3 The $\sim$13 $\mu$m feature in AGB star spectra

As discussed above, there is virtually no evidence for the 12.5 - 13.0 $\mu$m feature in supergiant spectra. It is, however, clearly present in some AGB star spectra (see Figs. 2-7; see also the ISO-SWS observations of Posch et al. 1999) and requires further investigation. The 12.5 - 13 $\mu$m feature is not ubiquitous amongst the AGB star spectra. In our sample, this feature is found rarely in the spectra which exhibit a broad feature extending from 8.5 to 12 $\mu$m, sometimes in spectra with the "classic'' silicate feature, and is most regularly found in the spectra that combine the broad and silicate features, although it is still not universal. The AGB star spectra in the broad+sil group, where the 12.5 - 13.0 $\mu$m feature is most frequently seen, have been divided further into those spectra which exhibit the 12.5 - 13.0 $\mu$m feature, and those which do not. The mean features of these two subgroups are plotted together in Fig. 17a, where the 12.5 - 13.0 $\mu$m feature is clearly seen. In Fig. 17b, we have subtracted the mean of the broad+sil spectra which do not exhibit the 13.0 $\mu$m feature from the mean of those spectra that do, in order to isolate this feature. From this we have found the peak position of the mean 12.5 - 13 $\mu$m feature to be 12.92 $\mu$m. This is very close to the position measured by Posch et al. (1999), 12.95-13.05 $\mu$m, although is notably on the short wavelength side of their measurement. This discrepancy may be due to the feature's proximity to the long wavelength limit of our observed spectra, which may have caused the loss of a small portion on the long wavelength side of the feature. This would also account for the smaller full width half maximum (FWHM) of our mean 12.5 - 13 $\mu$m feature of 0.45 $\mu$m, compared to the FWHM for this feature of 0.5-0.8 $\mu$m measured by Posch et al. (1999) in their higher resolution SWS spectra spectra of 11 stars. Their mean spectrum shows the feature to have a pronounced long-wavelength asymmetry, which could however be largely due to CO₂ and other narrow emission features which are present in this wavelength region of their spectra. If we look for differences between the stars which exhibit the 13 $\mu$m feature, and those which do not, we find that, within the broad+sil group, all the stars with the feature are non-Mira semi-regular variables, whereas those stars without the feature are all Miras (see Table 7). There are three sources (AZ Mon, UW Cep and V462 Cyg) which show slight perturbations at 12.5 - 13 $\mu$m, however it is unclear whether these sources exhibit the feature or not. Therefore these sources have been classified as not showing the feature. Furthermore, in the other spectral feature groups, where the 12.5 - 13.0 $\mu$m feature is less common, we find the same situation: those stars with the feature are non-Mira semi-regular variables and those stars without the feature are Miras. As discussed earlier, Sloan et al. (1996) found that 75-90% of the SR variables in their sample exhibited the feature, while it was seen in only 20-25% of their Mira spectra. This is similar to the results of Begemann et al. (1997), who found that 30% of the Miras in their sample exhibited the 12.5 - 13.0 $\mu$m feature. The smaller size of our sample may explain why we do not find any 12.5 - 13.0 $\mu$m feature amongst the Mira spectra. However, the result still stands that the major difference between stars with or without the 12.5 - 13.0 $\mu$m feature is the variability type. We therefore need to ask the question: why is this feature more visible in SR spectra than in Mira spectra? Is it that there is a dust species that forms around SRs but not around Miras? Or is it that we are seeing high temperature refractory grains in SRs which become coated with other material around Miras? How would this explain the appearance of this feature in the spectrum of the supergiant S Per?

