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A&A 368, 497­526 (2001) DOI: 10.1051/0004-6361:20000554
c ESO 2001

Astronomy & Astrophysics

Structure and physical properties of the rapidly evolving dusty envelope of IRC +10 216 reconstructed by detailed two-dimensional radiative transfer modeling
A. B. Men'shchikov
1 2

1,3

, Y. Balega2 , T. Bl¨ ker3 , R. Osterbart3 , and G. Weigelt3 oc

3

Stockholm Observatory, 133 36 Saltsj¨ aden, Sweden ob Special Astrophysical Observatory, Nizhnij Arkhyz, 357147 Karachaevo-Cherkesia, Russia e-mail: balega@sao.ru Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, 53121 Bonn, Germany ¨ ¨ e-mail: bloecker@mpifr-bonn.mpg.de; osterbart@mpifr-bonn.mpg.de; weigelt@mpifr-bonn.mpg.de

Received 13 July 2000 / Accepted 12 December 2000 Abstract. We present the first detailed, two-dimensional radiative transfer model of the dusty envelope around the carbon star IRC +10 216. Our goal was to find a self-consistent model of the star and its envelope which takes into account as many observational constraints as possible. The model reproduces very well the entire beam-matched spectral energy distribution of IRC +10 216 from optical to centimeter wavelengths (at several phases of stellar luminosity), observed intensity profiles of the ob ject at 1.25, 2.2, 10.5, 50, 100 µm, and 1.3 mm, a 10.5 µm lunar occultation intensity profile, our high-resolution J, H , K , and H - K bispectrum speckle-interferometry images, and visibilities in J, H, K, L, M , and N bands. For the adopted distance of 130 pc, the model of IRC +10 216 implies that the ob ject changes its luminosity between 13 000 and 5200 L , its effective temperature between 2800 and 2500 K, and its radius between 500 and 390 R . There is a dense non-spherical dust shell around the star, with outflow cavities at position angle PA 20 . The southern cavity with a full opening angle of 36 is tilted toward us by 40 from the plane of sky, causing the observed bipolar appearance of the ob ject on a subarcsecond scale. If the envelope's outflow velocity of 15 km s-1 applies to the material making up the dense core, then just 15 years ago the star was losing mass at a rate of 9 10-5 M yr-1 . Dust exists in the envelope of IRC +10 216 everywhere from the stellar photosphere up to a distance of 3 pc from the star. The total mass of the envelope lost by the central star is 3 M and the dust-to-gas mass ratio is 0.004. The total optical depth V toward the star in the visual is 40, in the polar cavities it is 10. The innermost parts of the envelope are optically thick even at 10.7 µm due to a strong resonance absorption of silicon carbide grains at that wavelength. In addition to SiC dust, the model contains inhomogeneous grains made of a mixture of SiC and incompletely amorphous carbon with thin [Mg0.5 Fe0.5 ]S mantles. This is the simplest dust mixture required to fit all observations of IRC +10 216 and to correctly interpret the well-known 11.3 µm and 27 µm emission bands. The dust model found in this study can also be successfully applied to many other carbon stars exhibiting broad emission features in the 10.3­12.6 µm and 25­37 µm wavelength regions. An important and firm result of our modeling is that the brightest compact peak observed in IRC +10 216 is not the direct light from the underlying central star. In contrast to previous suggestions, the brightest southern component, labeled A in our high-resolution near-infrared images (Weigelt et al. 1998a,b; Osterbart et al. 2000), is only the radiation emitted and scattered in the optically thinner southern cavity of the bipolar dense shell moving away from the central star. The carbon star is at the position of the fainter component B in our H and K images, which is 0. 21 away from A along the symmetry axis. Direct stellar light (component B) is not seen at all in the Hubble Space Telescope 0.8 µm and 1.1 µm images, being absorbed by the dense dusty material. The even fainter components C and D in the H and K images are probably due to smaller deviations of the dense shell from the spherical shape. IRC +10 216 seems to have entered a phase immediately before moving off the asymptotic giant branch and started developing asymmetries in its envelope.

