A&A 411, 123-147 (2003)
DOI: 10.1051/0004-6361:20031068
D. González Delgado1 - H. Olofsson1 - F. Kerschbaum2 - F. L. Schöier1,3 - M. Lindqvist4 - M. A. T. Groenewegen5
1 - Stockholm Observatory, AlbaNova, 10691 Stockholm, Sweden
2 - Institut für Astronomie, Türkenschanzstrasse 17, 1180 Wien, Austria
3 - Leiden Observatory, PO Box 9513, 2300 RA Leiden, The Netherlands
4 - Onsala Space Observatory, 43992 Onsala, Sweden
5 - Instituut voor Sterrenkunde, PACS-ICC, Celestijnenlaan 200B, 3001
Leuven, Belgium
Received 28 January 2003 / Accepted 3 July 2003
Abstract
An extensive radiative transfer analysis of circumstellar
SiO "thermal'' radio line emission from a large sample of M-type AGB stars has been performed. The sample contains 18 irregulars of type
Lb (IRV), 7 and 34 semiregulars of type SRa and SRb (SRV),
respectively, and 12 Miras. New observational data, which
contain spectra of several ground vibrational state SiO rotational lines,
are presented. The detection rate
was about 60% (44% for the IRVs, and 68% for the SRVs). SiO fractional abundances have been determined through radiative transfer
modelling. The abundance distribution of the IRV/SRV sample has a
median value of
,
and a minimum of
and a maximum of
.
The high mass-loss
rate Miras have a much lower median abundance,
10-6.
The derived SiO abundances are in all
cases well below the abundance expected from stellar atmosphere
equilibrium chemistry, on average by a factor of ten. In addition, there is a
trend of decreasing SiO abundance with increasing mass-loss rate. This
is interpreted in terms of depletion of SiO molecules by the formation
of silicate grains in the circumstellar envelopes, with an efficiency
which is high already at low mass-loss rates and which increases with
the mass-loss rate. The high mass-loss rate Miras
appear to have a bimodal SiO abundance distribution, a low
abundance group (on average
)
and a high abundance
group (on average
). The estimated SiO envelope
sizes agree well with the estimated SiO photodissociation radii using an
unshielded photodissociation rate of
s-1.
The SiO and CO radio line
profiles differ in shape. In general, the SiO line profiles are narrower than the CO line profiles, but they have
low-intensity wings which cover the full velocity range of the CO line profile. This is interpreted as partly an effect of selfabsorption
in the SiO lines, and partly (as has been done also by others) as due
to the influence of gas acceleration in the region which produces a
significant fraction of the SiO line emission. Finally, a number of
sources which have peculiar CO line profiles are discussed from the
point of view of their SiO line properties.
Key words: stars: AGB and post-AGB - circumstellar matter - stars: mass-loss - stars: late-type - radio lines: stars
The atmospheres of and the circumstellar envelopes (CSEs) around
Asymptotic Giant Branch (AGB) stars are regions where many different
molecular species and dust grains form efficiently. The molecular and
grain type setups are to a large extent determined by the C/O-ratio of
the central star. For instance, SiO is formed in the extended
atmospheres of both M-type [;
O-rich] and C-type [
]
AGB stars,
but its abundance is much higher in the former. Therefore, the SiO "thermal'' line emission (i.e., rotational lines in the v=0 state;
the term "thermal'' is used here to distinguish the v=0 state
emission from the strong maser line emission from vibrationally
excited states) is particularly strong towards M-stars, with the
intensity of e.g. the J=2
1 line comparable to, or even
stronger than, that of the CO J=1
0 emission.
Nevertheless, the initial observations of SiO thermal radio line
emission from AGB-CSEs (Wolff & Carlson 1982; Lambert & Vanden Bout 1978) and
their interpretation (Morris et al. 1979) suggested
circumstellar SiO abundances (several) orders of magnitude lower than
those expected from the chemical equilibrium models (Tsuji 1973).
Over the years the observational basis has improved considerably (Bujarrabal et al. 1989; Olofsson et al. 1998; Bieging & Latter 1994; Bieging et al. 2000; Bujarrabal et al. 1986; Bieging et al. 1998), and even some interferometer data exist (Sahai & Bieging 1993; Lucas et al. 1992). These data suggest that the SiO line emission originates in two regions, one close to the star with a high SiO abundance, and one extended region with a low SiO abundance. The relative contributions to the SiO line emission from these two regions depend on the mass-loss rate.
This structure has been interpreted as due to accretion of SiO onto
dust grains (Bujarrabal et al. 1989; Sahai & Bieging 1993). After the grains nucleate
near the stars, they grow in
part because of adsorption of gas-phase species. In O-rich CSEs,
refractory elements like Si, together with O, are very likely the main
constituents of the grains, which are identified through the 9 and 18 m silicate features in the infrared spectra of the stars
(Pégourié & Papoular 1985; Forrest et al. 1975). Therefore, molecules like SiO are expected to be
easily incorporated into the dust grains. As a result, the SiO gas
phase abundance should fall off with increasing distance from the star
as SiO molecules in the outflowing stellar wind are incorporated into
the grains. The depletion process is, however, quite uncertain since
it does not proceed at thermal equilibrium. Eventually,
photodissociation destroys all of the remaining SiO molecules.
The grain formation is important not only for the chemical composition of the CSE, but also because it affects its dynamical state (the radiation pressure acts on the grains which are dynamically coupled to the gas, e.g., Kwok 1975). The SiO radio line profiles are narrower than those of CO and have mostly Gaussian-like shapes (e.g., Bujarrabal et al. 1989,1986), a fact suggesting that the SiO line emission stems from the inner regions of the CSEs, where grain formation is not yet complete and where the stellar wind has not reached its terminal expansion velocity. This result is corroborated by interferometric observations which show that the size of the SiO line emitting region is independent of the line-of-sight velocity (Lucas et al. 1992). Lucas et al. explained this as a result of a rather extended acceleration region. However, Sahai & Bieging (1993), using a more detailed modelling, were able to explain both the line profiles and the brightness distributions with a "normal'' CSE, i.e., with a rather high initial acceleration.
Therefore, "thermal'' SiO radio line emission is a useful probe of the formation and evolution of dust grains in CSEs, a complex phenomenon that is yet not fully understood, as well as the CSE dynamics.
In this paper we present a detailed study of SiO radio line emission from the CSEs of a sample of M-type AGB stars. The sample includes irregular (IRVs), semiregular (SRVs) and Mira (M) variables. The IRVs and SRVs have already been studied in circumstellar CO radio line emission (Olofsson et al. 2002), yielding estimates of the stellar mass-loss rates. Using these estimates a radiative transfer modelling of the SiO radio line emission is performed. A complete analysis of the circumstellar CO and SiO line emission is done for the Mira sub-sample.
