A&A 369, 132-141 (2001)
DOI: 10.1051/0004-6361:20010086
F. Kemper1 - L. B. F. M. Waters1,2 - A. de Koter1 - A. G. G. M. Tielens3,4
1 - Astronomical Institute "Anton Pannekoek'', University of
Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
2 -
Instituut voor Sterrenkunde, Katholieke Universiteit Leuven,
Celestijnenlaan 200B, 3001 Heverlee, Belgium
3 - SRON Laboratory
for Space Research, PO Box 800, 9700 AV Groningen, The Netherlands
4 - Kapteijn Institute, University of Groningen, PO Box 800, 9700
AV Groningen, The Netherlands
Received 9 October 2000 / Accepted 5 January 2001
Abstract
Infrared Space Observatory (ISO) observations have shown that O-rich
Asymptotic Giant Branch (AGB) stars exhibit crystalline silicate
features in their spectra only if their mass-loss rate is higher
than a certain threshold value. Usually, this is interpreted as
evidence that crystalline silicates are not present in the dust
shells of low mass-loss rate objects. In this study, radiative
transfer calculations have been performed to search for an
alternative explanation to the lack of crystalline silicate features
in the spectrum of low mass-loss rate AGB stars. It is shown that
due to a temperature difference between amorphous and crystalline
silicates it is possible to include up to 40% of crystalline
silicate material in the circumstellar dust shell, without the spectra
showing the characteristic spectral features. Since this implies
that low mass-loss rate AGB stars might also form crystalline
silicates and deposit them into the Interstellar Medium (ISM), the
described observational selection effect may put the process of dust
formation around AGB stars and the composition of the predominantly
amorphous dust in the
Interstellar Medium in a different light.
Our model calculations result in a diagnostic tool to determine
the crystallinity of an AGB star with a known mass-loss rate.
Key words: stars: AGB and post-AGB - circumstellar matter - dust, extinction - infrared: stars - radiative transfer
Oxygen-rich
Asymptotic Giant Branch (AGB) stars are M-type stars of intermediate mass (
)
in the late stages of stellar evolution,
which exhibit He- and H-shell burning
(for a review on AGB stars, see Habing 1996, and references herein).
These stars undergo an
increasing mass loss while they evolve along the AGB; the stars with low
mass-loss rates (
10
10-6
yr-1) are referred to as Miras, whereas the stars with high mass-loss
rates (
10
10-3
yr-1) are the
so-called OH/IR stars. In the cooling outflow dust formation occurs,
which adds an infrared excess to the Spectral Energy Distribution
(SED). In case of Miras, the dust shell is optically thin, and the
underlying stellar spectrum is still visible, but
the optically thick dust shell of OH/IR stars
completely obscures the stellar
spectrum, making these objects only detectable at infrared wavelengths
(Bedijn 1987; van der Veen & Habing 1988).
Important reasons for studying the nature of dust in AGB stars can be found in the fact that these stars are the main contributors of dust into the interstellar medium. The properties of the dust in the ISM can thus be directly compared to the dust properties in shells around evolved stars. This will provide information on the processing of the dust in the ISM and will improve our insight into the life cycle of dust. Moreover, studying the condensation of dust in the outflows of AGB stars will provide useful diagnostics for the determination of the physical conditions in these outflows, thus increasing our understanding of this important stage of stellar evolution.
Most AGB stars exhibit an oxygen-rich chemistry, i.e. a number ratio
C/O < 1, in their
dust shells, which gives rise to the condensation of oxygen-rich dust
species. Based on early infrared observations, the presence of
silicate species has been proposed by several authors
(e.g. Gilman 1969; Jones & Merrill 1976). Pre-ISO studies almost
exclusively pointed toward the presence of amorphous Fe-bearing
silicates; such dust shells are for example studied by
Butchart & Whittet (1983); Pegourie & Papoular (1985) and Bedijn (1987).
