A&A 367, 189-198 (2001)
DOI: 10.1051/0004-6361:20000411
S. Lorenz-Martins1 - F. X. de Araújo2 - S. J. Codina Landaberry2 - W. G. de Almeida2 - R. V. de Nader1
1 - Observatorio do Valongo/UFRJ,
Ladeira Pedro Antonio 43,
20080-090, Rio de Janeiro, Brazil
2 -
Observatorio Nacional/MCT,
Rua Gal. Jose Cristino 77,
20921-400, Rio de Janeiro, Brazil
Received 4 August 2000 / Accepted 9 November 2000
Abstract
A set of 45 dust envelopes of carbon stars has been modeled. Among them, 34
were selected according to their dust envelope class (as suggested by Sloan
et al. 1998) and 11 are extreme carbon stars. The models were
performed using a code that describes the radiative transfer in dust envelopes
considering core/mantle grains composed by an -SiC core and an
amorphous carbon (A.C.) mantle. In addition, we have also computed models with
a code that considers two kinds of grains -
-SiC and A.C. -
simultaneously. Core-mantle grains seem to fit dust envelopes of evolved carbon
stars, while two homogeneous grains are more able to reproduce thinner dust
envelopes. Our results suggest that there exists an evolution of dust grains in
the carbon star sequence. In the beginning of the sequence, grains are mainly
composed of SiC and amorphous carbon; with dust envelope evolution, carbon
grains are coated in SiC. This phenomena could perhaps explain the small
quantity of SiC grains observed in the interstellar medium. However, in
this work we consider only
-SiC grains, and the inclusion of
-SiC
grains can perhaps change some of these results.
Key words: stars: carbon - circumstellar matter - radiative transfer
Asymptotic giant branch (AGB) stars are often surrounded by circumstellar dust
shells. The chemical composition of these media reflects that of the stellar
photosphere. Thus, carbon-rich grains, such as amorphous carbon (A.C.),
are one of the expected components of the dust envelopes around carbon
stars. In addition, almost all these stars show an emission feature around
11.3 m due to Silicon carbide (SiC) grains which are also condensed there.
The existence of SiC grains in the atmospheres of carbon stars was predicted at
first on the basis of chemical equilibrium calculations by Gilman (1969).
This prediction was supported by the observations of Hackwell (1972), Treffers
& Cohen (1974) and Forrest et al. (1975). Nowadays infrared satellites provide
several characteristic features of these grains.
After the observations with IRAS satellite, several works have dealt with the
classification of dust envelopes around carbon stars. Little-Marenin
et al. (1987) have discovered 176 new carbon stars using the feature at
11.3 m as a selection factor. Willems (1987) has analyzed 304 such
objects, suggesting a SiC-index to the stars which present the emission feature
varying between 11.2-11.6
m. Papoular (1988) has classified carbon dust
envelopes using the 11.3
m feature and a secondary feature at 8.6
m.
The sample of Chan & Kwok (1990) was composed of 356 objects which were
classified in two distinct classes. According to the authors, the difference
between the classes is due to an evolution of
-SiC and
-SiC particles. More recently Sloan et al. (1998,
hereafter SLMP) proposed a classification of 89 carbon-rich stars in 6
different types based on their infrared emissions. All stars of their sample
show the SiC feature at 11.3
m.
In general, differences between each class can be interpreted as an evolution of the dust envelope itself due to an increasing amount of grains; consequently, optical depth also increases, affecting radiative transfer and the emission feature. On the other hand, the resonance features of small SiC grains are very sensitive to size, morphology and chemical composition of impurities in the surrounding medium (Bohen & Huffman 1998). This fact suggests that the variety of emission features assigned to SiC grains is probably related to the formation process of the dust in circumstellar envelopes, reflecting the physical and chemical conditions. The classification criteria cited above are useful, but if one is interested in a deeper insight into the nature of the circumstellar dust grains, it is necessary to solve the radiative transfer problem, and to reproduce the features seen in the mid-IR LRS together with the overall behavior of the spectral energy distribution.
Several authors have calculated the radiative transfer in circumstellar dust
shells (CDS) of carbon stars (Chan & Kwok 1990; Lorenz-Martins & Lefèvre
1993, 1994; Groenewegen 1995; Bagnulo, 1996; Bagnulo et al. 1998).
Lorenz-Martins & Lefèvre (1994) have employed the Monte Carlo method for
solving the radiative transfer for two species simultaneously. SiC grains were
supposed to form closer to the star than graphite grains (McCabe 1982).
Correlations between SiC/A.C. ratio and extinction opacity as well as
SiC/A.C. ratio and period of luminosity were found. These correlations indicate
that the quantity of SiC grains relative to amorphous carbon grains decreases
with carbon star evolution. Mass loss from cool stars is the
major source of refractory grains in the interstellar medium. Carbon stars
provide carboneous material and extreme carbon stars, with their large mass-loss
rate, are the main contributors. A study by Whittet et al. (1990) shows that
there is a low fraction (<5%) of Si in the form of SiC in the interstellar
medium. The enrichment rate for a kind of grain depends on the composition of
the dust envelopes of stars which have high mass-loss rate. Lorenz-Martins &
Lefèvre (1994) also suggested that SiC grains are the minor component in
carbon star envelopes. In addition, stars which have low SiC/A.C. ratios
(0.01-0.06) have also high mass-loss rates (1.5 10-4 - IRC+10216 --
6.1 10-6
yr - IRAS 15194-5115). These results can
perhaps explain the small quantity of SiC grains in the interstellar medium.