The sample contains all the M-type IRVs and SRVs detected
in circumstellar CO radio line emission by Kerschbaum & Olofsson (1999)
and Olofsson et al. (2002). The
original source selection criteria are described in Kerschbaum & Olofsson (1999),
but basically these stars are the
brightest 60 m-sources (IRAS S60 typically above 3 Jy, with
IRAS quality flag 3 in the 12, 25, and 60
m bands) that appear as IRVs or SRVs in the General Catalogue of Variable Stars (GCVS4;
Kholopov 1990). The detection rate of circumstellar CO
was rather high, about 60% (Olofsson et al. 2002; 69 stars detected). The basic properties of the stars are listed in
Kerschbaum & Olofsson (1999) and Olofsson et al. (2002).
The distances, presented in Table 4, were
derived using an assumed bolometric luminosity of 4000
for
all stars. We are aware of the fact that such a distance estimate have a
rather large uncertainty for an individual object but it is adequate for a
statistical study of a sample of stars (see discussion by Olofsson et al. 2002).
The apparent bolometric fluxes were
obtained by integrating the spectral energy distributions ranging from
the visual data over the near-infrared to the IRAS-range (Kerschbaum & Hron 1996).
The SiO (v=0, J=2
1; hereafter all SiO transitions are in the ground
vibrational state) data were obtained using the 20 m telescope at
Onsala Space Observatory (OSO) and the 15 m Swedish-ESO Submillimetre
Telescope (SEST) on La Silla, Chile. At SEST, a sizable fraction of
the stars were observed also in the SiO J=3
2 line, and four
additional sources were observed with the IRAM 30 m telescope at Pico Veleta,
Spain, in this line. The
higher-frequency lines, J=5
4 and 6
5,
were observed towards 10 and 3 stars, respectively. The observing
runs at OSO were made over the years 1993 to 2000, at SEST over
the years 1992 to 2003, and at IRAM between October 18 and 22 in 1997.
Telescope and receiver data are given in
Table 1.
and
stand for
the representative noise temperature of the receiver (SSB) and the
main beam efficiency of the telescope, respectively.
Two filterbanks at OSO (
kHz, and
MHz),
two acousto-optical spectrometers at SEST (86 MHz bandwidth with 43 kHz channel separation, and 1 GHz bandwidth with 0.7 MHz channel
separation), and a 1 MHz filter bank at IRAM were used as spectrometers.
Dual beam switching (beam
throws of about 11
), in which the source was placed alternately
in the two beams, was used to eliminate baseline ripples at OSO and SEST, while
a wobbler switching with a throw of 150
in azimuth was used at IRAM. Pointing and focussing were checked every few hours. The line
intensities are given in the main beam brightness temperature scale (
), i.e., the antenna temperature has been corrected for
the atmospheric attenuation (using the chopper wheel method) and
divided by the main beam efficiency.
Table 1: Data on telescopes and receivers.
A total of 60 stars were observed in circumstellar SiO line emission
(i.e., about 85% of the stars detected in circumstellar CO): 34 stars
were detected in the SiO J=2
1 line, 21 in the
J=3
2 line, and 3 in the J=5
4 and J=6
5 lines.
Clear detections of SiO lines were obtained towards 36 sources, i.e.,
the detection rate was about 60%: 8 IRVs (detection rate 44%) and 28 SRVs (detection rate 68%) were detected.
Tables A.1 and A.2 in the
Appendix list all our SiO observations. The names in the GCVS4 and
the IRAS-PSC are
given. The first letter of the code denotes the observatory
(IRAM, OSO, or SEST), the rest the transition observed.
Another code reflects the "success'' of the observation (Detection, Non-detection).
The stellar velocity is given with respect to the heliocentric (
)
and LSR frame [
;
the Local Standard of
Rest is defined using the standard solar motion (B1950.0):
km s-1,
,
]. The stellar velocity, the expansion
velocity, and the main beam brightness temperature were obtained by
fitting the function
to the line profile. The integrated intensity,
dv, is obtained by integrating the line
intensities over the line profile. The uncertainty in I varies with
the S/N-ratio, but we estimate that it is on avarage <15%. To this
should be added an estimated uncertainty in the absolute calibration
of about 20%. For a non-detection an upper limit to I is estimated
by measuring the peak-to-peak noise (
)
of the spectrum
with a velocity resolution reduced to 15 km s-1 and calculating
I = 15
.
The Q-column gives a quality ranking: 5 (not
detected), 4 (detection with very low S/N-ratio
3), 3 (detection, low S/N-ratio
5), 2 (detection, good S/N-ratio
10), and 1 (detection, very good S/N-ratio
15).
Finally, in cases of complex velocity profiles the measured component
is indicated in the form
,
,
.
All the spectra are shown in Figs. B.1 to B.4. The velocity scale is given in the heliocentric system. The velocity resolution is reduced to 0.5 km s-1, except for some low S/N-ratio spectra where a resolution of 1 km s-1, or even 2 km s-1, is used, and for some low expansion velocity sources for which 0.25 km s-1 is used.
In order to make a more extensive study of circumstellar SiO line
emission in the CSEs of M-type AGB-stars, a sample of 12 Mira
variables with higher mass-loss rates was added. The
distances are obtained using the period-luminosity relation of
Whitelock et al. (1994). Through modelling of their
circumstellar CO radio line emission (Sect. 5), we
determined that 4 of the Miras have very high mass-loss rates
(10
yr-1), 6 are intermediate to high mass
loss rate objects (
10
yr-1) and 2 are low mass-loss rate sources
(a few 10
yr-1).
For this sample data has been gathered from a number of sources.
The CO(J=1
0) data were taken from Olofsson et al. (1998), while the CO(J=2
1, J=3
2, and J=4
3) data were obtained from the archive of the James
Clerk Maxwell Telescope on Mauna Kea, Hawaii. The JCMT data
are taken at face value after converting to the main beam brightness
scale. However, in the cases where there are more
than one observation available, the derived line intensities are
generally consistent within
20% (as was found also by Schöier & Olofsson 2001). The
SiO(J=2
1) data were obtained from Olofsson et al. (1998).
The SiO J=5
4 line was observed in four objects, and
the J=6
5 line in one object using SEST with
the same observational equipment and procedure as described above.
The relevant observational results are summarized in Table A.3, and the SiO spectra are shown in Fig. B.5. The names in the GCVS4 and the IRAS-PSC are given. The first letter of the code denotes the observatory (JCMT, OSO, or SEST), the rest the transition observed.
Apart from presenting new observational results on thermal SiO radio line emission from AGB-CSEs a rather detailed modelling of the emission will be performed. In some senses this is a more difficult enterprise than the CO line modelling. The SiO line emission predominantly comes from a region closer to the star than does the CO line emission, and this is a region where the observational constraints are poor. The SiO excitation is also normally far from thermal equilibrium with the gas kinetic temperature, and radiative excitation plays a larger role (hence the term "thermal'' is really not appropriate). Finally, there exists no detailed chemical model for calculating the radial SiO abundance distribution. These effects make the SiO line modelling much more uncertain, and dependent on a number of assumptions.