Send offprint requests to : A. B. Men'shchikov, e-mail: sasha@astro.su.se


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1. Intro duction
After the first study by Becklin et al. (1969) and a series of photometric, spectroscopic, and polarimetric measurements by others (Lockwood 1970; Miller 1970; Herbig & Zappala 1970; Shawl & Zellner 1970), it has become clear that IRC +10 216 (CW Leo, AFGL 1381) deserves special attention. An extended ob ject (2 â4 ) outside the galactic plane, IRC +10 216 was the brightest source on the sky in the near infrared (IR). Its almost featureless spectral energy distribution (SED) resembled that of a 650 K blackbody (or 1200 K at wavelengths below 1 µm); its brightness at 2.2 µm varied by 2m with a period of 600 days; its small proper motion implied a distance D > 100 pc. The 1 µm linear polarization was in excess of 20% at a position angle PA 120 , perpendicular to the elongation of the optical image (PA 30 ), indicating scattering by solid particles in a non-spherical environment. IRC +10 216 was identified as a longest-period, pulsating carbon star surrounded by an opaque dust shell, perhaps in a state preceding that of a planetary nebula. During the three decades of studies, dust continuum radiative transfer calculations have been repeatedly applied to this well-observed ob ject (Crabtree & Martin 1979; Mitchell & Robinson 1980; Rowan-Robinson & Harris 1983; Le Bertre 1987; Martin & Rogers 1987; Orofino et al. 1990; Griffin 1990; Lorenz-Martins & Lef` evre 1993; Winters et al. 1994; Sloan & Egan 1995; Bagnulo et al. 1995; Ivezi´ & Elitzur 1996; Groenewegen 1997) in c order to understand in more detail physical, chemical, and evolutionary properties of the star and its dusty molecular envelope. All the models used an assumption of spherical geometry which seemed to be justified for this ob ject by the presence of the large-scale (several arcminutes) apparently symmetric envelope. The latter appears to have, however, not very smooth density distribution in the deep optical images by Crabtree et al. (1987) and Mauron & Huggins (1999), showing a series of incomplete concentric shells at radii of 15­60 . On the other hand, several speckle observations (McCarthy et al. 1980; Mariotti et al. 1983; Ridgway & Keady 1988; Dyck et al. 1991; Danchi et al. 1994) and especially recent highest-resolution observations (Osterbart et al. 1997; Weigelt et al. 1998a,b; Haniff & Buscher 1998; Osterbart et al. 2000; Tuthill et al. 2000) have demonstrated that the inner dust shell of IRC +10 216 is actually non-spherical and extremely clumpy. This well-established observational fact emphasizes the need of multidimensional radiative transfer calculations for proper interpretation of the observations. A lot of circumstellar structures seen in the high-resolution images of the last decade demonstrate that the spherical symmetry is no more a realistic basic assumption for understanding the observations. Clumpy and bipolar structures (often intrinsically related to the jets and outflows) are being widely observed in protostars, young stellar ob jects (YSO), protoplanetary nebulae, in the winds of evolved post-asymptotic giant branch (post-AGB) stars,