Alternatively, the weakness of the SiC absorption could be due to the fact that
SiC particles are embedded in thick carbon mantles. In fact, Kozasa et al.
(1996) have shown that the nucleation of SiC precedes that of carbon grains and
may lead to the formation of dust grains consisting of a SiC core and a carbon
mantle. Moreover they proposed that such core/mantle grains are the most
reasonable candidates to reproduce the feature seen around 11.3
m. They also
suggested that radiative transfer calculations should be used in order to verify
this model.
The main purpose of the present work is to present dust envelope models
considering core/mantle grains composed by an -SiC core and
an A.C. mantle. We also compare the data with models consisting of
-SiC
and A.C. homogeneous grains. Two samples of stars have been
considered. The first one contains objects classified by SLMP. They were
analyzed aiming to verify the classification proposed by the authors. The
second sample contains 11 extreme carbon stars, which have thicker dust
envelopes and a higher mass loss rate. The utilization of core/mantle
grains is satisfactory to describe some stars but most of them are better
reproduced using a two homogeneous grains model.
Besides carbon grains of different structures (e.g., graphite, amorphous carbon), SiC is the most important species for late-type carbon stars. SiC is one of the most refractory materials that may condense under the conditions of a carbon-rich chemistry. In such stars, almost all oxygen is chemically blocked in the CO molecule and, among the more abundant chemically active elements, carbon and SiC are the possible condensates. An important problem in the formation of SiC under the conditions present in circumstellar shells is that the abundance of SiC molecule is quite low. Beck (1992) has considered non-equilibrium effects and has shown that solid SiC can be stable against evaporation at temperatures below 1400 K. He also suggested that SiC may form on the surface of preexisting carbon grains instead of being the primary condensate at very high temperatures. On the other hand, McCabe (1982) has shown that SiC particles can be formed at high temperatures due to the greenhouse effect. Following this suggestion, Kozasa et al. (1996) have demonstrated that the nucleation of SiC grains always precedes that of carbon grains when the non-LTE effect, i.e., the difference between the temperature of gas and small clusters, is taken into account.
We have considered this latest suggestion and modeled 45 envelopes of carbon
stars using core/mantle grains consisting of a -SiC core
and a A.C. mantle. The method employed is an improved version of that described
by Lorenz-Martins & Araújo (1997). We have modified the code to include a
new option about grain properties. The absorption and scattering efficiencies,
as well as the albedo, were calculated using the Mie theory for core/mantle
grains (e.g. Bohren & Huffman 1984; Hoyle & Wickramasinghe 1991) and optical
constants (or dielectric functions) tabulated in the literature. The optical
constants which we have used are the ones determined by Pegourié (1988) for
-SiC, and by Rouleau & Martin (1991) for amorphous carbon.
The propagation of stellar and grain radiative energy is simulated photon by photon following a Monte Carlo scheme. For each interaction between a "photon'' and a grain, a fraction of the energy is stored (absorption) and the remaining part is scattered according to the scattering diagram. The stellar radiation leads to an initial distribution of dust temperature and the thermal radiation from grains is simulated, giving after several iterations the equilibrium temperature. Computations give the spectral repartition of the total flux and of its different components (direct, scattered, emitted), and the temperature law for the grains. For more details see Lorenz-Martins & Lefèvre (1993, 1994) and Lorenz-Martins & Araújo (1997).
