should now be run using uncorrected SiC data.

Chan & Kwok (1990) proposed a scenario for the evolution of SiC dust particles with the evolution of the carbon star that produces them. They suggested that the dust produced when the star has a relatively low mass-loss rate is of the alpha-SiC variety, since the high densities needed for grain condensation require grain formation to take place close to the star; at the relatively high temperatures that characterise these regions, only alpha-SiC would be able to condense. As the mass-loss rate increases and the dust shell becomes denser and more optically thick, beta-SiC could begin to condense at the lower temperatures characteristic of the regions further out in the circumstellar envelope. Thus beta-SiC might be detected, as the envelope could be highly opaque to the inner alpha-SiC emission. If this model were correct, we should be able to see a difference

between the feature shapes and peak wavelengths observed from optically thick and optically thin envelopes. As discussed above, the correlations found in Fig. 6.7(c) support the view that those carbon stars which have relatively high 8-13µm colour temperatures have optically thin circumstellar shells and lower mass loss rates. Likewise those carbon stars with cooler 8-13µm colour temperatures are likely to have optically thick shells and higher mass loss rates. However, Fig. 6.7(b) shows that the peak wavelength of the SiC feature is not correlated with the 8-13µm colour temperature, whereas if beta-SiC was to become more predominant at higher mass-loss rates we would have expected to see a shortward shift of the peak wavelength with decreasing 8-13µm colour temperature. Inspection of Tables 6.3, 6.4, 6.5, 6.6 in which the sources are listed in order of increasing 8-13µm colour temperature, shows that, for all the sets of results, there is no tendency for the hotter sources to have alpha-SiC features and the cooler ones to be better fitted by beta-SiC features. In fact, for the fitting of the sources with emission features, all sources are fit by beta-SiC. There are no fits to alpha-SiC. This contradicts previous work, however, the KBr-correction factor, discussed in chapter 4, led many previous studies to use erroneous laboratory data. The correction of the data led to the shifting of the alpha-SiC peak to the position at which uncorrected beta-SiC peaks. We find that all circumstellar SiC emission is consistent with being due to the cubic, beta- form. This result is reinforced by the fact that all SiC found in meteorites, attributed to formation around C-rich AGB stars, is of the beta-SiC form (see chapter 3).

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