Infrared spectroscopy
performed with the Infrared Space Observatory (Kessler et al. 1996)
revealed the presence of
crystalline silicates next to the amorphous silicate dust in the circumstellar
dust shells of some evolved stars (Waters et al. 1996). In addition,
the observed wavelengths of the emission bands of the crystalline
silicates in evolved stars suggest that these grains contain little or
no Fe, but are very Mg-rich (Molster et al. 1999). The data are
consistent with no Fe in the grains. There seems to be a correlation
between the peak of the SED, i.e. the optical depth toward the central
star, and the presence of spectral features of crystalline olivine
(forsterite, Mg2SiO4) and crystalline pyroxene (enstatite,
MgSiO3) (Waters et al. 1996; Cami et al. 1998; Sylvester et al. 1999), in the
sense that this material is not seen in stars that are not obscured.
This is usually interpreted as evidence that crystalline silicates are
not present in the dust shells around low mass-loss rate AGB stars,
which have an optically thin dust shell. Apparently, a
threshold value for the mass-loss rate
is required to enable
the condensation of crystalline silicate in the stellar outflows. This
critical density would thus put constraints on the dust condensation
sequence. Various explanations have been offered for this threshold density
(Tielens et al. 1998; Gail & Sedlmayr 1999; Sogawa & Kozasa 1999). Yet, its
existence is not well established.
In this study, we will evaluate the existence of the threshold value for the mass-loss rate below which crystalline silicates are not detected. Does the lack of crystalline silicate features in the SED of Miras really imply that the crystalline silicates are not present, or is some other effect at work suppressing the characteristic narrow features? We will study this issue by calculating a grid of detailed model spectra of circumstellar dust shells for a wide range of mass loss and degree of crystallinity.
In Sect. 2 the model for the circumstellar dust shell will be described, including the applied optical constants for the silicates. In Sect. 3 the results will be discussed for varying mass-loss rate and degree of crystallinity. Section 4 contains the physical explanation of the obtained results and highlights possible implications for the evolution of dust. A summary of this study is given in Sect. 5.
The dust radiative transfer program MODUST (de Koter et al., in prep.) has been used to calculate detailed spectra of circumstellar dust shells. The code solves the transfer equations subject to the constraint of radiative equilibrium, fixing the temperature distribution of the dust grains. The solution technique focuses on the combined moment form of the transfer equation, such that the scattering term in the source function can be solved for explicitly, updating the Eddington factors throughout the lambda iteration by means of a ray-by-ray formal solution.
In the mode used in this paper, the dust is assumed to be distributed
in a spherical shell with a radial density profile
,
i.e. that of a time-independent stellar wind outflow at constant
velocity
The models in this study cover a wide range in mass-loss rates and
degree of crystallinity. The mass-loss rate is varied from
5
10-8 to 10-4 yr-1. The crystallinity x,
defined as
Previous studies of the SED of dust shells surrounding AGB stars
(Bedijn 1987; Justtanont & Tielens 1992; Le Sidaner & Le Bertre 1993; Le Sidaner & Le Bertre 1996) used
so-called astronomical or dirty silicates, of which the
optical constants were observationally determined
(Jones & Merrill 1976; Draine & Lee 1984). The chemical
composition of astronomical silicate is not known, although likely the
extra absorption is due to the presence of iron in the form of Fe2+
in the mineral (Schutte & Tielens 1989).