IRAS | Name | Sp.Type | Var. | Period | Env.classi | Phot. |
00172+4425 | VX And | C4,5J | SRa | 369a | SiC++ | 9 |
01246-3248 | R Scl | C6,5 | SRb | 370a | SiC++ | 1, 7 |
02270-2619 | R For | C4,3e | Mira | 388c | SiC | 8 |
03075+5742 | C* 131 | C4,5J | Lb | -- | N: | 9 |
03374+6229 | U Cam | C6,4 | SRb | -- | SiC+ | 9 |
04459+6804 | ST Cam | C5,4 | SRb | 300a | SiC+: | 9 |
04483+2826 | TT Tau | C7,4 | SRb | 166a | SiC+: | 9 |
04573-1452 | R Lep | C7,4e | Mira | 427a | SiC | 2, 8 |
05028+0106 | W Ori | C5,4 | SRb | 212a | SiC+ | 2, 9 |
05418-4628 | W Pic | C | Lb | -- | SiC++: | 7 |
05426+2040 | Y Tau | C6,4 | SRb | 241a | SiC | 7 |
05576+3940 | AZ Aur | C8 | Mira | 416a | Br2 | 9 |
06225+1445 | BL Ori | C6,3 | Lb | -- | Br2 | 3, 9 |
06331+3829 | UU Aur | C7,4 | SRb | 23a | SiC | 2, 9 |
06529+0626 | CL Mon | C6,3e | Mira | 497a | SiC | 9 |
07045-0728 | RY Mon | C5,5 | SRa | 278a | SiC+ | 9, 12 |
07057-1150 | W CMa | C6,3 | Lb | -- | SiC+: | 7, 9 |
07065-7256 | R Vol | Ce | Mira | 454a | SiC | 5 |
08538+2002 | T Cnc | C5,5 | SRb | 482a | SiC++ | 2, 3 |
09452+1330 | IRC+10216 | C9,4 | Mira | 649c | Red | 11 |
10329-3918 | U Ant | C5,3 | Lb | -- | SiC+: | 7 |
10350-1307 | U Hya | C5,3 | Lb | -- | SiC | 2, 5, 9 |
10491-2059 | V Hya | C6,5 | SRa | 531a | Red | 2, 5, 9 |
12226+0102 | SS Vir | C6,3 | SRa | 364a | Br1 | 9 |
12427+4542 | Y CVn | C5,5J | SRb | 158a | SiC+: | 2, 9, 11 |
12447+0425 | RU Vir | C8,1e | Mira | 433a | SiC | 5 |
12544+6615 | RY Dra | C4,5J | SRb | 200a | SiC+ | 2, 9 |
15094-6953 | X TrA | C5,5 | Lb | -- | SiC+ | 5, 11, 12 |
18306+3657 | T Lyr | C6,5J | Lb | -- | SiC++ | 9 |
19017-0545 | V Aql | C6,4 | SRb | 353a | SiC+ | 5, 9 |
19555+4407 | AX Cyg | C4,5 | Lb | -- | SiC+: | 9 |
21032-0024 | RV Aqr | C6,3e | Mira | 454a | SiC | 5 |
21399+3516 | V460Cyg | C6,4 | SRb | 263a | SiC+: | 2, 9 |
23587+6004 | WZ Cas | C9,2J | SRb | 186a | Br1 | 3, 10 |
SLMP have studied 89 carbon-rich stars and organized the dust emission in
several classes. Red class contains only 3 stars which present a
11.3 m feature and a strong dust continuum. SiC class is the most
numerous, with 40 objects. They have the 11.3
m feature and a weak dust
continuum. In the SiC+ they put 32 stars which show two features: the
11.3
m one and a weak feature at 8-9
m. These objects also have a
weak dust continuum. The SiC++ class contains 6 stars with comparable
11.3
m and 8-9
m features. The five stars in the Broad 1 class
have an unusual 11.3
m feature profile with short-wavelength excess.
Finally, the Broad 2 class contains only 3 stars which present an unusual
11.3
m feature profile with long-wavelength excess.
In Table 1 we present our sample of 34 stars taken from SLMP. We restrict our
study to the objects with IR fluxes published in the literature. Fortunately, we
have been able to obtain data from stars belonging to all different classes.
Table 1 lists the IRAS number (Col. 1) followed by the usual name (Col. 2).
Spectral type and variability class are listed in Cols. 3 and 4 respectively.
Column 5 gives the period and Col. 6 shows the envelope class attributed by
SLMP. Some stars have a doubtful classification; they are designated by a colon.
Finally the photometry used in the fit of the models is presented in the last
column. Table 2 list the extreme carbon stars sample. The columns are analogous
to those of Table 1. The stars analyzed are variables and self-consistent
models for them require data from similar phase of luminosity. However this is
difficult due to the scarcity of observations. We have worked with the
photometry available in the literature and considered the phase whenever
possible. In order to minimize the uncertainties, we have used average LRS
(IRAS, 1986) spectra for SiC emission. The 12, 25, 60, 100 m fluxes were
taken from Gezari et al. (1987) and SIMBAD.
Tables 3 and 4 present the results of the best models to our first and
second samples, respectively. These results were obtained considering a
core/mantle grain. IRAS number (Col. 1) is followed by the temperature
of the central star (
in K) in the second column. Third and fourth
columns present inner (R1 in
)
and outer (R2 in
)
envelope radii, respectively. The dimension of the
-SiC core
(
in Å) of the grains is given in the fifth column, followed by
the dimension of the amorphous carbon mantle (
in Å) in the
sixth column. Finally, the optical depth (
)
at 1
m and the abundance
ratio between
-SiC and amorphous carbon grains are given, respectively,
in Cols. 7 and 8. In Table 3 we have added one last column with the SLMP's
envelope classes.
IRAS | Name | Sp.Type | Period | Phot. |
05377+1346 | AFGL 799 | C8,4 | 372c | 1,4 |
05405+3240 | AFGL 809 | C | 780b | 5 |
06012+0726 | AFGL 865 | ? | 696c | 6 |
06291+4319 | AFGL 954 | C | -- | 5 |
06342+0328 | AFGL 971 | C | 653c | 6 |
07098-2112 | AFGL 1085 | N | 725c | 6 |
08088-3243 | AFGL 1235 | C | 571c | 2 |
15082-4808 | AFGL 4211 | ? | -- | 3 |
19594+4047 | AFGL 2494 | C | 783b | 5 |
20570+2714 | AFGL 2686 | C8,5 | 750b | 5 |
23257+1038 | AFGL 3099 | C | 484c | 5 |
In addition, we have calculated models for the stars in the sample using a code
with two homogeneous grains. Some stars of this sample were analyzed in
Lorenz-Martins & Lefèvre (1994), where the authors describe the method. The
differences between parameters of both codes are the size of the grains and the
way in which the SiC/A.C. ratios were calculated. In the core/mantle models, we
consider the core (
)
and mantle (
)
size. SiC/A.C.
ratios in this method are obtained by mass, based on the mantle and core size,
and we find the corresponding value as obtained in the two homogeneous grains
model. Others parameters are obtained the same way as in the two homogeneous
grains
code.