   

Table 6: Comparing classifications - Supergiant silicate features

Source	Variability	Our	SP98
	Type	Class	Class
AH Sco	SRc	Sil1	SE5t
KW Sgr	SRc	Sil1	SE6
BU Per	SRc	Sil2	SE7
ST Cep	Lc	Sil2	SE7
V358 Cas	Lc	Sil2	SE6
V540 Sgr	Lc	Sil2	SE6
XX Per	SRc	Sil2	SE7
KY Cyg	Lc	Sil3	SE5
NR Vul	Lc	Sil3	SE4
RS Per	SRc	Sil3	SE5t
SU Per	SRc	Sil3	SE4
UW Aql	Lc	Sil3	SE5
S Per	SRc	Sil4	SE4
UY Sct	SRc	Sil4	SE4

3.1 Miras vs. Semiregular variables

Since we have found a difference in the dust features for Miras and semiregular variables, it seems appropriate to discuss the differences between types of red variables. The basic categories are: Miras, which have regular pulsation with large amplitude ($V\geq 2.5$ mag) and periods longer than 60 days; semiregular (SR) variables, which have less regular pulsation and smaller amplitudes ($V\leq 2.5$ mag); and irregular (L) variables. Furthermore, the SRs can be split into four subgroups; SRa, which have relatively regular periods; SRb with more irregular periods; SRc, which are more luminous and associated with supergiants; and SRd which are warmer as defined by their colours or spectral types. However, the differences and similarities between these groups and their relationships to one another have caused some disagreement in recent years and therefore require further discussion.

   

Table 7: AGB stars in the broad+silicate group with and without the $\sim$13 $\mu$m feature

with	without	variable
$\sim$13 $\mu$m	$\sim$13 $\mu$m	type
BX Eri		SR
RX Boo		SR
RZ Cyg		SR
SAO 37673		SR
SV Peg		SR
	AZ Mon$^{\ast}$	Mira
	UW Cep$^{\ast}$	Mira
	V462 Cyg$^{\ast}$	Mira
	RR Per	Mira
	RW And	Mira
	UW Cep	Mira
	W Aqr	Mira
	Y Cas	Mira
	Z Cas	Mira

$^{\ast}$ These spectra may exhibit the feature very weakly.

However it is so weak that we feel it is best to class these

spectra as not showing the 13 $\mu$m feature.

Figure 11: Continuum-subtracted supergiant spectra classed as showing group 1 silicate features. x-axis is wavelength in $\mu$m. y-axis is flux in W m$^{-2}~\mu$m-1

It has been suggested in the past that SRs were less evolved than Miras (e.g. Feast & Whitelock 1987), however, given that apart from the 12.5 - 13.0 $\mu$m feature, the observed mid-IR spectral features are basically identical for the SR variables and Miras and cover the full range of classifications, this is apparently not reflected in the state of evolution of the dust. Kerschbaum & Hron (1992) also suggested that the SRs and Miras form a continuous sequence, with the SRs the progenitors of the Miras. Furthermore, it has recently been suggested that evolution from SR to Mira is unlikely to be monotonic and that stars may alternate between being Miras and SRs (P. Whitelock, pers. comm.; Kerschbaum & Hron 1992). The Miras and SRs have also been found to have separate period-luminosity relations (Whitelock 1986), but whether the separation of these two relations is due to differences in pulsation or stellar structure is unknown (Bedding & Zijlstra 1998). Habing (1996) has suggested that a combination of dust shell structure and mass-loss rate evidence for SRs and Miras implies that Miras are in fact the progenitors of the SR variables. Add this to the uncertainties raised over whether SRs are indeed a separate class to the Miras (Kerschbaum & Hron 1992), and we have a very confused picture.

Mattei et al. (1997) re-investigated the differences between Miras and semiregular variables and found that the groups were indeed distinct from one another based on an examination of the amplitudes of variability and their stabilities. Miras have much more stable amplitudes, while the amplitudes of SRs are much more variable. Furthermore, they were able to divide the SRs into two subgroups based on the amplitude of pulsation and the multiperiodicity. These groups are basically SRa and SRb. Thus, we have evidence that the red variables can be classified into discrete groups rather than a continuous sequence, although whether one variability type is the progenitor of another is still unclear.