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Figure 1:
Fluxes
calculated for a completely amorphous dust shell, i.e. x = 0,
for a wide range of mass-loss rates, calculated for
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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In the last few years, accurate laboratory measurements of the optical constants of amorphous silicates (Dorschner et al. 1995) and crystalline silicates (Koike et al. 1993; Koike & Shibai 1998; Jäger et al. 1998) have become available. Together with the high spectral resolution of the ISO Short Wavelength Spectrometer (SWS) (de Graauw et al. 1996) and Long Wavelength Spectrometer (LWS) (Clegg et al. 1996) this opens the possibility to determine the dust composition in great detail, at least in principle. However, model calculations have shown that the SED can not be fitted using only the optical constants of amorphous and crystalline silicates. An additional source of opacity in the NIR appears to be missing (Kemper et al., in prep.). This is a well-known problem which dates back to Jones & Merrill (1976); Bedijn (1987) and Schutte & Tielens (1989). Although it is a fundamental issue, for the present study it suffices to use the optical constants of the amorphous silicates calculated from the observed spectra of AGB stars (Suh 1999). The thus obtained optical constants of the AGB silicate cannot provide information on the exact composition of the amorphous component of the dust shell, however for our studies of the appearance and strength of the crystalline silicate features, the use of the "Suh-silicate'' will not affect our results. As the peak position of the crystalline features in laboratory samples is strongly dependent on the Fe-content, ISO observations of AGB and post-AGB stars demonstrate that the dust shells only contain Mg-rich crystalline silicates (Molster et al. 1999; Sylvester et al. 1999). For these crystalline silicates, we used optical constants of two different types: forsterite (Mg2SiO4) and enstatite (MgSiO3) (Jäger et al. 1998). It is important to realize that because of the low Fe-content, their absorptivity in the Near Infrared (NIR) is very low. Equal mass fractions of both crystalline species have been used, unless stated otherwise.
Here we present the model results for increasing mass-loss rates (Sect. 3.1) and increasing degree of crystallinity (Sect. 3.2). In Sect. 3.3 the observational constraints of ISO will be taken into account and applied to the model spectra.
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Figure 2:
Normalised fluxes
calculated for a dust shell containing silicates with a degree
of crystallinity x = 0.10, for the same mass-loss rates as
in Fig. 1.
The narrow
features due to crystalline silicates start to appear in the
20-50 ![]() ![]() ![]() ![]() |
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Figure 3:
Normalised fluxes
calculated for a dust shell containing silicates with a degree
of crystallinity x = 0.20, for the same mass-loss rates as
in Fig. 1. The narrow
features due to crystalline silicates in the 20 - 50 ![]() ![]() ![]() ![]() |
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In Figs. 1, 2 and 3
results of the model calculations are presented. Each figure
shows the fluxes
for mass-loss rates
varying from 10-7 to 10-4
yr-1 for a
constant degree of crystallinity. In Fig. 1
results for a dust shell consisting of completely amorphous dust are
shown. Clearly visible are the bands due to Si-O stretching and
O-Si-O-bending around 10 and 20
m respectively. The strength of these
bands varies with increasing mass-loss rate; for low
the
dust shell is optically thin and the amorphous silicate bands appear
in emission. The strength of the emission bands increases with
increasing mass-loss rate. When the radial optical depth of the peaks of the
spectral
features approaches unity, the features become self-absorbed.
This occurs around
yr-1 in case
of the 10
m feature. For the 20
m feature this transition
is less well defined, and occurs at a somewhat higher mass-loss rate.
Figures 2 and 3 show the emerging
spectra for a crystallinity of 10% and 20% respectively. The overall
shape of these spectra resemble that of the amorphous silicate dust
shell spectra in Fig. 1. However, while the degree
of crystallinity remains constant,
the narrow crystalline silicate features at 23.6, 27.6, 32.5,
36.1, 41.2 and 43.2
m become quite apparent at relatively high mass-loss
rates.
In the models with low mass-loss rate, the narrow crystalline
silicate features are not discernible. Let us first investigate
the relative strength of the crystalline silicate features with
respect to the amorphous dust continuum in some more detail. For
this purpose the contrast is calculated by dividing the spectrum of a
dust model of a given crystallinity by the spectrum of a model
with equal properties and the same amorphous silicate dust mass, but
which is lacking the mass component taken up by the crystalline
silicates. Figure 4 shows the contrast for three
different mass-loss rates, including 10% crystalline material.