The features seen in the mid-IR LRS must be reproduced and the properties of
complete CDS must be determined simultaneously. In order to fit the dust
emission, we have calculated grids of about fifty models for each star, and we
inspect visually the model which best reproduces the complete CDS. We pay
special attention to the LRS feature and accept errors of about 15 per cent in
all parameters (such as grain size, effective temperature, optical depth...) to
fit this emission feature; in fact it is this feature that defines the best
model.
Stars |
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SiC/A.C. | Env. Class. |
00172+4425 | 2200 | 5.0 | 1000 | 453 | 1000 | 0.02 | 0.10 | SiC++ |
01246-3248 | 2400 | 5.0 | 1000 | 500 | 1200 | 0.10 | 0.08 | SiC++ |
02270-2619 | 2500 | 5.0 | 5000 | 407 | 1050 | 7.00 | 0.06 | SiC |
03075+5742 | 2400 | 5.0 | 800 | 453 | 1000 | 0.01 | 0.10 | N: |
03374+6229 | 2650 | 4.6 | 1000 | 500 | 1200 | 0.50 | 0.08 | SiC+ |
04459+6804 | 2700 | 4.8 | 1000 | 500 | 850 | 0.03 | 0.26 | SiC+: |
04483+2826 | 2650 | 3.0 | 1000 | 236 | 400 | 0.02 | 0.26 | SiC+: |
04573-1452 | 2250 | 5.0 | 1000 | 294 | 700 | 0.60 | 0.08 | SiC |
05028+0106 | 2650 | 5.2 | 1000 | 332 | 700 | 0.10 | 0.12 | SiC+ |
05418-4628 | 2400 | 5.0 | 1000 | 500 | 1200 | 0.10 | 0.08 | SiC++: |
05426+2040 | 2600 | 4.5 | 1000 | 554 | 1000 | 0.20 | 0.20 | SiC |
05576+3940 | 2200 | 4.6 | 1000 | 403 | 1000 | 1.20 | 0.07 | Br2 |
06225+1445 | 2700 | 4.9 | 1000 | 400 | 850 | 0.03 | 0.12 | Br2 |
06331+3829 | 2550 | 3.7 | 1000 | 340 | 700 | 0.10 | 0.13 | SiC |
06529+0626 | 2200 | 4.6 | 1000 | 282 | 700 | 1.00 | 0.07 | SiC |
07045-0728 | 2400 | 6.5 | 1000 | 270 | 500 | 0.10 | 0.18 | SiC+ |
07057-1150 | 2650 | 3.0 | 1000 | 440 | 740 | 0.04 | 0.27 | SiC+: |
07065-7256 | 2400 | 4.6 | 1000 | 282 | 700 | 2.20 | 0.07 | SiC |
08538+2002 | 2400 | 5.0 | 1000 | 400 | 1200 | 0.20 | 0.04 | SiC++ |
09452+1330 | 2100 | 5.5 | 8000 | 110 | 500 | 10.0 | 0.01 | Red |
10329-3918 | 2700 | 4.5 | 1000 | 390 | 850 | 0.04 | 0.11 | SiC+: |
10350-1307 | 2700 | 4.5 | 1000 | 468 | 850 | 0.03 | 0.20 | SiC |
10491-2059 | 2050 | 5.6 | 10 000 | 270 | 950 | 0.70 | 0.02 | Red |
12226+0102 | 2700 | 5.0 | 1000 | 487 | 1200 | 0.35 | 0.07 | Br1 |
12427+4542 | 2700 | 4.9 | 1000 | 317 | 700 | 0.05 | 0.10 | SiC+: |
12447+0425 | 2200 | 4.3 | 1000 | 307 | 700 | 2.50 | 0.09 | SiC |
12544+6615 | 2650 | 3.7 | 1000 | 155 | 400 | 0.04 | 0.06 | SiC+ |
15094-6953 | 2650 | 5.3 | 1000 | 416 | 700 | 0.03 | 0.26 | SiC+ |
18306+3657 | 2200 | 5.0 | 1000 | 317 | 700 | 0.03 | 0.10 | SiC++ |
19017-0545 | 2550 | 4.9 | 1000 | 315 | 800 | 0.10 | 0.07 | SiC+ |
19555+4407 | 2400 | 4.0 | 1000 | 761 | 1500 | 0.08 | 0.15 | SiC+: |
21032-0024 | 2200 | 4.5 | 1000 | 294 | 700 | 2.50 | 0.08 | SiC |
21399+3516 | 2800 | 4.0 | 10 000 | 500 | 1000 | 0.04 | 0.14 | SiC+: |
23587+6004 | 2500 | 3.0 | 800 | 554 | 1000 | 0.01 | 0.20 | Br1 |
SiC Class
We analyzed 9 out of 40 SLMP objects in this class. We found that
effective temperatures vary between 2200 K and 2700 K. Inner radii vary
between 3.7 R* and 5.0 R*, while most of the outer radii are 1000 R*. It
must be kept in mind that the results are not very sensitive to this last
parameter, as has been pointed out in previous works. The -SiC core
(
)
grains vary between 280 to 550 Å, and the amorphous carbon
mantle (
)
between 700 and 1050 Å. Optical depths for this
class vary between 0.10 and 2.5, with two exceptions: U Hya (
= 0.03)
and R for (
= 7.0). Finally SiC/A.C. ratios vary from 0.06 to
0.20. In Figs. 1a-d we show out fits to RV Aqr and Y Tau. Solid
lines represent the core/mantle grain model and dashed lines the two homogeneous
grains model. Figures 1b and 1d show an enlarged view centered on the
11.3
m feature. In all cases, best fits to this class were obtained using
the two homogeneous grains model.