and in active galactic nuclei. An axially symmetric geometry of an optically thick toroidal distribution of matter around a central energy source emerges as a good basic approximation for the modeling of the physically different non-spherical ob jects. From a practical point of view, axisymmetric geometries are much more time-consuming for modeling, because of two additional parameters, the density structure in the polar direction and the viewing angle. Furthermore, to find a self-consistent and realistic model, one has to derive also the properties of dust grains, which makes the whole problem enormously difficult and requiring many more observational data sets to constrain the modeling. In a series of recent papers (Men'shchikov & Henning 1997; Men'shchikov et al. 1998, 1999; White et al. 2000), we applied our two-dimensional radiative transfer code to detailed modeling of toroidal envelopes around YSOs (L1551 IRS 5, HL Tau) and around a close binary postAGB star (the Red Rectangle). The models demonstrate that a derivation of reliable physical parameters requires using all available (spatial) information in a detailed radiative transfer modeling. The less constraints are used, the easier is to find a model and the higher is the risk that the model is unrealistic (Men'shchikov & Henning 2000). The common practice of sketchy fitting of SEDs alone can only give source parameters that are highly uncertain. In the present study, we utilized our approach and twodimensional radiative transfer code to find a self-consistent model of the dusty environment of IRC +10 216, which would match quantitatively al l available dust continuum observations. In Sect. 2, we briefly describe the most substantial results obtained for IRC +10 216 during the three decades of very active studies, that will enable the reader synthesize a large amount of information and follow easier our subsequent discussion. In Sect. 3, all details of our approach and radiative transfer model are described. In Sect. 4, we confront the model with available observations of IRC +10 216. In Sect. 5, we briefly touch upon its present evolutionary state. In Sect. 6, we summarize results obtained in this study.

2. IRC +10 216: Three decades of observations
In the years following the initial discovery, a great number of observations in a wider wavelength range and with higher sensitivity, spectral and angular resolution painted quite a detailed and complex (yet incomplete) picture of this carbon star.

2.1. Prop erties of the envelop e
Geometry. Although on scales of more than several arcseconds the envelope of IRC +10 216 seems to have a roughly spherical shape, large optical and near-IR polarization measured by Dyck et al. (1971) and Capps & Knacke (1976) suggested significant deviations from spherical symmetry. Near-IR speckle interferometry by Mariotti et al. (1983), Dyck et al. (1984), and Ridgway & Keady (1988) revealed asymmetries in the envelope on


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subarcsecond scales and two scattering lobes of a lower density. Polarimetric imaging by Tamura et al. (1988) detected an extended envelope also in highly polarized light. A weakly-bipolar reflection nebula (Kastner & Weintraub 1994) or a geometrically thick disk (Dyck et al. 1987) or a dusty torus (Skinner et al. 1998) must be significantly inclined toward an observer. A complex, clumpy subarcsecond structure in the near IR is changing on time scales of a few years, as has been demonstrated by interferometric observations of Weigelt et al. (1998a) and Haniff & Buscher (1998). Osterbart et al. (2000) concluded that it is the southern scattering lobe that dominates the optical Hubble Space Telescope (HST) and near-IR images and polarization pattern. See also Sects. 3.2, 4.5.1, 4.5.2, 4.6, and 6. Density profile. Near-IR interferometry observations by McCarthy et al. (1980) indicated large departures from the expected smooth r-2 density distribution on an arcsecond scale. Deviations indicating an enhancement by a factor of 3 were found also over much larger distances by Bieging et al. (1984) and a flatter density distribution (1 + r/25 ) r-2 was deduced by Fazio et al. (1980). Having analysed far-IR scans of the envelope on large scales, Harvey et al. (1991) concluded that dust density distribution is inconsistent with the picture of a smooth, constant-velocity outflow. Keady & Ridgway (1993) presented evidence for by a factor of 2­3 higher densities 1000 years ago. Two periods of enhanced density 200 and 850 years ago were identified by Groenewegen et al. (1997). Direct evidence of periodic outbursts with higher densities on a time scale of 200­800 years was found in deep optical images by Crabtree et al. (1987) and Mauron & Huggins (1999). See also Sects. 4.3, 4.4, 4.5.3, and 6. Mass-loss rate. From a radiative transfer modeling of the CO line emission, Groenewegen et al. (1998) derived a mass-loss rate of 1.5 10-4 M yr-1 . A similar estimate of 2 10-5 M yr-1 was obtained by Keady et al. (1988) and Kastner (1992). Somewhat higher mass-loss rate of 3.25 10-5 M yr-1 was derived by Crosas & Menten (1997) from their modeling of the CO radiation, whereas Truong-Bach et al. (1991) obtained 4 10-5 M yr-1 for the outer envelope. Molecular spectroscopy and a spectral synthesis modeling allowed Keady & Ridgway (1993) to derive an upper limit of 4 10-5 M yr-1 . Sahai (1987) estimated 4.8 10-5 M yr-1 in the outer envelope, whereas Knapp & Morris (1985) obtained 5.5 10-5 M yr-1 . Note that the above estimates are based on different distances and need to be rescaled (see Table 5). See also Sects. 4.4 and 6. Outflow velocity. From molecular line observations, Morris et al. (1975) derived an expansion velocity of the envelope of 12 km s-1 . Betz et al. (1979) detected NH3 in the inner dense region, concluding that the gas flow was accelerated to 14 km s-1 on subarcsecond scales. Olofsson et al. (1982) observed several molecules in the envelope with an outflow velocity of 14.4 km s-1 . Kuiper et al. (1976) resolved a large CO envleope expanding at 15 km s-1 and Knapp & Morris (1985) obtained almost