The narrow bands due to crystalline silicates at 27.6, 32.5,
36.1, 41.2 and 43.2 m show that the relative strength increases with
mass-loss rate. Note that the continuum between the
crystalline silicate features does not necessarily return to
unity, as the "extra'' IR emission from crystalline silicates
raises the temperature of the amorphous silicates slightly.
For
yr-1 the contrast between the crystalline silicate
peaks and the surrounding continuum is less than 1% for all features;
for
yr-1 some
peaks have a relative strength of
% above continuum;
whereas the strongest peaks of the
yr-1 model show a contrast of
10% above continuum.
The detection limit of ISO for broad spectral features in this
wavelength region is - depending on the quality of the spectrum -
around 5% of the continuum level, which implies that of the three
curves plotted in Fig. 4 only the ISO spectrum of a
star with an outflow of 10-5
yr-1 would result
in a unambiguous detection of crystalline silicate features. A
detection in the spectrum of an AGB star with
yr-1 would be dubious. A typical Mira, with
yr-1, with a crystallinity of
10% would not show the characteristic features. This result is
consistent with the threshold mass-loss rate above which crystalline
silicates are detected with ISO observations
(Waters et al. 1996; Cami et al. 1998; Sylvester et al. 1999).
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Figure 4:
Contrast plot of the 25-50 ![]() ![]() ![]() |
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Figure 5:
Contrast plot for
![]() ![]() ![]() ![]() ![]() |
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In order to determine the amount of crystalline silicates that should
be present in a typical Mira dust shell such that the narrow features
would be detected in an ISO spectrum, model spectra with different degrees of
crystallinity have been calculated. For a typical Mira mass-loss
of
yr-1 the crystallinity has
been varied from 5% to 50%. The
spectra of the x=0.10 and x=0.20models, discussed in Sect. 3.1, are included in the overview.
The contrast has been calculated in the
same way as described above. The result is
shown in Fig. 5, for models with
yr-1. The dashed line indicates the 5% detection
limit of ISO for solid state features, typical for
25-50
m, and thus gives an impression of
which features will be discernible. As stated before, the relative
flux of the crystalline silicate model in between the narrow
crystalline silicate features is not necessarily equal to that of the
amorphous model fluxes.
The peak strength should therefore be compared to the local continuum,
rather than to unity. For this purpose an additional
base-line has
to be subtracted. Following this method one easily sees that very high mass
abundances of crystalline silicates are required for a marginal
detection of crystalline silicate features in a typical Mira spectrum.
For a crystallinity of x = 0.40 only the 43.2
m and 32.5
m features can be
detected by ISO.
From Sects. 3.1 and 3.2 it becomes clear that
the comparison of the ISO detection limit with the contrast of the
crystalline silicate features is essential for studying the
correlation between mass-loss rate and crystallinity of AGB stars.
From Fig. 5 the 43.2 m feature due to
crystalline pyroxene (enstatite, MgSiO3)
has been selected for closer examination, which
is a conservative choice. It shows the largest contrast with the
local continuum, and would therefore be the first feature to be
detected in the spectrum when mass loss or crystallinity increases,
under the assumption that the mass fractions of crystalline pyroxene
and forsterite are equal.
For a range of enstatite mass fractions and mass-loss rates the
contrast spectra have been calculated. To determine the relative peak
strength with respect to the local continuum, a first order polynomial
base-line has been subtracted from the feature, such that the local
continuum is equal to unity. Then the peak value of the 43.2 m
feature was measured, and plotted in Fig. 6. Note that the
enstatite mass fractions differ a factor 2 with
the elsewhere used crystallinity x, because it was assumed in
Sect. 2.1 that enstatite and forsterite are equally
abundant. Figure 6 is a diagnostic tool to determine
the crystalline pyroxene content of the silicates present in the
dust shell around an AGB star. To do so, one has to determine
the relative peak strength of the 43.2
m feature with respect
to the local continuum, a quantity plotted on the vertical axis,
and combine this with the mass-loss rate of the object.