The aim is to investigate to what extent the thermal SiO line emission
is a useful probe of e.g. the dust formation and the CSE dynamics.
There are observational indications that this is the case but the
interpretation is normally not straightforward. As an example,
Olofsson et al. (1998) found that the line intensity ratio
I(SiO, J=2
1)/I(CO, J=1
0) decreases
markedly as a function of a mass-loss rate measure. Their results are
reproduced here, but now including all stars of our IRV/SRV and Mira
samples, Fig. 1. A straightforward interpretation would
be that the SiO abundance decreases with mass-loss rate due to
increased depletion efficiency and hence this limits severely the SiO line strength. However, excitation may play an important role here,
both for SiO and CO, and a detailed modelling is required.
![]() |
Figure 1:
The line intensity ratio
I(SiO, J=2
![]() ![]() |
Open with DEXTER |
In order to model the circumstellar SiO line emission a non-LTE radiative transfer code based on the Monte Carlo method has been used (Bernes 1979). It has been previously used to model circumstellar CO radio line emission in samples of both C- (Schöier et al. 2002; Schöier & Olofsson 2000,2001) and O-rich (Olofsson et al. 2002) AGB-CSEs, and also to model the HCN and CN line emission from a limited number of C-rich AGB-CSEs (Lindqvist et al. 2000).
In the excitation analysis of SiO 50 rotational levels in both the ground and the first excited vibrational state are considered. The energy levels of this linear rotor are calculated using the molecular constants from Mollaaghababa et al. (1991). The radiative rates are calculated using the dipole moment from Raymonda et al. (1970). Collisional deexcitation rates have been calculated by Turner et al. (1992) in the temperature range 20-300 K and up to J=20. The original data set has been extrapolated in temperature and to include levels up to J=50(Schöier et al., in prep.).
The CSEs around AGB-stars are intricate systems where an interplay between different chemical and physical processes takes place. This makes the modelling of circumstellar radio line emission a quite elaborate task. In the analysis presented here, a relatively simple, yet realistic, model for the geometry and kinematics of the CSEs has been adopted. Below follows a short description of the main features of the circumstellar model. For more details we refer to Schöier & Olofsson (2001) and Olofsson et al. (2002).
A spherically symmetric geometry of the CSE is adopted. The mass loss is assumed to be isotropic and constant with time. The gas expansion velocity is assumed to be constant with radius. There is a possibility that neither the mass-loss rate nor the expansion velocity are constant in the regions of interest here. This should be kept in mind when interpreting the results. There is growing evidence for mass-loss modulations of AGB-stars on a time scale of about 1000 yr (Mauron & Huggins 2000; Fong et al. 2003; Marengo et al. 2001), and the CO line emission comes from a much larger region than that of the SiO lines, and hence averages over a longer time span. Furthermore, the SiO line emission comes from the inner part of the CSE, where it is likely that the gas has not fully reached the terminal velocity. We have not allowed for the presence of gas acceleration nor a time-variable mass loss in the modelling in order to limit the number of free parameters.
The inner boundary of the CSE was set to 1 1014 cm (
3 R*). This parameter is specially important in
the case of SiO where radiative excitation is expected to play a role. A
turbulent velocity of 0.5 km s-1 is assumed throughout the
entire CSE (see discussion by Olofsson et al. 2002).
The outer boundaries of the molecular abundance distributions are, for
both CO and SiO, determined by photodissociation due to the
interstellar UV radiation field. For CO we use the modelling of
Mamon et al. (1988). The procedure for SiO is presented in Sect. 6.
The radiation field is provided by two sources. The central radiation emanates from the star. This radiation was estimated from a fit to the spectral energy distribution (SED) by assuming two blackbodies, one representing the direct stellar radiation and one the dust-processed radiation (Kerschbaum & Hron 1996). In the case of optically thin dust CSEs the stellar blackbody temperature derived in this manner is generally about 500 K lower than the effective temperature of the star. The dust mass-loss rates of the IRV/SRVs are low enough that the dust blackbody can be ignored. For the sample of Mira variables both blackbodies were used, since for these high mass-loss rate stars, the excitation of the SiO molecules may be affected by dust emission. The second radiation field is provided by the cosmic microwave bakground radiation at 2.7 K.
In the SiO line modelling the gas kinetic temperature law derived in the modelling of the circumstellar CO radio line emission was used. This is reasonable since the SiO line emission contributes very little to the cooling of the gas. However, the SiO line emission comes mainly from the inner CSE, where the CO lines do not put strong constraints on the temperature, and where other coolants, specifically H2O, may be important. We estimate though that the kinetic tempartures used in our modelling are not seriously wrong. In addition, for at least the lower mass-loss rates the SiO molecule is mainly radiatively excited, and hence the exact gas kinetic temperature law and the collisional rate coefficients play only a minor role, see Sect. 4.4.
In Sect. 4.4 some implications of these assumptions are discussed.
The mass-loss rates for the sample of IRV/SRVs were already presented
in Olofsson et al. (2002). They were derived through
modelling of circumstellar CO radio line observations. A median mass
loss rate of
yr-1 was found for this
sample. These mass-loss rate estimates are expected to be accurate to
within a factor of a few for an individual object. Nevertheless, they
are probably the best mass-loss rate estimates for these types of
objects (also in agreement with the mass-loss rate estimates by
Knapp et al. 1998 for five sources in common).
The modelling of the circumstellar CO radio line emission for the Mira
sample is presented in this paper. The same approach as in
Olofsson et al. (2002) has been used, i.e., the energy balance
equation is solved simultaneously with the CO excitation. A
number of (uncertain) parameters describing the dust are introduced.
They are grouped in a global parameter, the h-parameter, which is given by
Table 2:
The effect on the integrated model SiO intensities (in percent),
due to changes in various parameters. Three model stars with mass
loss rate and gas expansion velocity characteristics typical for our
samples are used. They lie at a distance of 250 pc, and have
luminosities of 4000
(the model stars with mass-loss
rates of 10-7 and 10
yr-1) and 8000
(the
model star with a mass-loss rate of 10
yr-1), and blackbody
temperatures of 2500 K. The nominal CSE parameters are h=0.2 (for
the lowest mass-loss rate model star) and h=0.5 (for the other two
model stars),
cm,
km s-1, and
.
The size of the
SiO envelope,
,
is given by Eq. (13) for the given mass-loss rate. The
SiO J=2
1, J=3
2,
J=5
4, and J=6
5 lines are
observed with beam widths of 57
,
38
,
23
,
and 19
,
respectively (appropriate for a 15 m telescope).
The model integrated line intensities, I in K km s-1, are given for the nominal
parameters. For comparison, also the integrated CO line intensities for the model stars are
given [for a 15 m telescope; 45
(J=1
0;
I=0.14, 3.8, and 45 K km s-1 for 10-7,10-6, and 10
yr-1, respectively), 23
(J=2
1), 15
(J=3
2), 9
(J=5
4), 7
5 (J=6
5)].