Hron et al. (1997) examined dust features in the IRAS-LRS spectra of Mira and SR variables and found a difference between these two stellar types. While they suggested that the Miras are just an extension of the SRs with lower effective temperature, they also found that both Miras and SRs exhibit the full range of mid-IR emission features, from broad to the classic, narrow 9.7 $\mu$m feature. Furthermore, they found an intriguing difference between these variability types. The Mira spectra behave as we would expect if the sequence from broad to narrow silicate feature is indeed evolutionary, with the optical depth increasing as the feature narrows (i.e. more dust = more evolved dust). However, the SRs showed no such trend and in fact, based on radiative transfer modeling, tended to have more optically thin dust shells for the narrower features (Ivezic & Elitzur 1995). Furthermore, Ivezic & Knapp (1998) found that there was a link between mass-loss rate and variability type for AGB stars. They found that, while Miras could be fit by "standard'' steady-state radiatively driven models, with inner dust-envelope radii defined by the typical condensation temperature (800 - 1000 K), their models required SRs to have a much lower condensation temperature of $\sim$300 - 400 K. They interpret this as a decrease in the mass-loss, which equates to a less dense dust shell, in agreement with Hron et al. (1997). This is evidence that the SRs should be treated as a distinct group from the Miras, at least as far as dust formation is concerned.

As mentioned above, it has also been suggested that the transition between Miras and SRs is not a single event and happens many times (e.g. Kerschbaum & Hron 1992). A star may have regular, strong, large amplitude pulsations for a time and then have weaker, more irregular pulsation and then go back to strong, regular pulsation as the thermal pulses of the star disrupt the stellar structure. Therefore, it is possible that the 12.5 - 13.0 $\mu$m feature needs to be explained in terms of a dust species that can only form in the environment of an SR, and is either rapidly destroyed or over-coated by a lower condensation temperature material in the environment of the Miras or has been ejected by the stellar wind prior to the Mira phase. The small percentage of Miras found by Sloan et al. (1996) to exhibit the 12.5 - 13.0 $\mu$m feature might be explained in terms of stars that have recently changed from SR to Mira and have not yet destroyed/lost their complement of the carrier of the 12.5 - 13.0 $\mu$m feature.

As discussed in the introduction, Justtanont et al. (1998) found a correlation between CO₂ emission lines and the 12.5 - 13.0 $\mu$m feature. This was taken as evidence that both the CO₂ and the carrier of the 12.5 - 13.0 $\mu$m feature were formed in warm gas layers close to stars with low mass-loss rates, in particular the lower density dust shells around SRs. Since the strengths of the 12.5 - 13.0 $\mu$m and CO₂ emissions are correlated and higher mass-loss rates appear to preclude formation/excitation of the CO₂ lines, higher mass-loss rates may also inhibit the formation of the 12.5 - 13.0 $\mu$m carrier.

Figure 12: Continuum-subtracted supergiant spectra classed as showing group 2 silicate features. x-axis is wavelength in $\mu$m. y-axis is flux in W m$^{-2}~\mu$m-1

Figure 13: Continuum-subtracted supergiant spectra classed as showing group 3 silicate features. x-axis is wavelength in $\mu$m. y-axis is flux in W m$^{-2}~\mu$m-1

Figure 14: Continuum-subtracted supergiant spectra classed as showing group 4 silicate features. x-axis is wavelength in $\mu$m. y-axis is flux in W m$^{-2}~\mu$m-1

3.2 Which minerals?

Previously, the 12.5 - 13.0 $\mu$m feature has been identified with Al₂O₃ grains (Hackwell 1972; Vardya et al. 1986; Onaka et al. 1989; LML90, Glaccum 1995), however there are problems with this attribution. Al₂O₃, or alumina is found in several different forms. Only one form occurs naturally on the earth: corundum or $\alpha$-Al₂O₃. This has rhombohedral crystal structure and is known by various other names including ruby or sapphire depending on the trace impurities (Deer et al. 1966, hereafter DHZ). There are known synthetic polytypes: $\beta$-Al₂O₃, which has hexagonal crystal structure; and $\gamma$-Al₂O₃ which is cubic. However both these forms convert to corundum on heating (DHZ). It is also possible to make amorphous samples (e.g. Begemann et al. 1997). Some condensation models (Salpeter 1974; Sedlmayr 1990; Tielens 1990; Kozasa & Sogawa 1997, 1998) suggest that Al₂O₃ should be the first dust type to condense around O-rich stars. According to some previous research (e.g. Vardya et al. 1986; Onaka et al. 1989; Tielens 1990; Kozasa & Sogawa 1997, 1998), Al₂O₃ then forms a nucleation seed on which the silicates can form a mantle. Alternatively, Nuth & Hecht (1990) and Stencel et al. (1990) suggested that the condensate is a "chaotic silicate'' in which, initially, the emission from Al-O bonds dominates the spectra, but is then overwhelmed by emission from the more abundant Si-O bonds. Both sets of authors agreed that the 12.5 - 13.0 $\mu$m band seen in the spectra of oxygen-rich stars can be attributed to Al-O bonds and that it signifies the presence of some form of aluminium oxide. Moreover, Al₂O₃ grains found in meteorites (Nittler et al. 1994a,b, 1997; Huss et al. 1995) have isotopic signatures which suggest they were formed around oxygen-rich AGB stars. However, the abundance of such AGB star Al₂O₃ grains is very low (<1 ppm; cf. 6 ppm for presolar SiC and 400 ppm for presolar diamond). Furthermore, the polytype (i.e. the crystal structure) of these presolar Al₂O₃ grains is as yet unknown (L. Nittler, pers. comm.) so that no information on the exact spectral features we should expect has yet been gleaned from these meteoritic grains.