The data
points of the sample of AGB stars previously analysed by Sylvester et al. (1999)
are presented to illustrate the method. The
relative strength is measured from
ISO spectra with an accuracy of 2 percent of the continuum
(Table 1). We adopted an
accuracy of a factor 2 for the mass-loss rates.
Using these data, one can estimate from Fig. 6
that the enstatite makes up around 3%
2% of the total silicate
dust mass around WX Psc and OH 26.5+0.6, and around
6%
2% in
OH 127.8+0.0 and OH 32.8-0.3. In CRL 2199 and
OH 104.9+2.4 the
enstatite mass fraction is well below 2-3%,
whereas the upper limit obtained for o Cet (Mira itself)
does not put interesting constraints on the enstatite content.
The dust shell of o Cet could still easily contain
a mass fraction of 20% of crystalline pyroxene.
A constant enstatite mass fraction
of
5% is consistent with the observed strength
of the 43.2
m feature for a wide range of mass-loss rates.
Star | rel. flux | rel. flux | ![]() |
ref. |
32.5 ![]() |
43.2 ![]() |
![]() |
||
o Cet | < 0.05 | < 0.05 | 1.0 10-7 | 1 |
CRL 2199 | < 0.05 | < 0.05 | 1.5 10-5 | 2, 3 |
WX Psc | 0.115 | 0.090 | 1.9 10-5 | 2, 4, 5, 6 |
OH 104.9+2.4 | 0.064 | < 0.05 | 6.0 10-5 | 6 |
OH 127.8+0.0 | < 0.05 | 0.15 | 2.0 10-4 | 3 |
OH 26.5+0.6 | 0.062 | 0.095 | 1.6 10-4 | 3, 6, 7 |
AFGL 5379 | 0.077 | 0.093 | ||
OH 32.8-0.3 | < 0.05 | 0.16 | 1.0 10-4 | 3, 6, 8 |
1: Planesas et al. (1990), 2: Knapp & Morris (1985), 3: Justtanont & Tielens (1992),
4: Sopka et al. (1989), 5: Le Bertre & Winters (1998), 6: Schutte & Tielens (1989), 7: Justtanont et al. (1996), 8: Groenewegen (1994). |
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Figure 6:
Relative strength of the 43.2 ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 7:
Relative strength of the 32.5 ![]() ![]() ![]() ![]() ![]() ![]() |
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A similar analysis can be performed on the forsterite
(Mg2SiO4, crystalline olivine) mass fraction,
using the 32.5 m feature,
which has the best contrast. For the same range of mass-loss rates
the emerging dust spectrum has been calculated.
The mass fraction of the crystalline
olivine varied from
0% to 20%. All other input parameters had equal values as
the parameters in the
analysis of the crystalline pyroxene mass fraction.
We calculated the relative peak value of the 32.5
m feature,
by subtracting a first order polynomial from the forsterite contrast
plots.
Figure 7 shows the relative peak fluxes as a function of
mass-loss rate, calculated for different mass fractions of forsterite.
From this plot it is obvious that in low mass-loss rate AGB stars,
the strength of the 32.5
m feature is less than 5% of the continuum,
which makes it imperceptible for ISO, as is illustrated with the data
for o Cet.
For higher mass-loss rate AGB stars,
the strength of the feature provides a reliable measure to determine
the crystalline olivine mass fraction. The forsterite mass fraction
of our
sample of high mass-loss stars however, is at most 5%
2%
for WX Psc. There is no evidence for an increasing forsterite mass
fraction for higher mass-loss rates.
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Figure 8:
Relative peak strength of the 43.2 ![]() ![]() ![]() ![]() ![]() |
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Figures 8 and 9 illustrate
that an observational selection
effect is present in the correlation between mass-loss rate and
crystallinity reported in previous studies by
Waters et al. (1996); Cami et al. (1998); Sylvester et al. (1999).
The OH/IR stars with
yr-1 only have to contain a small mass fraction of crystalline
pyroxene in their dust shells in order to exhibit the 43.2
m or 32.5
m feature. A few percent is already perceptible with
ISO. However, the
43.2 and 32.5
m
features in the spectra of Miras, with
yr-1, will only be detected for
high crystallinity.