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Figure 1:
Best models for SiC class. In Figs. 1a-d we plotted the
best
models using core/mantle grains (solid line) and two homogeneous grain model
(dashed line). Triangles represent the photometric data. In Figs. 1b and 1d we show an enlarged view of the 11.3 ![]() |
Open with DEXTER |
SiC+ Class
We have modeled 7 out 32 SLMP SiC+ stars. According to our results,
the temperatures of central stars vary from 2400 K to 2650 K. Outer dust
envelope radii are the same for all stars (
R*) and inner
radii vary between 3.7 R* and 6.5 R*. Sizes of mantle grains (
)
show a great dispersion: 400 Å to 1200 Å. The same occurs with
the sizes of
-SiC core (
)
which vary from 155 Å to 500
Å. Optical depths have values between 0.03 and 0.50, and SiC/A.C.
ratios between 0.06 and 0.26. Almost all stars were best described using the
two homogeneous grains model; the unique exception is V Aql, which is better
reproduced with a core/mantle grain code. Figure 2 shows best fits to RY
Mon and U Cam.
As a rule, we can say that the envelope of SiC and SiC+ stars are
nicely described by the existence of -SiC and A.C. homogeneous
grains simultaneously.
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Figure 2:
This figure shows the best models for RY Mon and U Cam, which are in
the SiC+ class. In Figs. 2a-d we plotted models using core/mantle
grain (solid line) and two homogeneous grain model (dashed line).
Triangles represent the photometric data. In Figs. 2b and 2d we show an
enlarged view of the 11.3 ![]() |
Open with DEXTER |
SiC++ Class
We analyzed 5 out of 6 SLMP objects. According to our models, effective
temperatures are either 2200 K or 2400 K. Almost all inner and outer radii have
the same values: R1 = 5 R* and
R2 = 1000 R*. Mantle sizes
(
)
vary between 700 and 1200 Å, and core sizes (
)
between 300 and 500 Å. Optical depths vary between 0.02 and 0.20,
which indicates very thin dust envelopes, and SiC/A.C. ratios between 0.04 and
0.10. Due to the absence of optical constants to describe the 8-9
m and
13
m features, it is difficult to choose between the core/mantle grain or
the two homogeneous grains model. We will discuss these results in the next
section. Figure 3 shows two stars of this class.
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Figure 3:
This figure shows best models for TCnc and R Scl, which are in
SiC++ class. In Figs. 3a-d we plotted models using core/mantle
grain (solid line) and two homogeneous grain model (dashed line).
Triangles represent the photometric data. In Figs. 3b and 3d we show an
enlarged view of the 11.3 ![]() |
Open with DEXTER |
Broad 1 and Broad 2 Classes
We have modeled 2 out 5 SLMP Broad 1, and 2 out 3 SLMP Broad 2
stars. Our results indicate very similar properties for both classes. The
temperatures of the central stars are in the range of 2200 K to 2700 K. Core and
mantle sizes vary between 400-500 Å and 850-1200 Å, respectively. They
have thin envelopes with analogous dimensions. SiC/A.C. ratios varying between
0.07 and 0.20 were found. We have obtained our best fits using a two homogeneous
grains code for 3 stars. WZ Cas presents an absorption at about 14 m, which
is usually seen in J-type carbon stars, and it's difficult to distinguish
between the models. SS Vir shows features at about 8
m and 14
m, too.
Figure 4 presents best fit models to SS Vir (Broad 1 class) and AZ Aur
(Broad 2 class).
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Figure 4:
This figure shows best models for SS Vir, which belongs to Broad
1 class and AZ Aur to Broad 2 class. In Figs. 4a-d we plotted
models using core/mantle grain (solid line) and two homogeneous
grain model (dashed line). Triangles represent the photometric data. In Figs.
4b and 4d we show an enlarged view of the 11.3 ![]() |
Open with DEXTER |
Red Class
We have modeled 2 out of 3 SLMP stars: IRC+10216 and V Hya. Both objects
are very well studied and supposed to have asymmetrical dust envelopes. They
are believed to be in the latest stages of stellar carbon evolution. We will
discuss them below.
