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Astron. Astrophys. 333, L51-L54 (1998)

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3. Discussion

3.1. Evolutionary status

IRC +10 216 is in a very advanced stage of its AGB evolution due to its low effective temperature, long period and high mass-loss rates. Its carbon-rich chemistry indicates that a significant number of thermal pulses with corresponding dredge-up events did take place. The mass of the hydrogen-exhausted core, [FORMULA], can be expected to be already close to the later final mass, due to the high mass-loss rates and limited core growth-rates per pulse of only a few [FORMULA] in its stage of evolution (depending on mass) partially compensated or even canceled by dredge-up episodes. The conjecture that IRC +10 216 has entered a phase immediately before moving off the AGB seems to be supported by its non-spherical appearance (Fig. 1 ; see also Kastner & Weintraub 1994 ). In contrast to their progenitors, AGB successors often expose prominent features of asphericities, mostly in axisymmetric geometry. Note, that IRC +10 216 is already considerably elongated in NS direction probably even with a bipolar structure (Fig. 1).

The measured bolometric flux S at maximum light ([FORMULA] ; Sopka et al. 1985 ) leads to [FORMULA] for recent distance estimates of [FORMULA] (Le Bertre 1997 , Winters et al. 1994a ). Introducing these luminosities into the core-mass luminosity relation will give upper limits for [FORMULA] since S requires corrections for the mean variability phase and the thermal-pulse cycle phase. Evolutionary models of Blöcker (1995 ) give [FORMULA] for [FORMULA]. Note, that the [FORMULA] -L relation breaks down for massive AGB models (Blöcker & Schönberner 1991 ) due to the penetration of the envelope convection into the hydrogen-burning shell ("hot bottom burning", HBB). Accordingly, the upper luminosity value indicates [FORMULA] and possibly HBB. Since the present core mass will not deviate much from the final mass, it can be applied in initial-final mass relations. Taking the AGB calculations of Blöcker (1995 ) and Vassiliadis & Wood (1993 ), resp., we finally arrive at initial masses lower than [FORMULA] for [FORMULA] pc and [FORMULA] for [FORMULA] pc. The chemistry of the circumstellar envelope gives further constraints. Guelin et al. (1995 ) compared the observed isotopic abundance ratios with evolutionary models. Particularly the C, N and O isotopic ratios led to the conclusion that the initial mass ranges between 3 and [FORMULA], and that moderate HBB has taken place, favouring an initial mass close to [FORMULA].

3.2. Discrete dust layers

As a demonstrative example Fig. 3 shows a one-dimensional synthetic intensity profile resulting from a consistent time-dependent model calculation for a carbon-rich circumstellar dust shell. These model calculations assume spherical symmetry and include a consistent treatment of time-dependent hydrodynamics, chemistry, dust formation, growth and evaporation and of the radiative transfer problem (Fleischer et al. 1992 , Winters et al. 1994b ). A general result of the calculations is the formation of discrete dust layers with the characteristic step-like intensity profile shown in Fig. 3 (top). The location and height of the steps vary in time since the dust layers are moving outwards and, thereby, become geometrically diluted (see Winters et al. 1995 ). In the calculation, these structures are produced by thermal dust emission which, via the dust opacity, depends on wavelength. Note also, that the steps are separated by only a few stellar radii (lower abscissa; the upper abscissa gives the angular extension assuming [FORMULA] pc). The bottom diagram of Fig. 3 shows the intensity profile convolved with the ideal point spread function (PSF) of the 6 m telescope (FWHM diameter 76 mas). At this resolution the step-like structures in the intensity profile disappear completely. Comparing this intensity profile (Fig. 3, bottom) with our measured one (same figure) shows that there is a good agreement, but the wings of the measured profile are slightly higher.