the same velocity of 15.2 km s-1 , whereas Knapp et al. (1982) measured an outflow velocity of 17 km s-1 . See also Sect. 3.2 and Appendix A.

2.2. Prop erties of dust grains
Composition. A broad emission feature at about 11 µm in the spectra of IRC +10 216 obtained by Treffers & Cohen (1974) indicated that silicon carbide dust must be present, as well as other carbonaceous particles with featureless emissivity. A broad far-IR emission band beginning at 24 µm was discovered by Forrest et al. (1981). It was shown to extend beyond 37 µm and peak at 30 µm by Herter et al. (1982). Magnesium sulfide dust grains were proposed by Goebel & Moseley (1985) as the carrier of the band. See also Sects. 3.3.1, 3.3.4, 3.3.5, 3.3.6, 4.2, and 6. Sizes. Spectrophotometry of the 11 µm feature by Treffers & Cohen (1974) showed that there exist small grains with radii a 1 µm. Near-IR low-resolution spectra obtained by Witteborn et al. (1980) indicated a presence of grains with radii a < 0.25 µm. Jura (1983) argued that grains are rather small, having a 0.05 µm, and later Jura (1994) proposed that dust in the outer envelope has a wide distribution of sizes, including both large and small grains (a < 0.015 µm, a > 0.5 µm). See also Sects. 3.3.1, 3.3.6, and 4.2. Condensation. Modeling of dust formation by McCabe (1982) demonstrated that small SiC grains can condense very close to the stellar photosphere (r 1.5 R , T 1500 K), whereas graphite grains form at lower temperatures further away from the star (5 R < r < 20 R , 1000 K < T < 600 K). Danchi et al. (1990) interpreted in terferometry data as indicating that dust grains form at higher temperatures (1000­1800 K), and closer to the star (1.5­3 R ) than usually assumed. See also Sects. 3.3.2, 4.3, and 6. Emissivity. Submillimeter photometry by Phillips et al. (1982) showed that the far-IR opacity of the grains is close to -1 . Comparing the far-IR and ultraviolet extinction of dust in the envelope, Jura (1983) argued that -1.3 . Photometry in the far IR by Rengara jan et al. (1985) and at submm wavelengths by Sopka et al. (1985) confirmed that the dust emissivity is rather flat at long wavelengths ( -1 to -1.2 ). A similar result was also found by Le Bertre (1987) from his radiative transfer fitting of the observed SED. See also Sects. 3.3.3 and 4.2.