A sensitivity test has been performed in order to determine the
dependence of the calculated SiO line intensities on the assumed
parameters for a set of model stars. They are chosen such that they
have nominal mass-loss rate and gas expansion velocity combinations
which are characteristic of our samples: a low mass-loss rate
(10
yr-1, 7 km s-1), an intermediate
mass-loss rate (10
yr-1, 10 km s-1),
and a high mass-loss rate (10
yr-1,
15 km s-1) model star. They are placed at a distance of
250 pc (a typical distance of the stars in the IRV/SRV sample). We
have also taken nominal values for the luminosity (
for the low and intermediate mass-loss rate model stars, and
for the high mass-loss rate model star), the
effective temperature (
K), the h-parameter
(h=0.2 for the low mass-loss rate model star, and h=0.5 for the
other two), the envelope inner radius
(
cm, which is twice the inner radius
used in the modelling), the turbulent velocity
(
km s-1), and the SiO abundance (
(close to the median value for our
IRV/SRV sample, see below); throughout this paper the term abundance
means the fractional abundance with respect to H2, the dominating
molecular species in the CSEs). The SiO envelope outer radius is
calculated for each model star following the same relation that is
used in the modelling of the sample stars (see
Sect. 6.4). The SiO lines are observed with beam
widths characteristic of our observations. All parameters (except the
mass-loss rate and expansion velocity) are changed by -50% and +100% and the velocity-integrated line intensities are calculated.
In order to check the effect of the h-parameter on the modelled
intensities the radial gas kinetic temperature law is scaled by -33% and +50%. The results are summarized in
Table 2 in terms of percentage changes. To see how the
SiO/CO line intensity ratios vary with mass-loss rate, the CO line
intensities derived from the models with the nominal parameters are
also included.
Despite the fact that the dependences are somewhat complicated there are some general trends. The line intensities are, in general, sensitive to changes in the outer radius, but less so for the high-J lines, a fact which is more evident for the low mass-loss rate stars. There is also a dependence of all line intensities on the SiO abundance, irrespective of the magnitude of the mass-loss rate. These particular dependences of the line intensities on the envelope outer radius and the SiO abundance allowed us to derive envelope sizes for those stars with multi-line observations (see Sect. 6.3). The line intensities are rather insensitive to a change in the kinetic temperature. Only the high-J lines for high mass-loss rates show a weak dependence on this parameter. The dependence on the inner radius is marginal, and so is the dependence on the turbulent velocity width (as long as it is significantly smaller than the expansion velocity).
The dependece on luminosity is also weak, with only small
changes in high-J line intensities for low mass-loss rates and in
low-J line intensities for high mass-loss rates. However, the
radiation field distribution may be of importance here, in particular
for the high mass-loss rate objects. We have checked this for the high
mass-loss rate model star. If half of the luminosity is put in a 750 K
blackbody, the J=2
1, J=3
2,
J=5
4, and J=6
5 line intensities increase
by a factor of 1.7, 1.3, 1.1, and 1.1, respectively. That is, the
lower J-lines are most affected, partly because of maser
action (in particular in the J=1
0 line). This means
that the SiO abundance estimates for the high mass-loss rate Miras are
particularly uncertain, and the line saturation makes things even
worse.
A velocity gradient may affect the SiO line intensities since it
allows the central pump photons to migrate further out in the CSE. We
have tested a velocity law of the form (appropriate for a dust-driven
wind, see Habing et al. 1994)
Finally, the line intensity ratio I(SiO, J=2
1)/
I(CO, J=1
0) decreases with mass-loss rate: 0.79 for a
mass-loss rate of 10
yr-1, 0.33 for 10
yr-1, and 0.24 for 10
yr-1. This result is in line with the
observational result presented in Fig. 1, and suggests
that at least part of the trend is an excitation effect.
Table 3: CO model results for the Mira sample.
In order to obtain mass-loss rates for the Mira sample we have modelled
the circumstellar CO radio line emission observed towards these stars
using the procedure described above and in
Schöier & Olofsson (2001). The estimated mass-loss rates are given in
Table 3, rounded off to the number nearest to 1.0, 1.3, 1.5, 2.0, 2.5, 3, 4, 5, 6, or 8, i.e., these values are
separated by about 25%. The distribution of derived mass-loss rates
have a median value of
yr-1.
Therefore, these Miras sample the high mass-loss rate end of AGB stars. Only two of them (R Hya and R Leo) have
low to intermediate mass-loss rates (a few times
10
yr-1). h was used as a free parameter in
the fit for those sources with more than two lines observed. The
average value is 0.6, i.e., very similar to what
Schöier & Olofsson (2001) found for the more luminous stars in the
their carbon star sample. We used h=0.5 for those stars observed in
only one or two lines. The quality of the fits are given by the chi-square
statistic
(see Sect. 7.1 for the
definition).
A CO fractional abundance of
has been used
following the work of Olofsson et al. (2002) on the CO modelling of low to intermediate mass-loss
rate IRV/SRVs of M-type. It is quite possible that, for the high
mass-loss rate stars involved here, the CO abundance is higher due to
a more efficient formation of CO at higher densities and lower
temperatures. A higher CO abundance would lower somewhat the derived
mass-loss rates.
Among the Miras with the highest mass-loss rates there is a trend that the
model J=1
0 line intensities are low for a model which
fits well the higher-J lines. The reason is that the CO lines reach the
saturation regime at about 10
yr-1, with the
higher-J lines saturating first.
Therefore, we chose to put more weight on the high-J lines in the
model fit. The reported values for the mass-loss rates of these stars
are, in this context, therefore considered to be lower limits. This
type of problem has also been encountered by
Kemper et al. (2003). For WX Psc, the only star in common with us, they derived a
mass-loss rate of
yr-1 by
fitting the J=2
1 line, and successively lower mass-loss
rates for the higher-J lines reaching about
10
yr-1 by fitting the J=6
5 and
J =7
6 lines. In this work a value of
yr-1 is derived based on the
J=2
1, J=3
2, and J=4
3 lines, but a fit to the J=1
0 line requires a mass-loss
rate about a factor of three higher. Kemper et al. speculate that
variable mass loss and gradients in physical parameters (e.g., the
turbulent velocity width) may play a role. To this we add that the
size of the CO envelope, which mainly affects low-J lines, is
important.
The CO expansion velocities given in Table 3 are
obtained in the model fits. Hence, they are somewhat more accurate
than a pure line profile fit, since for instance the effect of
turbulent broadening is taken into account. The uncertainty is estimated to be
of the order 10%. The gas expansion velocities have a
distribution with a median value of 15.3 km s-1, while the
IRV/SRV sample has a median gas expansion velocity of 7.0 km s-1. Again, only R Hya and R Leo have
low CO expansion velocities, below 10 km s-1.