For example, in the dust shell of o Cet,
with
yr-1, a
dust mass fraction of 20% of enstatite could be present without
showing the 43
m feature in its spectrum. The same goes for
the 32.5
m forsterite feature. If we assume that equal
amounts of crystalline pyroxene and olivine are present, the ISO
detection limit only provides an upper-limit to the crystallinity of
x = 0.40. If a constant crystallinity of x=0.10 (i.e. a mass
fraction for both enstatite
and forsterite of 5% of the total silicate mass) is assumed,
while the star evolves along the AGB, the 32.5
m and
43.2
m features will
appear in the spectrum when the mass loss is sufficiently high. The threshold
value, defined by the ISO detection limit, is found at
yr-1. This is consistent with
observational studies that conclude that crystalline silicate features
only appear to be present in high mass-loss rate objects.
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Figure 9:
Relative peak strength of the 32.5 ![]() ![]() ![]() ![]() ![]() |
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The appearance of crystalline silicate features with increasing mass-loss rate for a constant degree of crystallinity may be caused by the difference in absorptivity in the NIR of crystalline and amorphous silicates. This difference is due to a difference in Fe-content of the amorphous and crystalline components. The crystalline silicates investigated do not contain any iron, whereas in the amorphous silicates the iron and magnesium contents are roughly equal. Previous laboratory studies (Koike et al. 1993; Jäger et al. 1998) have shown that the peak positions of crystalline silicate features strongly depend on the Fe-content of the silicate. At present, there have not been any detections of crystalline silicates containing iron around evolved stars, which justifies the use of laboratory data of pure Mg2SiO4 and MgSiO3.
The absorptivity in the NIR and at shorter wavelengths
increases with increasing
Fe-content.
The amorphous silicates thus absorb more radiation from the central star,
which emits most of its flux at NIR wavelengths,
than the crystalline
silicates do, resulting in a large temperature difference between
amorphous and crystalline material, the latter staying much cooler.
In the mid and far infrared the absorptivity of both dust
types are more or less equal. In an optically thick dust shell, where
the stellar flux is absorbed and re-radiated several times by the
dust, the grains in the outer regions are illuminated by a
radiation field that typically
peaks at mid infrared wavelengths. As in this wavelength regime only a small
difference in absorptivity occurs, a large temperature difference
between the amorphous and crystalline dust components will not
develop. Summarising, at the inner radius of an optically thick dust shell the
crystalline silicates are much colder than the amorphous silicate
grains, but the temperature difference decreases at larger distances.
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Figure 10:
ISO SWS spectrum of AFGL 2999. The spectrum of this star is
typical for that of an object somewhere in between typical Miras and
OH/IR stars. High resolution and high signal-to-noise observations may
perhaps reveal crystalline silicate features as sub-structure in the
broad amorphous 10 ![]() ![]() ![]() |
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The implications for the strength of the crystalline silicate features due to this temperature difference are quite dramatic. In low mass-loss rate AGB stars (Miras), the dust shell is optically thin, implying the entire dust shell is visible and contributes to the SED. The relatively hot amorphous silicates at the inner radius then dominate the SED of a Mira, and the contrast of the crystalline silicates with respect to the amorphous silicate spectrum becomes very poor. In case of a high mass-loss rate AGB star, only the outer regions of the dust shell are visible, because the shell is optically thick at IR wavelengths. The temperature differences in the outer layers are small, as explained above, and therefore the crystalline and amorphous dust components both contribute in comparable amounts to the spectrum. This improved contrast of the crystalline silicates with respect to the amorphous dust emission enables the detection of the narrow crystalline features in the spectrum of OH/IR stars.