(a) IRC+10216
IRC+10216 has been extensively observed at optical, radio and infrared
wavelengths. The central object is a long-period variable, with a period of
640 days, and it is commonly considered to be a late-type carbon star. Its
envelope has been continuously surveyed and 380 molecular lines were detected,
of which 317 have been identified (Cernicharo et al. 2000). Deep B
and V image-bands, reveal its extended circumstellar envelope in the dust
scattered
and show an episodic mass loss rate. The circumstellar envelope is roughly
spherically symmetrical but it is likely to be composed of a series of discrete,
incomplete, concentric shells (Mauron & Huggins 1999).
IRC+10216 was modeled by several authors. Michell & Robinson (1980)
have used graphite grains and radiative transfer calculations were
performed considering, as usual, a spherically symmetric envelope with a
central star. Rowan-Robinson & Harris (1983), Le Bertre (1987, 1988b),
Martin & Rogers (1987) and Griffin (1990) treated radiative transfer
in the envelope of this star in a similar way. Lorenz-Martins & Lefèvre
(1993, 1994) have modeled this star by considering a two homogeneous grain
model consisting of -SiC and amorphous carbon grains
simultaneously, as already cited. More recently, Groenewegen (1997) has computed
a spherically symmetrical dust model and suggested that IRC+10216 is in the
latest phases of carbon stars evolution, like V Hya.
The effective temperature of IRC+10216 is 2100 K and our results lead to an
extensive (
R* and
R*) but thick (
)
dust envelope. The size of the amorphous carbon mantle grains (
)
was 500 Å with an
-SiC core of 110 Å. Our best model was
obtained considering core/mantle grains as can be seen in Figs. 5a and 5b.
(b) V Hya
V Hya was classified as C6,5 by Yamashita (1972). It is a variable
star with overlapping periods: a period of about 530 days with amplitude
of about 1.5 mg and a longer period of 6500 days with amplitude of 3.5 mg. This
object is surrounded by an extended expanding molecular envelope, resulting from
extensive mass-loss. Mass-loss rate is in the range of 3.0-4.0 10-6
yr (Knapp & Morris 1985; Olofsson et al. 1990). Polarimetric
measures have been obtained by Johnson & Jones (1991) and more recently by
Trammell et al. (1994). Johnson & Jones (1991) have classified V Hya as a
proto-planetary nebula and measured
P(V) = 0.75%
0.02% at
=21
1
.
Trammell et al. (1994) have observed this object
in April 1992 and January 1993, and found that the polarization varied over this
interval. The envelope properties found from molecular line observations
by Knapp et al. (2000), like the fast molecular wind and the high mass loss
rate, suggest that V Hya has entered its "superwind'' phase. However, its
spectral type, period, colors, and lack of ionizing radiation indicate that this
star is still on the AGB. Then, V Hya is believed to be in the latest phases of
mass loss on the AGB.
Our results show that the temperature of the central star is 2050 K.
Contrary to what is expected for this evolved phase, we have found a thin
(
= 0.7) and extensive dust envelope (
R* and
R*). The size of the amorphous carbon mantle (
)
is 950
Å and the
-SiC core is 270 Å. SiC/A.C. ratio is very small,
0.02. The best fit can be seen in Figs. 5c and 5d. We can say that a
core/mantle grain model fits this star well, but a two homogeneous grain
model cannot be discarded.
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Figure 5:
This figure shows the best models for IRC+10216 and VHya which belong
to Red class. In Figs. 5a-d we plotted models using core/mantle
grain (solid line) and two homogeneous grain model (dashed line).
Triangles represent the photometric data. In Figs. 5b and 5d we show an
enlarged view of the 11.3 ![]() |
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![]() |
Figure 6: This figure shows best models for Y Cvn and W CMa which belong to SiC+: class. In Figs. 6a-b we plotted models using core/mantle grain (solid line) and two homogeneous grain model (dashed line). Triangles represent the photometric data |
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IRAS |
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SiC/AC | Env. Class |
05377+1346 | 2350 | 3.0 | 2000 | 282 | 700 | 3.0 | 0.07 | E1 |
05405+3240 | 2200 | 7.1 | 10 000 | 215 | 700 | 10.6 | 0.03 | E2 |
06012+0726 | 2000 | 4.5 | 4000 | 189 | 900 | 12.5 | 0.01 | E2 |
06291+4319 | 2300 | 6.5 | 1000 | 226 | 700 | 3.5 | 0.04 | E1 |
06342+0328 | 2500 | 4.0 | 7000 | 256 | 700 | 7.0 | 0.05 | E2 |
07098-2112 | 2450 | 6.5 | 1000 | 236 | 700 | 4.0 | 0.04 | E1 |
08088-3243 | 2300 | 6.4 | 1000 | 215 | 700 | 4.0 | 0.03 | E1 |
15082-4808 | 2050 | 4.6 | 1000 | 273 | 1000 | 9.4 | 0.02 | E2 |
19594+4047 | 2000 | 5.0 | 7000 | 232 | 800 | 13.0 | 0.025 | E2 |
20570+2714 | 2200 | 8.0 | 1000 | 156 | 500 | 5.2 | 0.03 | E1 |
23257+1038 | 1900 | 7.0 | 1000 | 254 | 700 | 13.0 | 0.05 | E2 |
SiC+: Stars
We analyzed 7 out 11 SLMP objects classified as SiC+:, where the
colon means a more uncertain classification. Almost all stars are well
reproduced by a core/mantle grain model. The only exception is AX Cyg, which
seems to need single particles of -SiC, amorphous carbon and core/mantle
grains simultaneously. The results obtained with the core/mantle grain code are
similar to those found for SiC+ class stars. The temperatures of the
central stars vary from 2400 K to 2800 K. Inner radii vary between 3 to 4.9
.