The results of the SiO line modelling will depend strongly on the adopted sizes of the SiO envelopes. Unfortunately, these are not easily observationally determined nor theoretically estimated. Early work assumed that the whole CSE contributes to the observed SiO thermal line emission (e.g., Morris et al. 1979). The mostly Gaussian-like SiO profiles found by Bujarrabal et al. (1989,1986) towards O-rich CSEs suggested that this is not the case. The generally small size of the SiO thermal line emitting region requires interferometric observations in order to resolve it. Results from SiO multi-line modelling and interferometric data will be combined here to estimate the sizes of the SiO envelopes.
Previous work strongly suggests that the SiO abundance in the CSE is markedly lower than that in the stellar atmosphere. The decrease in the SiO abundance with radius is very likely linked to two different processes taking place in the CSE. Photodissociation due to interstellar UV radiation is a well-known mechanism which reduces the abundances of molecules in the extended CSE, but for SiO the depletion onto grains closer to the star must also be taken into account. We outline here in a simplified way the effects of these processes (based on the works by Huggins & Glassgold 1982; Jura & Morris 1985). However, the theoretical results are not used in our modelling, but they serve as a guide for the assumptions and the interpretation.
Since the rate of evaporation is very large
for
> (
/50) (where
is the grain temperature, and
the binding energy of
the molecule onto grains), there is a critical radius,
,
such that for smaller radii there is effectively no condensation,
while for larger radii almost every molecule that sticks onto the
grain remains there. The value of
can be estimated from
the condition that the characteristic flow time,
,
is
equal to the evaporation time
.
A classical
evaporation theory has been used to obtain the rate for CO
(Léger 1983), and the result is
Using the formulation by
Jura & Morris (1985), the radial variation of the SiO abundance in a CSE, taking into consideration the depletion of molecules onto dust
grains, is given by
![]() |
(5) |
![]() |
(6) |
The particular radius at
which the photodissociation becomes effective depends essentially on
the amount of dust in the envelope, which provides shielding against
the UV radiation, and the abundance of various molecular species if
the dissociation occurs in lines. Huggins & Glassgold (1982) describe the radial dependence of the
abundance of a species of photospheric origin that is
shielded by dust (in the case of SiO,
shielding due to H2O may be important but we ignore this here).
Adopting this description in the case of SiO the result is
![]() |
(8) |
![]() |
(9) |
Most likely the radial distribution of the SiO molecules is determined
by a combination of the condensation and photodissociation processes.
Thus, one can imagine an initial SiO abundance determined by the
stellar atmosphere chemistry. For low mass-loss rates, the abundance
decreases only slowly beyond the condensation radius until the
photodissociation effectively destroys all remaining SiO molecules.
For high mass-loss rates, the abundance declines exponentially beyond
the condensation radius with an e-folding radius that can be estimated
from Eq. (4),
![]() |
(11) |
For the radial distribution of the SiO abundance in the CSEs we
adopt a Gaussian fall-off with increasing distance from the star,
This is a considerable simplification to the complicated SiO abundance
distribution. However, as shown above, the expected distribution depends so
sensitively on the parameters adopted (in particular the dust mass
loss rate) that a more sophisticated approach is, for the moment, not
warranted. We expect Eq. (12) to be a reasonable
approximation to the SiO abundance distribution inside the
photodissociation radius for the low and intermediate mass-loss rate
objects. Equation (12) is a reasonable
approximation for also the high mass-loss rate objects, but the size
is either determined by condensation (high )
or
photodissociation (low
).
We have checked whether the region within the condensation radius, with a
high SiO abundance, contributes substantially to the observed line
intensities. For the model stars used in Sect. 4.4 it
is found that a high SiO abundance (5 10-5) inside the
condensation radius contributes by at most 20% of the line
intensities from the rest of the SiO envelope.
The model code used in this work allow us to estimate SiO envelope sizes provided that multi-line SiO observations are available. The emission from higher-J lines comes very likely from the warmer inner regions of the SiO envelope. Therefore, the intensities of these lines can be fitted by varying only the SiO abundance, i.e., they are rather insensitive to the outer radius of the SiO envelope (see Table 2). Once the SiO abundance has been found, the lower-J lines can be used as constraints to derive the size of the SiO envelopes, since their emission is photodissociation limited (i.e., not excitation limited).
It turns out that high-J line data, e.g., J=8
7, are
required to constrain both the abundance and the size. These crucial high-J
line data were taken from Bieging et al. (2000). In the case of data
including only moderately high-J lines, e.g., J=5
4,
only a lower limit to the size can be obtained. This is illustrated in
Fig. 2 where
maps are given for two cases (see the
definition of the chi-square statistic below). In this
way, through the use of
maps, we managed to estimate the SiO envelope
sizes in 4 cases (RX Boo,
R Cas, IRC-10529, IRC+50137), and obtain
lower limits to them in 7 cases (TX Cam, R Crt, R Dor,
R Leo, GX Mon, L2 Pup, IRC-30398).
![]() |
Figure 2:
![]() ![]() |
Open with DEXTER |
The resulting :s from the modelling are plotted as a
function of the density measure
,
in Fig. 4. We have here chosen to use
the lower limits to the SiO envelope sizes for all sources in
order to be consistent. The minimum least-square correlation between these SiO
envelope radii and the density measure is
We have checked our model results against those of the photodissocation
model. The photodissociation radii are estimated
from Eq. (10) assuming Q = 1 (Suh 2000)
and using the appropriate - and h-values for each source.
A very good agreement with the estimated SiO envelope sizes
(for all sources with detected SiO lines),
from Eq. (13), is obtained with an unshielded photodissociation
rate
s-1 (the average
deviation is about 30%),
see Fig. 3. This value is lower by about a factor of two to
three than those reported by
van Dishoeck (1988) and Tarafdar & Dalgarno (1990), and higher by about a factor of two than that
reported by Le Teuff et al. (2000). The latter report
an uncertainty by (at least) a factor of two in their estimate. Thus,
within the considerable uncertainties, our line modelling results are in excellent
agreement with those of the photodissociation model.
The
:s for our sample are given in
Table 4. On average, the photodissociation
radii of SiO are about a factor of 6 smaller than those of CO (the CO results are given in Olofsson et al. 2002).
![]() |
Figure 3:
SiO photodissociation radii (obtained using the unshielded
photodissociation rate G0 = 2.5 ![]() |
Open with DEXTER |
We have also checked our modelling results by comparing with the interferometric
SiO(J=2
1) data toward a number of O-rich
CSEs of Lucas et al. (1992). They derived the sizes of the
SiO line emitting region from direct
fits, assuming exponential source-brightness distributions, to the
visibility data.
Their observations thus yielded the half-intensity angular radii of
the SiO(J=2
1) emitting regions. Sahai & Bieging (1993)
observed a smaller
sample of CSEs interferometrically, and claimed that the source
brightness distribution is rather of a power-law form (i.e.,
scale-free). This would explain why Lucas et al. derived essentially
the same angular sizes for most of the sources independent of their
distances. To resolve this issue requires more detailed observations, and
we will only use the results of Lucas et al. to compare with our modelling
results.