The ISO detection limit allows the presence of a significant fraction of crystalline silicates in the circumstellar shells of low mass-loss rate AGB stars. In fact, the ISO data are consistent with model calculations assuming that the crystallinity of the dust is constant with mass-loss. Until now, most theoretical studies (Tielens et al. 1998; Gail & Sedlmayr 1999; Sogawa & Kozasa 1999) assumed that crystalline silicates are only formed in high density outflows. The results presented in this study suggest that the possibility of the condensation of crystalline silicates in low mass-loss rate AGB stars should be considered in future studies.
To date, there are no significant detections of crystalline silicates
in low mass-loss rate AGB stars reported. As shown above,
this provides a relatively
high upper limit to the mass fraction taken by crystalline silicates
in the shells around these stars. In order to lower this upper limit
and to investigate the presence of crystalline silicates in Miras,
additional observations with a better detection limit than that of
ISO, are required. Unfortunately, the most prominent and
characteristic features of crystalline silicates appear in the
25-50 m region, and with the end of the ISO mission the
opportunities to observe in this wavelength region are limited.
An important future
mission covering part of this wavelength region is SIRTF, which can
perform intermediate resolution spectroscopy (
)
up to
m. The crystalline silicate feature with the largest
contrast value within this wavelength range is the 32.5
m
forsterite feature. In Fig. 9, the contrast of
this feature with respect to the continuum is presented as a
function of mass-loss rate and Mg2SiO4 mass fraction.
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Figure 11:
Predicted flux levels in the 7-13 ![]() ![]() ![]() |
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In addition, it is also possible to study the 10 and 20 m silicate
features, which both can be observed from the ground. Since it is
already known that the high mass-loss rate OH/IR stars contain
crystalline silicates in their circumstellar dust shells, it is
particularly interesting to study the 10
m feature of low and
intermediate mass-loss rate objects, with
yr-1. From Figs. 2 and
3 it one can conclude that the 10
m feature of
intermediate mass-loss rate AGB stars (
to
10-5
yr-1) would be the most likely to reveal the
presence of crystalline silicates. The 10
m region has the
intrinsically strongest resonance peaks of crystalline silicates. Superposed
on the 10
m feature of amorphous silicates which is just optically
thick (
)
these strong resonances appear as absorption features
in the spectrum. The intermediate mass-loss rate
AGB stars can be easily recognised from the ratio between the strength
of the 10 and 20
m features. For example AFGL 2999, of which the
ISO SWS spectrum is shown in Fig. 10, can be identified as
a
yr-1 AGB star.
Figure 11 shows predicted 10 m features. The
flux levels are calculated for models with
yr-1 and
x = 0.00, 0.10, 0.20. The broad amorphous
silicate feature is partially optically thick and shows
a flattened profile due to
self-absorption. The additional opacity provided by the crystalline
silicates appears as narrow absorption superposed on the broad
amorphous silicate feature. The ISO spectrum of AFGL 2999 is plotted
for reference, but the substructure in this spectrum is observational
noise and it is therefore hard to disentangle the crystalline silicate
mass fraction. However,
it would certainly be possible reach a high S/N ratio
and detect a
crystallinity of 10% with the current ground-based spectrometers that
cover the 10
m region, such as TIMMI2 mounted on the 3.6 m ESO
telescope.
AGB stars are considered
the main contributors of dust to the ISM, so one would
expect a match between the dust composition in the ISM and in the
shells of AGB stars. However, despite all evidence for crystalline
silicates in AGB stars, there has as yet not been found any reliable
evidence for
crystalline silicates in the line of sight toward the Galactic Center
(GC) (Lutz et al. 1996), or other lines of sight through the ISM
(Demyk et al. 1999). In fact, the line of sight toward the
GC is found to resemble closely the silicate feature of the evolved
star
Cep,
and can be fitted with completely amorphous olivine
(Vriend 1999; Bouwman et al. in prep.). Cesarsky et al. (2000) report a questionable detection of
crystalline silicates in the Orion Bar.