2.3. Uncomfortable reality
Huge amounts of detailed observational information for IRC +10 216 present a real challenge to theoretical models attempting to explain the data in a consistent way. In addition to the usual difficulties and uncertainties of modeling and interpretation, the star and its envelope have significantly varied in time due to both periodic pulsations and non-periodic, long-term changes. What we observe is a complex result of a very long evolution of the


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central star, with its history recorded in the structure and chemical composition of the parsec-sized envelope. Many usual simplifying assumptions are invalid for IRC +10 216: (1) we clearly have a non-stationary, timedependent problem, (2) spherical symmetry cannot be adopted for dense inner regions and even axial symmetry is questionable there, (3) the mass-loss rate and the wind velocity are not constant, (4) the envelope's density and chemical composition cannot be described by simple power laws, (5) dust grains are very likely to have inhomogeneous structure and composition, non-spherical shapes, and different size distributions in various parts of the envelope, (6) the grains are accelerated by the radiation pressure to different velocities, which leads to their collisions and possible growth by coagulation or to destruction in the dense inner regions, (7) the observational constraints used in models are not coeval. The last point is potentially very troublesome, because of the observed non-periodic changes which imply that the data from different epochs may well be fundamentally incomparable. An important question is how far one can go making simplifying assumptions while modeling very complex phenomena. The finer details are observed, the more simplifications we have to abandon, and the more complex the models should become.

3.2. Geometry and assumptions
The model assumes axially-symmetric geometry shown schematically in Figs. 1 and 2. Departures from spherical symmetry appear only on a subarcsecond scale, in the inner dense core. In our recent images (Osterbart et al. 2000) the bipolar holes appear very small, comparable to the stellar diameter (see also Sect. 4.5). The perfect conical shape of the polar cavities should be considered as only a first approximation to reality. In this 2D radiative transfer modeling, we had to ignore the possibility that the immediate environment of IRC +10 216 may be threedimensional. One needs to keep this in mind, however, when comparing our results with observations. Although it may contradict intuitive perception, in our model the star is located at the position of the fainter component B, whereas the brightest peak A is produced by the hot dust emission from the far side of the outflow cavity (Fig. 1). The even fainter components C and D may be, for example, optically thinner zones due to density fluctuations along a ring surrounding the outflow cavity (Fig. 2). High-resolution observations, in particular a 1.1 µm polarization map and the components' proper motions presented in our previous paper (Osterbart et al. 2000), support this picture. We have shown that the most natural and symmetric velocity field can be derived if one assumes the star at the position of B. In fact, only in this case, both symmetrically located components C and D are moving away from B (within the plane of sky) with the same apparent velocity vC vD 5kms-1 ; the component A is moving away from the star with an apparent velocity of vA 14 km s-1 (Table 2 in Osterbart et al. 2000). A velocity being different by factor of 3 is most likely a pure pro jection effect implying that the radiusvectors rC and rD to C and D are more inclined toward the observer than is the vector rA to component A (Fig. 2). The actual depro jected radial velocity vr 15 km s-1 (see Appendix A) is the same for all the components and equal to the general expansion velocity of the envelope around IRC +10 216. It is instructive to list here our general simplifying assumptions, which are relevant (and essential) for the model: (1) dust distribution is axially-symmetric close to the star, (2) outer parts of the envelope are sphericallysymmetric, (3) dust density depends only on the radial coordinate, (4) dust population consists of spherical, compact solid grains, (5) size distribution of the grains can be described by a power law, (6) wherever a dust component exists, its composition, structure, and grain sizes are spatially invariant, (7) light scattering by the dust particles is isotropic, (8) dust-to-gas mass ratio of a dust component is spatially homogeneous, (9) dust is in radiative equilibrium with the radiation field, (10) there are no sources or sinks of radiative energy in the envelope, (11) the contribution of molecular line emission to the observed fluxes is small, (12) the star radiates as a blackbody at long wavelengths.