We have six stars in common with Lucas et al. (1992) (RX Boo,
R Cas, W Hya, R Leo, WX Psc, IK Tau). Figure 4 shows the
intensity radii as a function of the density measure
,
using our derived mass-loss rates, gas expansion velocities, and
distances. The minimum least-square correlation between these intensity
radii and the density measure is
![]() |
Figure 4:
The sizes of the SiO envelopes estimated from the
SiO line modelling are plotted versus a density measure (open circles).
The dashed line gives
the relation between the SiO envelope size and the density measure
given in Eq. (13). Half intensity radii derived from interferometric
SiO(J=2
![]() |
Open with DEXTER |
Thus, the scaling with the density measure of the intensity radii
is in perfect agreement with our modelling result for the
envelope sizes. The estimated SiO envelope sizes that are required to model the
data are about three times larger than the SiO(J=2
1)
brightness region. This may at first seem somewhat surprising, but a test
using the 10
yr-1 model star of
Sect. 4.4, which has an SiO envelope radius of 1
7,
shows that the resulting SiO(J=2
1) brightness
distribution has a half-intensity radius of 0
4, i.e., about
four times smaller.
The radiative transfer analysis produces model brightness
distributions. These are convolved with the appropriate beams to allow
a direct comparison with the observed velocity-integrated line
intensities and to search for the best fit model. As observational constraints
we have used the data presented in this paper and the high-frequency data
obtained by Bieging et al. (2000). With the assumptions
made in the standard circumstellar model and the mass-loss rate and dust
properties derived from the modelling of circumstellar CO emission,
there remains only one free parameter, the SiO abundance (for all
stars
is taken from Eq. (13)). The SiO abundance was
allowed to vary in steps of
10% until the best-fit model was
found. The quality of a particular model with respect to the
observational constraints can be quantified using the chi-square
statistic,
Table 4: Source parameters and SiO model results.
We will here try to estimate the uncertainty in the derived SiO abundances. The uncertainties due to the adopted circumstellar model
are ignored since these are very difficult to estimate, and
focus is put on those introduced by the adopted parameters (see
Sect. 4.4). We start by considering the IRV/SRVs. The
results depend crucially on the validity of Eq. (13). A
change by -50% and +100% in the size of the SiO envelope results
in a variation of the J=2
1 line intensity by about
50%, and therefore an equal uncertainty in the abundance. The
product of
and
is essentially constant for a
best fit model. It is estimated that the mass-loss rate is uncertain
by at least a factor of two (due to the modelling). An uncertainty in
the distance has only a minor effect on the abundance (the change in
mass-loss rate compensates for the change in distance). The
dependence on the luminosity is moderate. We therefore estimate that,
within the adopted circumstellar model, the derived SiO abundances are
uncertain by at least a factor of three for those sources with
multi-line observations. The uncertainty increases to a factor of
five when only one transition is observed.
For the high mass-loss rate (i.e.,
yr-1) Miras the situation is even
worse. The radiation from these stars are significantly converted
into longer-wavelength dust radiation, which has been taken care of
only crudely by using two central blackbodies. Tests show that the
resulting SiO line intensities are sensitive to the structure of the
radiation sources, Sect. 4.4. In addition, the SiO lines are rather saturated and hence the line intensities are, at
least partly, insensitive to the abundance. Therefore, it is
estimated that for these objects the SiO abundance is uncertain
by a factor of five (in all cases information on three, or more, lines is
available), but note that any reasonable change in the
radiation field structure will systematically lower the abundance
required to fit the data.
![]() |
Figure 5:
SiO fractional abundances versus the mass-loss rate
(IRV: square, SRV: circle, Mira: triangle). The horizontal line marks
the maximum abundance allowed by solar abundances. The dashed line
shows the expected ![]() ![]() |
Open with DEXTER |
It can be assumed that the stars in our samples have silicon abundances close
to the solar value,
(Anders & Grevesse 1989). If Si is fully associated with O as SiO, and all H
is in H2, the maximum SiO fractional abundance is
.
Detailed calculations on stellar atmosphere
equilibrium chemistry give abundances in the vicinity of this for M-stars,
about
(Duari et al. 1999). Duari et al.
also show that the SiO abundance is not affected by atmospheric shocks in the
case of M-stars.
The derived SiO abundances are given in Table 4.
The distribution for the IRV/SRV sample has a median value of
,
and a minimum of
and a maximum
of
.
For the IRVs and SRVs the median results are
and
,
respectively. This is
almost a factor of ten lower than expected from theory.
Figure 5 shows the SiO abundance as a function of
the mass-loss rate. In addition to the abundances being low, there
is also a trend in the sense that both the upper and the lower "envelope''
of the abundances decrease with increasing mass-loss rate.
![]() |
Figure 6: Comparison of observed CO (upper) and SiO (lower) line profiles (in histogram form) for R Dor (left) and R Hya (middle) and GX Mon (right). The corresponding best-fit (i.e., to all observed line intensities) model SiO lines are also shown as solid lines. |
Open with DEXTER |
The low mass-loss rate Miras follow the trend of the IRV/SRVs,
and for the high mass-loss rate (
yr-1)
Miras we find a substantially lower abundance, a median below 10-6.
Thus, the inclusion of the Miras shows that the trend of
decreasing SiO abundance with increasing mass-loss rate continues
towards high mass-loss rates. This is further discussed in
Sect. 8 where an interpretation in terms of increased
adsorption of SiO onto dust grains the higher the mass-loss rate is
advocated.
The spread in abundance, at a given mass-loss rate, is
substantial, but it is within the (considerable) uncertainties, except
possibly for the high mass-loss rate Miras, for which there seem
to be a division into a low
abundance group (on average
)
and a high abundance
group (on average
), while. This division into two
well-separated groups is
peculiar, but within the circumstellar model used here this conclusion
appears inescapable. One can argue that the modelling of the high
mass-loss rate Mira SiO line emission is particularly difficult, but we
find no reason why errors in the model should affect stars with essentially
similar properties (L,
,
)
so differently.
The observed SiO line profiles are used in the modelling to derive the gas expansion velocities in the regions of the CSEs where the observed SiO line emission stems from. A comparison of these values with the gas expansion velocities derived from the modelling of circumstellar CO line emission is indeed a direct probe of the CSE dynamics since the extents of the SiO and CO line emitting regions are very different.