Begemann et al. (1997) studied the laboratory spectra of various forms of aluminium oxide, both crystalline and amorphous, with a view to identifying more clearly the 12.5 - 13.0 $\mu$m feature seen in IRAS-LRS spectra. They found that amorphous aluminium oxide could not account for the observations and that, while the $\alpha$- crystalline form of Al₂O₃ could account for the 12.5 - 13.0 $\mu$m feature, a second feature seen at 21 $\mu$m in laboratory spectra of this material was not observed in astronomical spectra. Indeed, the two spectra of Al₂O₃ shown in Fig. 18 have peak positions in the 11.5-12.0 $\mu$m range, rather than at 12.5 - 13.0 $\mu$m. Begemann et al. (1997) suggested that the 12.5 - 13.0 $\mu$m feature may come from a form of silicate rather than from aluminium oxide. Furthermore, we may note that if the 12.5 - 13.0 $\mu$m feature was attributable to the first condensate, it would be expected to appear predominantly in the broad feature spectra. As stated above, the 12.5 - 13.0 $\mu$m feature appears most commonly in our spectra in the broad+sil class, and is certainly not ubiquitous. In addition, the appearance of the feature seems to be related to the variability type of the AGB star (i.e. Mira or SR). Given that Al₂O₃ is so important to the theoretical condensation sequence, and that the spectral features of Al₂O₃ do not seem to match the observed astronomical features, it seems doubly unlikely that the 12.5 - 13.0 $\mu$m feature is attributable to Al₂O₃.

Kozasa & Sogawa (1997, 1998) proposed grains consisting of Al₂O₃ cores and silicate mantles for the carrier of the 12.5 - 13.0 $\mu$m feature. However, this was investigated by Posch et al. (1999) who found that: 1) there would have to be a large population of grains of $\sim$85% Al₂O₃; and 2) there would have to be an even larger number of pure silicate particles to produce anywhere near the correct ratio of 13 $\mu$m to 10 $\mu$m flux strengths. They, therefore, concluded that such core-mantle grains were unlikely to be the carriers of the 12.5 - 13.0 $\mu$m feature.