Carbon mantle sizes (
)
vary from 400 Å to 1500 Å
with core (
)
values between 236 Å and 761 Å. Optical depths are
lower: 0.02
0.08. On the other hand SiC/A.C. abundance
ratios vary from 0.10 to 0.27. (For these stars we could say that the
core/mantle grain models are more adequate, even with such small optical depths,
since the SiC/A.C. ratios are higher.) Figure 6 shows an enlarged view of the
two stars in this class, Y CVn and W CMa. We can see that the emission feature
is shifted to longer wavelengths. This is a result of Mie's theory applied to
core/mantle spheres. Suh (2000) has found a similar behavior in his models.
Except for one case (R For), all SiC classes of the SLMP sample contains
carbon stars which have thin dust envelopes (
2.5). Our sample of
extreme carbon stars contains objects that have optical depths varying between
3.0 and 13. In order to make our analysis easier, we have decided to separate
them according to this physical quantity: 3.0
5.2 (E1
group) and 7.0
13.0 (E2 group).
The stars belonging to our E1 group were better described by a two
homogeneous grains model. Temperatures of the central stars are between 2200 K
and 2450 K. Inner radii are about 6.5 R* and outer radii 1000 R* for all
stars. Core (
)
and mantle (
)
sizes are respectively
about 200 Å and 700 Å in almost all cases. The abundance ratios SiC/A.C.
vary from 0.03 and 0.07. These results can indicate that such stars are related
to the SiC SLMP class.
On the contrary, stars belonging to our E2 group were better fitted with the
core/mantle grain code and are similar to the stars in the Red
class. They are cooler (1900 K
2200 K) and present a
dust envelope more extensive than those of the E1 group. Core and mantle sizes
vary between 190 to 270 Å and 700 Å to 1000 Å, respectively. The
SiC/A.C. abundance ratios are also low, with values between 0.01 and 0.05. In
the E2 group, three stars were better represented by taking into account
-SiC, amorphous carbon and core/mantle grains simultaneously. We can
speculate that these three stars represent a transition phase between SiC
and Red classes. Figure 7 shows an enlarged view of AFGL 954 (E1 group)
and AFGL 809 (E2 group).
![]() |
Figure 7: This figure shows the best models for AFGL 954 and AFGL 809 which belong to E1 and E2 classes respectively. In Figs. 7a-b we plotted models using core/mantle grain (solid line) and two homogeneous grain model (dashed line). Triangles represent the photometric data |
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As commented in the previous section, the IR fluxes and the feature around
11.3 m present in most sources that we have analyzed, are likely to be
better reproduced using two homogeneous grains (A.C. and
-SiC)
simultaneously. This is true for SiC, SiC+ and our E1
stars. On the other hand, a few objects (those in Red and in our E2
class) are better described by a core/mantle grain model. However, the
SiC++ and Broad 1 classes cannot be reproduced with the existing
optical constants.
The SiC++ class presents both the 8-9
m emission and also a very
prominent 14
m absorption feature. The stars belonging to the Broad 1
class also show a 14
m absorption. This absorption feature is weaker in
Mira variables than in SR variables. This may be explained by a stronger dust
emission in Mira variables which fills the molecular absorption (see Yamamura
et al. 1998). Regarding the origin of the 8-9
m emission feature, Aoki
et al. (1999) have suggested that it may be a result of molecular
absorption at 7.5
m and SiC emission at 11.3
m. This absorption could
be due to HCN and/or C2H2 photospheric absorption bands. On the other
hand, the absorption feature at about 14
m was attributed by the same
authors to HCN and C2H2 absorption in the photosphere or in the warm
envelope close to the star. This absorption feature would be formed in the
inner envelope where the mid-infrared radiation originates. On the other hand,
Yamamura et al. (1998) have studied the 14
m absorption in the ISO SWS
spectra of 11 carbon stars with mass-loss ranging from 10
to 10
/yr. According to these authors, all stars clearly show an
absorption band at about 13.7
m due to C2H2 while the contribution
from HCN molecules is small in this region.
The stars of the SiC++ class have thin envelopes that can favor
the misidentification of spectral features like the 8-9 m one. On the other
hand, this feature is also observed in some dust-enshrouded carbon stars, such
as IRAS 15194-5115, IRAS 18239-0655 and IRAS 18240+2326. Consequently, this feature
could perhaps be produced by a solid component. Indeed, Goebel et al.