The SiO and CO radio line profiles are clearly different, although this conclusion is mainly based on the limited number of sources where the S/N-ratio of the data are high enough for both species. In Table 4 different values for the gas expansion velocity estimated from the SiO and the CO data are reported in the 11 cases where these are regarded as significantly different. In all cases the SiO velocities are smaller than those obtained from the CO data. Indeed, the SiO line profiles are narrower in the sense that the main fraction of the emission comes from a velocity range narrower than twice the expansion velocity determined from the CO data. On the other hand, the SiO line profiles have weak wings so that the total velocity width of its emission is very similar to that of the CO emission. This is illustrated in Fig. 6, where we also show the corresponding best-fit (i.e., to all observed line intensities) model SiO lines. It is clear that the model line profiles do not provide perfect fits to the observed line profiles, but they show that for the lower mass-loss rate objects the SiO line profiles are strongly affected by selfabsorption on the blue-shifted side. This explain partly why the SiO lines are narrower than the CO lines. The remaining discrepancy is interpreted as due to the influence of gas acceleration in the region which produces a significant fraction of the SiO line emission, as suggested already by Bujarrabal et al. (1986). This interpretation is quantitatively corroborated by our modelling results when a velocity gradient is included, see Sect. 4.4. The extent of the effect is though uncertain. Bieging et al. (2000), by comparing high-J SiO lines with CO line data, concluded that the SiO lines are formed predominantly in the part of the CSE where the gas velocity exceeds 90% of the terminal velocity. We suspect that the discrepancy between the widths of the SiO and CO lines decreases with the mass-loss rate of the object. In addition, we find that for at least some of the high-mass-loss-rate sources the higher-J SiO lines become essentially triangular, see GX Mon in Fig. 6. The model does a fairly good job in reproducing these SiO line profiles, except that the model lines are less sharply peaked. A high sensitivity, multi-line study combined with interferometric observations are required to fully tackle this problem.
In this connection we also present Fig. 7 which shows the
gas expansion velocity (determined from CO line modelling) as a function of mass
loss rate for the IRV/SRV and Mira samples. This is an extension of
the result of Olofsson et al. (2002), and it shows that
low to intermediate mass-loss rate winds have a scaling of
,
and that this gradually goes over into a wind
of close to 20 km s-1, for higher mass-loss rates. This is as
expected for a dust-driven wind (Elitzur & Ivezic 2001).
![]() |
Figure 7: The derived CO gas expansion velocities as a function of the mass-loss rates for the IRV (squares), SRV (circles), and Mira (triangles) samples. The dashed line shows the correlation found for the IRV/SRV sample (see text). |
Open with DEXTER |
To single out peculiar sources is a highly subjective process, and it also depends strongly on the S/N-ratio of the data (at high enough S/N-ratio probably most sources show a deviation from the expected). Here, a few sources in the IRV/SRV sample which qualify as peculiar or for which we have problems in the SiO line modelling are discussed.
Kerschbaum & Olofsson (1999) found four objects in their
sample of circumstellar CO radio line emission, which clearly show
double-component line profiles, a narrow feature centred on a broad plateau
(EP Aqr, RV Boo, X Her, and SV Psc), all of them SRVs.
Olofsson et al. (2002) determined mass-loss rates and gas expansion
velocities by simply decomposing the emission into two components and
assuming that the emissions are additive. They found that the mass
loss rates are higher for the broader component by, on average, an
order of magnitude. The gas expansion velocities derived from the
narrow components (1.5 km s-1) put to question an
interpretation in the form of a spherical outflow. The origin of such
a line profile is still not clear (see
Olofsson et al. 2002 for a discussion on this issue). These four sources
are also included in our SiO sample, and the spectra are shown in
Figs. B.2 and B.3.
Towards EP Aqr there is no sign of the narrow feature in the
SiO J=2
1 and J=3
2 lines, only the broad
feature is clearly present. This suggests that the broad feature
originates in a "normal'' CSE, while the narrow feature may have a
different origin. We note though that the SiO line profile of the
broad component deviates somewhat from a smooth symmetric profile.
SV Psc is very similar to EP Aqr in CO in the sense
that the narrow feature is very much narrower than the broad feature.
Unfortunately, the SV Psc SiO data are of low quality, but
both components appear to be present. In the cases of RV Boo
and X Her the CO and SiO line profiles are very similar, and
the widths of the narrow components are about half of those of the
broad ones. The SiO abundances of both components have been obtained,
assuming that the emissions are additive. The results are given in
Table 5. For all sources, and for both
components, the results appear normal.
![]() |
Figure 8:
L2 Pup SiO line spectra and a CO(J=3
![]() |
Open with DEXTER |
Table 5: Source parameters and model results for those objects with double component line profiles.
L2 Pup was singled out in
Olofsson et al. (2002) as a low mass-loss rate
(
yr-1), low gas expansion
velocity (2.1 km s-1) object. This star has been recently
discussed also by Jura et al. (2002) and
Winters et al. (2002). In the latter paper comparisons are made with wind
models, and it is concluded that stars with the mass-loss properties
of L2 Pup can be understood in terms of a pulsationally
driven wind, where dust plays no dynamic role. Our SiO line profiles
resemble to some extent those of CO in the sense that the narrow
feature is also present. However, the SiO lines clearly show broad
line wings, Fig. 8. The full
velocity width of these lines are
12 km s-1, i.e.,
larger than the CO line width, but narrower than the
SiO(v=1, J=2
1) maser line width of
20 km s-1 measured by
Winters et al. (2002). In addition, the narrow feature, which appears
narrower in the SiO lines than in the CO lines (Fig. 8),
is not exactly centered on the broad component, its center lies at
km s-1 as opposed to 51.4 km s-1 for the latter.
This suggests a rather complicated dynamics in the
inner part of the CSE, but high-quality data, also in higher-J SiO lines, are required before progress can be made.
W Hya is one of the sources for which we have the highest
quality data. It is also one of the sources with the poorest best-fit model.
A much better fit is obtained by increasing the size of the SiO envelope to
cm (and
as determined from the high-J lines), i.e.,
almost a factor of three higher than that obtained from Eq. (13).
Considering the uncertainties this is of no major concern. However,
it is worth recalling that Olofsson et al. (2002)
derived a (molecular hydrogen) mass-loss rate of
yr-1 from CO data (this result
has been confirmed by including CO J=1
0 and 2
1
IRAM 30 m data
(Bujarrabal et al. 1989; Cernicharo et al. 1997), CO J=2
1,
3
2, and 4
3 JCMT archive data, and the CO ISO results
of Barlow et al. 1996), while Zubko & Elitzur (2000) required a
much higher mass-loss rate,
yr-1 (at the larger distance 115 pc) to explain the ISO H2O data. We have found that such a
high mass-loss rate produces CO radio lines that are at least a factor
of 30 too strong. However, the ISO CO J=16
15 and J=17
16 lines are only about a factor of two too strong.
Hence, there is some considerable uncertainty in the properties of
this CSE. A fit to the SiO line data using the larger distance and
mass-loss rate is as bad as that for the low distance and mass-loss
rate.
In the case of R Dor Olofsson et al. (2002) could not fit well the CO radio line profiles. The model profiles were sharply double-peaked, while the observed ones were smoothly rounded. We merely note here that there was no problem to fit the SiO line profiles with the nominal values for R Dor.