On the other hand, it is doubtful that Miras contribute significantly
to the dust population in the ISM. It is generally accepted that the
Mira phase lasts 3 105 yr, and the OH/IR phase
3000 yr
(Habing 1996). The mass-loss rates for Miras and OH/IR stars
(
yr-1, and
yr-1) can
be used to estimate the total mass lost in each of the two phases;
for OH/IR stars this is
0.3
,
for Miras
0.03
.
Under the
assumption that all Miras will eventually evolve into OH/IR stars,
only a minor fraction (
10%) of the interstellar dust
population is formed in a Mira dust shell. So, the possibility that Miras
contain a significant fraction of crystalline silicates in their dust
shells does not heavily aggravate the discrepancy between the dust
composition in the ISM and that in AGB dust shells, under the
assumption that all Miras eventually evolve into OH/IR stars.
However, if Mira stars indeed deposit dust with a high degree of crystallinity
into the ISM, and a significant fraction of Miras does not evolve into
OH/IR stars, it is more surprising that the interstellar
silicate grains appear to have an amorphous lattice structure.
Grain-grain collisions and ion
bombardments might cause the required amorphitization. Due to
the collision, the grain will partially melt and consequently
solidify in an amorphous form
on timescales shorter than the annealing timescales
(Sylvester et al. 1999). In a
future study (Kemper et al., in prep.) we will thoroughly
examine the differences between silicates in
the ISM and in circumstellar shells, and discuss possible mechanisms
of grain processing.
In this work, three important aspects of crystalline silicates around AGB stars have been studied by modelling the dust shell. First, we have calculated spectra emerging from circumstellar dust shells for different mass-loss rates. Moreover, the effects of different degrees of crystallinity on the SED have been taken into account, as a function of optical depth toward the central star. Finally, we provide a useful and easy to use diagnostic tool to determine the degree of crystallinity for an AGB star with a known mass-loss rate. The dust shells of low mass-loss rate AGB stars can contain a significant fraction of crystalline silicates, while the characteristic sharp spectral peaks are indiscernible with ISO. This is caused by a large temperature difference in the inner parts of these optically thin dust shells, such that the relatively warm amorphous silicate emission dominates the SED. The temperature difference between the warm amorphous dust and the cold crystalline dust is caused by a difference in absorptivity at NIR and visible wavelengths, where the amorphous dust component more efficiently absorbs the stellar radiation. The low absorptivity of the crystalline component is due to the very low Fe-content of these dust species. In case of high mass-loss AGB stars, the radiation from the central star is absorbed by the dust and re-radiated several times, so that the dust in the outer parts receives a relatively red radiation field, which peaks in the mid-IR. In that region the absorptivity of crystalline and amorphous silicates are similar, leading to similar temperatures of both species. The dust shell is optically thick, so only the outer layers, where crystalline and amorphous silicates have similar temperatures, are visible, leading to a high contrast of the crystalline silicate features.
From these results one may conclude that crystallinity is not
necessarily a function of mass-loss rate, as many observational and
theoretical studies have suggested. The threshold value for the
mass-loss rate above which crystalline silicates are observed
is consistent with the ISO detection limit if a constant
crystallinity of 10% is assumed. The strong observational selection
effect undermines previously drawn conclusions regarding this threshold value.
The meaning and the existence of the threshold mass-loss rate should
be reconsidered. Future observations of
the 10 m silicate feature of low mass-loss AGB stars
at high spectral resolution can
probably further constrain the upper limit for the crystalline
silicate content in Miras. The low degree of crystallinity of grains
in the interstellar medium with respect to grains in AGB shells, however,
remains subject to further study.
Acknowledgements
We wish to thank C. Dominik, J. Bouwman, F. J. Molster and T. de Jong for the useful discussions. We are grateful to I. Yamamura for the reduction of the ISO SWS spectrum of AFGL 2999. FK, LBFMW and AdK acknowledge financial support from NWO Pionier grant 616-78-333. We gratefully acknowledge support from NWO Spinoza grant 08-0 to E. P. J. van den Heuvel.