(1995) have suggested
:C-H, as described by Dischler et al.
(1983). Unfortunately, they have not published the set of optical
constants to this component. In order to try to reproduce the 8-9
m
emission, we have modeled SS Vir, considering optical constants of the amorphous
HAC as tabulated by Zubko (1996), but we have not been able to fit the emission.
Bagnulo et al. (1998) have shown that this feature can be reproduced
by a dust shell composed of a mixture of SiC grains and silicate grains. This
interpretation, however, does not seem to be consistent with the theory of dust
formation. Before discussing such results, let us comment now on some
alternatives that might be investigated.
On the basis of a simple model of circumstellar envelopes, Kozasa et al. (1996)
have proposed that the 11.3 m feature could be attributed to small spherical
core/mantle type grains (composed by a
-SiC core and a carbon mantle)
in most cases. In their calculations they have used optical constants for
SiC tabulated by Choyke & Palick (1985), which peak at about 10.7
m. In
fact, using this set of constants, the emission produced by a core/mantle grain
as proposed by them is about 11.3
m, and almost all sources of the SLMP
sample could be fitted using a core/mantle grain code. This is no longer true
when we use the constants proposed by Pégourié (1988), which peak at about
11.3
m. In this case, the emission is shifted to longer wavelengths, too.
We have computed our models considering the constants by Pégourié
(1988) because the full treatment consisting of the Kramers-Kronig analysis has
been taken into account.
Another possibility was raised by Speck et al. (1999): they have fitted
some carbon stars using -SiC grains. Silicon carbide grains can be
divided into two basic groups:
-SiC if the structure is one of the many
hexagonal or rhombohedral polytypes, and
-SiC if the structure is cubic.
-SiC feature occurs at about 0.4
m shortwards of that of
-SiC. Their results were obtained without the KBr correction and they
determined that
-SiC has an intense, broad band near 11.8
m and
-SiC peaks at 11.3 to 11.4
m. Silicon carbide grains found in
meteorites have isotopic compositions that imply that most of these grains were
formed around carbon stars. All studies to date of meteoritic SiC grains have
found them to be of the
-type (Bernatowicz 1997).
-SiC will
transform into
-SiC above 2100
C but the reverse process is
thermodynamically unlikely. The results obtained by Speck et al. (1999) show
that there is an obvious predominance of the
-SiC phase and that there is
now no evidence for the
-SiC phase at all. Their sample contains
SiC, SiC+:, Red and Extreme Carbon stars. However they do not solve
the radiative transfer in these media. Moreover, we should expect some
difference between "early'' and "late'' carbon stars with regard to dust
grains. Unfortunately, the optical constants for
-SiC were calculated in
a short range of wavelengths, about 7 to 12
m. In this case, we need to
adopt another set of optical constants at shorter wavelengths, where most of the
stellar radiation is concentrated. With this assumption we cannot prove that
-SiC grains are responsible for the 11.3
m emission alone.
SLMP have suggested the following carbon-rich dust sequence: SiC+
SiC
Red. The Red sources are
significantly cooler on average than the SiC+ sources. Following our
results, SiC+ stars have thinner envelopes than SiC stars.
Temperatures of the central stars are very similar but there is a tendency to
cooler temperatures in this sequence. Best models were obtained with
two homogeneous grains for both SiC+ and SiC class. Red
stars were best described with core/mantle grains. As mentioned before,
based on our results we suggest that our sample of extreme carbon stars contains
SiC and Red stars. In this sample, the thinner envelopes were best
represented by two homogeneous grains models (our E1 group) while thicker ones
by core/mantle grain models (E2 group). The temperature of these stars are also
cooler than in the SiC+ class. These results suggest that the sequence
proposed by SLMP can be interpreted as an evolutionary scenario. Moreover, it
seems reasonable to include our sample of extreme carbon stars in such a
scenario. In the beginning of the sequence, grains are mainly composed of
-SiC and amorphous carbon; with dust envelope evolution, carbon grains
become coated
-SiC ones. (Hence the emission is shifted to longer
wavelengths). This phenomenon could perhaps explain the small quantities of SiC
grains observed in the interstellar medium.
Concerning SiC++ class stars, SLMP have proposed that they lie in a
different evolutionary sequence, related to J-type carbon stars. In their
sample, which contains 96 objects, only nine are J-type stars. Two of them
are classed in the SiC++ class. One of us (Lorenz-Martins 1996) have
proposed that J-type carbon stars have an alternative evolutionary scenario
which differs from that proposed for ordinary carbon stars. In fact, according
to the results of the present paper, SiC++ stars have thicker (0.02
0.20)
envelopes than those of J-type stars (0.01
0.05, see Lorenz-Martins, 1996). It seems that some correlation between
SiC/A.C. ratios of both groups of stars also exists. Such results reinforce the
suggestion by SLMP linking SiC++ and J-type carbon stars.
Acknowledgements
S. Lorenz Martins acknowledges FUJB (FUJB 8635-5) for financial support. We would like to thank Dr. R. Rabaça for his careful reading of the manuscript and also the referee, Dr. I. Little-Marenin for constructive comments and suggestions. This research was performed using the SIMBAD database at Strasbourg.