3. IRC +10 216: The radiative transfer mo del 3.1. General formulation
Having mentioned many difficulties which may complicate thorough and detailed analyses, we are going to make a number of assumptions and simplifications, which we believe are reasonable, and present a model for IRC +10 216, which takes into account all existing dust continuum observations. Our goal is to find a snapshot structure of the dusty envelope, consistent with the recent high-resolution optical and near-IR images of the ob ject (Weigelt et al. 1998a,b; Haniff & Buscher 1998; Osterbart et al. 2000), as well as with most other measurements of the dust radiation. Although our model describes only the present structure of the ob ject (and as such is time-independent), in Sect. 5 we consider its evolutionary implications. The complex molecular chemistry of the envelope is largely ignored here and the gas component is described by means of a spatially constant dust-to-gas mass ratio. The assumed constancy of d / may not be realistic enough, thus contributing to the uncertainties of the derived properties of the gaseous envelope (e.g., the total mass M of the envelope, lost by the central star during its evolution). We utilized our 2D radiative transfer code based on a ray-tracing method which provides an accurate solution to the frequency-dependent radiative transfer problem, including isotropic scattering (we refer to Men'shchikov & Henning 1997, for a detailed description). Large parameter space was explored in many hundreds of runs by changing model parameters and comparing their SEDs, images, and visibilities to available observational constraints (see Appendix B for details).


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IRC +10 216: Geometry

6 â105 AU = 3pc =4600
6 0A U

IRC +10 216: Geometry F

E

Dense ~100 AU core

0 .5

G



B A

v

East

B C D

West

0. 2

A
to Ear th

pl of ane sk y

Outflow

cavity

144

o

v 40

o

South
Fig. 2. Three-dimensional representation of the innermost dense core of the circumstellar envelope of IRC +10 216 as it appears in the highest-resolution near-IR speckle images in pro jection onto the sky plane. Components A, B, C, D observed by Weigelt et al. (1998a) are shown schematically, as well as much fainter components E, F, G found by Osterbart et al. (2000). Contrary to intuitive expectations, our model puts the star at the position of the fainter component B. The model identifies the brightest peak A with the light escaping from the southern cavity. The components C and D (not modeled here) may appear on a ring around the cavity most likely due to dust density (optical depth) fluctuations along the ring. Weak emission from the obscured northern cavity and inhomogeneous dusty environment cause a somewhat irregular appearance of the components E, F, and G in the speckle images

Fig. 1. Geometry of the circumstellar envelope of IRC +10 216. Schematically shown are three regions of the model envelope ­ the innermost dense core with bipolar cavities (dark color), the less denser envelope where molecules are observed (medium color), and the outer extended envelope (light color). The model is basically spherically-symmetric, except for the inner axially-symmetric region with bipolar outflow cavities (see Fig. 2). The geometry is defined by the opening angle of the cavities, = - 36 ( 144 ) and the viewing angle, v 40 , between the equatorial plane and the line of sight. The bright components A and B labeled by Weigelt et al. (1998a) correspond to those shown in Fig. 2

There are no good reasons to believe that the above statements are extremely good approximations. One cannot avoid using them, however, primarily because of the obvious lack of sufficiently detailed and reliable observational constraints. The influence of the assumptions on model results is quite uncertain apriori and, therefore, it must be carefully investigated.

3.3. Dust particles 3.3.1. Chemical comp osition
Spectrophotometric observations of IRC +10 216 show an almost featureless continuum with only a couple of clearly detected broad bands (Sect. 2.2). The latter are the so-called 11.3 µm emission attributed to SiC grains (Treffers & Cohen 1974) and a very broad emission band at 30 µm, which is usually thought to be produced by MgS grains (Goebel & Moseley 1985). Also clearly visible is a 3.1 µm absorption feature attributed to the absorption by molecules (C2 H2 , HCN) in stellar photospheres (Ridgway et al. 1978). The continuum is undoubtedly produced by some kind of carbonaceous solid particles, although details of the chemical composition, internal structure of the dust material, and of the condensation process itself are still

a matter of debate. Most frequently, the observations have been interpreted in terms of amorphous carbon grains (which are conglomerates of highly disordered planar graphitic structures), although it seems very unlikely that any single form of carbon may be able to explain all observations. Moreover, there are good reasons to believe that properties of circumstellar dust are extremely complex. In the present modeling we assumed that dust is a mixture of compact spherical solid particles of radius a, composed of inhomogeneous materials which include different forms of carbon, silicon carbide, and magnesiumiron sulfides. Although polycyclic aromatic hydrocarbon (PAH) molecules may also exist in the carbon-rich envelope around IRC +10 216, the observations show no evidence of their emission features. The three components considered in this work constitute the simplest realistic set of materials; the addition of other solids or PAHs would not be justified. The radiative transfer code employed in this study (Men'shchikov & Henning 1997) treats separately an arbitrary number of dust components which may differ by