Another possible carrier for the 12.5 - 13.0 $\mu$m feature is spinel, MgAl₂O₄, as proposed by Posch et al. (1999) who compared laboratory and calculated spectra of various candidate minerals with ISO-SWS spectra of AGB stars which exhibit the 13 $\mu$m feature. Posch et al. argue against Al₂O₃ as the carrier for many of the reasons summarized here, and concluded that the most likely mineral to produce the 13.0 $\mu$m feature is spinel (MgAl₂O₄). Spinel is a very refractory, cubic mineral which is found naturally on the earth (DHZ). It has also been found as a presolar grain in meteorites (Nittler et al. 1994a, 1994b, 1997). However, this attribution is compromised by problems with the spinel optical data. Posch et al. (1999) used optical data from Tropf & Thomas (1991) which is potentially flawed, since the optical constants are based on a compilation of different data mostly from synthetic samples. Tropf & Thomas noted that where more than one data set exists for the same wavelength region, the measurements do not necessarily match up. Following Andreozzi et al. (2000), it has become clear that, for spinel in particular, the precise level of order/disorder of the crystal structure can have a large effect on the optical properties. The Mg/Al order varies among the synthetic samples and affects the IR spectra in both the width and number of peaks. Thus, the optical constants n and k depend on Mg/Al order, which in turn may depend on the formation temperature. This renders compilations of data for spinel, such as that of Tropf & Thomas (1991), moot since such compilations do not take into account the issue of the differing amounts of order/disorder in the differing samples. Therefore the positions of the spectral features derived by Posch et al. (1999) from the Tropf & Thomas data are unlikely to be valid for any one sample of spinel. Previous studies of crystalline spinel have found peaks at wavelengths longwards of 13.5 $\mu$m (e.g. Chopelas & Hofmeister 1991; Hafner 1961; Preudhomme & Tarte 1971). Indeed, it was these previously published spectra which prompted Speck (1998) to ignore spinel in her discussion of mid-IR dust features because it did not appear to have any features in the 7.5-13.5 $\mu$m window and would therefore not be a candidate for the 13 $\mu$m feature. Clearly the issue of spinel and its intriguing IR spectral behaviour requires more investigation, but that is beyond the scope of the current work.

Our results support the findings of Begemann et al. (1997) by associating the 13 $\mu$m feature with silicates. This observed feature appears to be best explained in terms of some form of silicate (Begemann et al. 1997) or SiO₂ (silica; Speck 1998). Both copper (Cu(II)SiO₄) and zinc (ZnSiO₄) silicates exhibit this spectral feature (Speck 1998), but it is not seen in the spectra of the more commonly expected magnesium, calcium or aluminium pyroxene or olivine silicates. Copper and zinc are not abundant enough to form observable quantities of such silicates. The silicates of magnesium, calcium and aluminium which are expected to form in these circumstellar environments are pyroxenes (i.e. chain silicates) and olivines (i.e. individual units of silicate tetrahedra; see Speck 1998 for a discussion of silicate structures). Silicon dioxide, on the other hand, forms a "fully polymerized'' crystal lattice. Intermediate between SiO₂ and the pyroxenes are the sheet silicates. From a spectral feature point of view, there is a progression from SiO₂, with a relatively strong 13 $\mu$m feature (Fig. 18d), through the sheet silicates, where the 13 $\mu$m feature diminishes, to pyroxenes which generally do not show this feature. Although silica is chemically an oxide, the structures and properties of the silica minerals are more closely allied to those of silicates. SiO₂ can be either crystalline or amorphous. There are three main polytypes for crystalline SiO₂: quartz, tridymite and cristobalite. These forms may be seen as a progression in the temperature of formation (DHZ). Silica can also exist in amorphous forms such as lechaterlierite, obsidian and silica glass. The different forms of silica and their stable temperatures are discussed in more detail by Speck (1998). Furthermore, the available atomic abundances are perfectly acceptable for the formation of observable quantities of SiO₂. Therefore, it is plausible on abundance grounds that silicon dioxide or a sheet silicate is responsible for the 13 $\mu$m feature, so an SiO₂ origin for the 13 $\mu$m feature deserves further exploration.

Figure 15: Comparison of the silicate features of AGB stars and supergiants. a) AGB silicate group A (solid line) vs. supergiant silicate groups 1 (dotted line) and 2 (dashed line); b) AGB silicate group B (solid line) vs. unclassified supergiant U Lac (dashed line); c) AGB silicate group C vs. supergiant silicate groups 3 (dashed line) and 4 (dotted line); d) AGB silicate group D vs. supergiant silicate group 4 (dashed line)

Figure 16: Comparison of the average broad features for AGB stars (solid line) and supergiants (dotted and dashed lines)

Figure 17: The 12.5 - 13.0 $\mu$m feature. a) the mean spectra for stars in the broad+silicate group, with (solid line) and without (dashed line) the $\sim$13 $\mu$m feature; b) the isolated $\sim$13 $\mu$m feature. This was achieved by subtracting the mean spectrum without the $\sim$13 $\mu$m feature from the mean spectrum with the $\sim$13 $\mu$m feature. The dashed line shows the peak position of the feature. FWHM = full width at half maximum