[FIGURE] Fig. 3. Synthetic intensity profile at [FORMULA] m (upper panel) resulting from a model calculation (see text). The lower panel shows the convolution (solid line) of the synthetic profile with the PSF of the 6 m telescope, the PSF of the 6 m telescope (dashed line), and the azimuthal average of the measured intensity (dotted line)

The most striking structures in our image (Fig. 1) are the three knots B, C, and D. Assuming a typical stellar radius of the central source of [FORMULA] cm and [FORMULA] pc (Winters et al. 1994a ), the (tangential) separation of the knots from the central peak is 10 [FORMULA] (B) and 7 [FORMULA] (C,D). In terms of the models, this could be interpreted as knots B, C, and D being connected to an outer dust layer, whereas knots E and F belong to the next layer inwards. This interpretation requires the fragmentation of inhomogeneous dust layers or that the knots result from spatially bounded separate dust formation events. Since dust nucleation is extremely sensitive to the local kinetic gas temperature, dust formation could be caused locally even by small temperature fluctuations. The radial velocity of the expanding dust shell is approximately 15 km s-1. This corresponds to [FORMULA] 3 AU/year or 18 mas/year at a distance of 170 pc for a movement perpendicular to the line-of-sight. Thus, if connected to this expansion, knot B should have formed at least 11.6 yr ago, while C and D would be [FORMULA] yr old. In terms of the pulsation period ([FORMULA] d) this would correspond to a time scale for the formation of new dust layers (or knots) of [FORMULA]. Then, the structures E and F would have been formed [FORMULA] ago. The formation of new dust layers on time scales longer than the pulsation period is a common phenomenon of the model calculations (e.g. Fleischer et al. 1992 , Winters et al. 1994b , 1995 ). Therefore, future observations can be used to test this model and to determine the dust formation frequency and the tangential velocity of the structures.

3.3. Inhomogeneuos mass loss

Since the present observations reveal that IRC +10 216's shell structure is highly fragmented in the immediate stellar vicinity, there seems to be evidence for an already inhomogeneous mass-loss process. Inhomogeneously outflowing matter implies corresponding stellar surface inhomogeneities which may be caused by magnetic activity, global pulsations or large-scale photospheric convection. In particular, the latter seems to be a common phenomenon of far-evolved stars.

Schwarzschild (1975 ) showed that the typical horizontal size of a solar granule, [FORMULA], is given by characteristic depth scales of the layers below the photosphere. With the pressure scale height, [FORMULA], as the major depth scale and assuming that the ratio of [FORMULA] is constant he found that for red giants the dominant convective elements become so large that only a few of them can occupy the surface at any time leading to large temperature variations on the surface and concomitant brightness fluctuations. Due to the prominent temperature contrasts at the surface the emitted radiation is highly anisotropic leading to a polarization of the light scattered by circmstellar dust. Schwarzschild (1975 ) already supposed that mass ejection is triggered by photospheric convection and Dyck et al. (1987 ) outlined its possible importance for IRC +10 216.

Indeed, based on a linear stability analysis of convective modes in the envelopes of red giants, Antia et al. (1984 ) found the pressure scale height to be the prevailing depth scale leading to dominant convective elements which are of comparable size to the stellar radius. More recently, Freytag et al. (1997 ) presented models for convection zones of main-sequence stars and subgiants with spectral type F to K based on 2D numerical radiation hydrodynamics calculations. They found a tight correlation between the characteristic photospheric scale height [FORMULA] and the size of the granules, [FORMULA], viz. [FORMULA] covering more than two orders of magnitudes in gravity. Due to this robustness a (cautious) extrapolation to the red giant regime seems to be justified. For IRC +10 216 (with [FORMULA] K, [FORMULA], and [FORMULA]) this leads to a typical granule size of [FORMULA] allowing the whole surface to be occupied by, at most, a few granules.

The resulting temperature fluctuations can be expected to be in the range of up to several hundred Kelvin (Antia et al. 1984 ) being large enough to cause observable brightness fluctuations and to influence the formation of the shock- and dust-driven stellar wind and, therewith, the shape of the circumstellar shell. Thus, one further implication of large-scale surface inhomogeneities could be a corresponding large-scale fragmentation of the outflowing matter possibly leading to knots within the multiple shell structure as observed for IRC +10 216.

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Online publication: April 20, 1998