An extensive radiative transfer analysis of circumstellar SiO "thermal'' radio line emission from a large sample of M-type AGB variable stars have been performed, partly based on a new, large, observational data base. It is concluded that, at this stage, the modelling of the circumstellar SiO radio line emission is considerably more uncertain than that of the CO radio line emission. Partly because the SiO line emission predominantly comes from the inner regions where the observational constraints are poor, but also partly because the behaviour of the SiO molecule is more complex, e.g., adsorption onto grains. A rather detailed sensitivity analysis has been done, in order to estimate the reliability of the derived results.
In particular, the size of the SiO envelope is crucial to the
modelling. Multi-line SiO modelling of eleven sources were used to
establish a relation between the size of the SiO envelope and the
density measure
.
This is of course rather
uncertain, both in the absolute scale and in the dependence on the
density measure. Comparison with estimates based on rather simple
condensation and photodissociation theories suggests that the derived
relation is not unreasonable. A very good agreement with the photodissociation
radii is obtained for an unshilded photodissociation rate of
2.5
10-10 s-1. It was also checked against
interferometeric SiO line brightness size estimates of six sources.
The SiO abundance distribution of the IRV/SRV
sample has a median value of
,
and a minimum of
and a maximum of
.
For these,
low to intermediate mass-loss rate objects, we expect the abundances
to be representative for the region inside the SiO photodissociation
radius. This applies also to the low and intermediate mass-loss rate Miras. The
high mass-loss rate Miras have a median abundance which is more than a
factor of six lower than that of the IRV/SRV sample. The
derived SiO abundances are in all cases (within the uncertainties)
below the abundance expected
from stellar atmosphere chemistry (
,
Duari et al. 1999), the median for the total sample is down by a factor
of ten. We regard this as a safe result, and interpret it in terms
of SiO adsorption onto grains, which is efficient already at low mass-loss
rates.
In addition, there is a trend of decrasing SiO abundance with
increasing mass-loss rate, Fig. 5. Here, we
cannot entirely exclude systematic effects of the modelling. In
particular, the adopted SiO envelope size relation can introduce such
effects. E.g., smaller envelopes at low mass-loss rates, as indicated
by the photodissociation model, would increase the estimated
abundances for these objects. This will actually strenghten the
observed trend. There is no obvious reason for a similar envelope
size decrease for the high mass-loss rate objects (however, see
below), but if present it would lead to a less pronounced trend. The
discussion in Sect. 4.4 on the sensitivity on the
radiation field distribution suggests that the abundance estimates for
the high mass-loss rate objects are upper limits. Therefore,
considering also that the effect is rather large, we regard the trend
as at least tentative. An interpretation in terms of increased
adsorption of SiO onto grains with increasing mass-loss rate is
natural. In Fig. 5 a depletion curve based on
the results in Sect. 6.1 is plotted, and it represents
well the general trend (the adopted parameters are
= 2500 K, L = 4000
,
= 10 km s-1,
= 0.002,
= 0.05
m,
= 2 g cm-3,
= 0.03,
= 29 500 K, and
= 1).
We emphasize once again how sensitive the theoretical condensation
results are to the adopted parameters, and the depletion curve can
easily be made to fit better the estimated abundances.
For the high mass-loss rate Miras the SiO abundance distribution appears
bimodal, a low
abundance group (on average
)
and a high abundance
group (on average
).
At this point we cannot identify any reason for this. The stars
and their CSEs are rather similar and there is no reason to expect the
modelling to artificially produce very different results for rather
similar objects, but the SiO line modelling of these objects are
particularly difficult as discussed above. The high values can be
explained if there is a
process which decreases the condensation onto, or leads to effective
evaporation from, dust grains for some objects. The former is
possible if the dust-to-gas mass ratio is low. If, on the other hand,
the dust-to-gas mass ratio is high, the region contributing to the SiO
line emission may be much smaller than used in our modelling, and
hence the SiO abundance is underestimated. This may be the case for the low
abundance objects. Substantial mass-loss rate variations with time may
of course lead to surprising results. This can possibly be checked by
high angular resolution observations of both CO and SiO radio line emission.
It is also interesting that Woods et al. (2003) found, in a
sample of high mass-loss rate C-stars, that the SiO abundance is one
of the few of their abundance estimates that vary significantly from
star to star. We note, though, that for the C-stars the estimated SiO
abundances are low, about
,
and that
Willacy & Cherchneff (1998) have shown that for C-stars shock
chemistry may significantly alter the SiO abundance. The same is not
the case for the O-rich chemistry according to
Duari et al. (1999), but grains are not included in their analysis.
The SiO and CO radio line profiles differ in shape. For those stars with high enough S/N-ratio data on both species, it is clear that the dominating parts of the SiO profiles are narrower than the CO profiles, but the former have low-intensity wings which cover the full velocity range of the CO profile. The effect is more evident in high-J lines, and less evident in high mass-loss rate objects. This is interpreted (as has been done also by others) as due to the influence of gas acceleration in the region which produces most of the SiO line emission. This points to a weakness in our analysis. Clearly, this acceleration region must be treated more carefully in the radiative modelling, but this is also the region where condensation occurs, a process which is difficult to describe in detail.
These results strongly suggest that SiO radio line emission can be
used as a sensitive probe of circumstellar dust formation and
dynamics. However, considerable progress in this area can only be
expected from a combination of high-quality SiO multi-line
observations, high-quality interferometric observations of a number of
SiO lines for a representative sample of sources, a detailed radiative
transfer analysis, which includes also the dust radiation, and a
detailed SiO chemical model. The rather high values of some
of our best-fit
models suggest that our circumstellar model needs to be improved.
Olofsson et al. (2002) identified a number of sources with peculiar CO line profiles, essentially consisting of a narrow feature centered on a (much) broader feature. These have been discussed here from the point of view of their SiO line properties. Except in one case, the SiO and CO line profiles are rather similar, and the derived SiO abundances are in no case peculiar. The low gas expansion velocity source L2 Pup has a very narrow SiO line profile as expected, but also a considerably broader, low-intensity component. Finally, W Hya imposes a problem for the SiO line modelling. In principle, a much larger SiO envelope than warranted by the mass-loss rate derived from the CO data is required to fit well the (high-quality) SiO data. This, in combination with other data, suggest that the CSE of this star is not normal, possibly as an effect of time-variable mass loss.
Acknowledgements
Financial support from the Swedish Science Research Council is gratefully acknowledged by DGD, FLS, ML, and HO. FK's work was supported by APART (Austrian Programme for Advanced Research and Technology) from the Austrian Academy of Sciences and by the Austrian Science Fund Project P14365-PHY. FLS further acknowledges support from the Netherlands Organization for Scientific Research (NWO) grant 614.041.004.
Table A.1: Observational results of circumstellar SiO radio line emission towards a sample of M-type IRVs and SRVs (Part 1).
Table A.2: Observational results of circumstellar SiO radio line emission towards a sample of M-type IRVs and SRVs (Part 2).
Table A.3: Observational results of circumstellar CO and SiO line emission towards our Mira sample.