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A. B. Men'shchikov et al.: Structure and properties of IRC +10 216 dust boundary R1 , dust grain size a and power-law exponent Bracketed values are uncertainties of the parameters given composition of dust components used in the models: "Gr" magnesium sulfide Reference Crabtree & Martin (1979) McCabe (1982) Griffin (1990) Skinner et al. (1999) Danchi et al. (1990) Winters et al. (1994) Bagnulo et al. (1995) Groenewegen (1997) Sloan & Egan (1995) Martin & Rogers (1987) Le Bertre (1987) Lorenz-Martins & Lef` re (1993) ev Rowan-Robinson & Harris (1983) Ivezi´ & Elitzur (1996) c Mitchell & Robinson (1980) Sloan & Egan (1995)

Table 1. Model estimates of the grain temperature T1 at the inner p (from Qabs -p ) adopted in previous models of IRC +10 216. in the referenced papers. Fifth column roughly classifies chemical graphite, "amC" amorphous carbon, "SiC" silicon carbide, "MgS" T1 (K) 1700 1500 1500 1500 1300 1300 1100 1075 (5%) 1000 1000 950 (25%) 850 750 750 (7%) 600 R1 (R ) 1.5 1.9 3.4 2.5­3 2.5 2.2­3 4.5 (10%) 4.0 4.5 6.6 6 5.6 5.1­8.5 20 a (µm) p 2 0.05 0.25 1

Composition Gr Gr + SiC amC + SiC amC + SiC + MgS amC amC + SiC amC + SiC amC + SiC amC amC amC amC Gr amC + SiC + SiC + SiC + SiC

0.008 0.16 (6%) 0.05 0.05 0.1 0.2 0.05 0.01

1.3

1 1.3 1.2 1 2

the composition, structure, shapes and sizes of grains. Following Kim et al. (1994) and Jura (1994), we adopted a size distribution in the form dn/da a exp (-a/aexp ), which is defined by the minimum grain radius and by the exponential cutoff radius for the largest particles (amin ,aexp ). Although we explored a very large range of various grain parameters and mixtures in the modeling, unknown details of the dust properties in IRC +10 216 prevented us from using more complex dust models in final runs.

3.3.2. Condensation
Laboratory experiments on dust condensation (Frenklach et al. 1989) suggest that SiC may be the first material to nucleate from the gas phase at fairly high temperatures Tg > 2000 K, i.e. very close to (or even inside of ) the stellar photosphere. At lower temperatures of Tg 1500 K (distances r of only a few R ) these very small SiC particles may provide sites for their further heterogeneous growth by the deposition of amorphous carbon (diamond, for Tg < 1300 K) layers. When temperatures in the stellar wind drop to Tg 1000­900 K, PAH molecules can form in the gas phase (Frenklach & Feigelson 1989). Their clustering may produce more nucleation sites, provided that chemical, thermal, and dynamic conditions in the wind are favorable for the formation of high enough number density of PAHs. The existing SiC-C core-mantle grains could also grow substantially by the deposition of PAHs on their surfaces. At even larger distances from the star (r > 10 R ), MgS could condense at temperatures Tg < 800 K, as indi cated by nucleation calculations (Gail & Sedlmayr 1986). Although laboratory experiments and theory suggest that condensation temperatures as high as 2000 K are possible for the abundant refractory C and SiC dust, radiative

transfer models have b