This dust-shell model and the possible existence of acceleration within the cavities may be understood in terms of the beginning operation of interacting winds which later lead to the shaping of planetary nebulae (Kwok 1982; Balick 1987). Within this scenario a fast stellar wind interacts with the fossil, slow AGB wind. The AGB mass-loss is thought to be aspherical and to take preferentially place in the equatorial plane. Accordingly, the polar regions show lower densities than the equatorial regions. Later, after a fast wind has developed, the less dense polar material is carved out leading to the formation of outflow cavities. This fast wind can be expected to turn on slowly at the very end of the AGB evolution resulting into the formation of biconical dust-shell structures on sub-arcsecond scales as observed for IRC +10216.

The high spatial and temporal resolution of the present observations reveals details of the mass-loss process even in the immediate vicinity of the dust condensation zone. The monitoring, covering more than 3 pulsation periods, shows that the structural variations are not related to the stellar pulsation cycle in a simple way. This is consistent with the predictions of hydrodynamical models that enhanced dust formation takes place on a timescale of several pulsation periods (Fleischer et al. 1995). In Sect. 3.3 simplified dust formation models are compared with the observations.

$\begin{figure} \includegraphics[width=14cm,clip]{h3683f5.ps}\end{figure}$

Figure 5: J-K (left) and H-K (right) color images (greyscale images) of the central region of IRC +10216 in March 2001, confined to regions which are brighter than 2% of the peak intensity in the J and K images (J-K color image) and 3% of the peak intensity in the H and K images (H-K color image), resp. The resolution is 115 mas. Contour lines refer to the K-band image and are shown from 0.2 mag to 3 mag relative to the peak brightness in steps of 0.7 mag. To construct the respective color images, the J, H, and K reconstructions were centered at the positions of maximum intensity. White regions refer to magnitude differences of 7.4 mag (J-K) and 3.9 mag (H-K); the regions shown in the darkest grey correspond to magnitude differences of 5.0 mag (J-K) and 2.7 mag (H-K). North is up and east is to the left. Dashed lines indicate the biconical geometry of the cavities according to the 2D radiative transfer model of Paper III.

3.2 Observed changes interpreted by 2D modeling

The large number of epochs available now seems to make the interpretation of the sub-arcsecond structures and their evolution even more difficult and puzzling than before. Here we suggest a physical picture of what presently is going on in this object based on the results of our previous 2D radiative transfer modeling (Paper III). The model was designed to derive the structure and physical properties of the star and its dusty envelope at a single moment, corresponding to the third epoch (January 23, 1997) of our images. Our simplified attempt to handle the difficult problem of self-consistent time-dependent multidimensional radiative transfer modeling will be presented elsewhere (Men'shchikov et al. 2002, submitted).

3.2.1 The star and its evolving environment

Key point to the understanding of the structure and evolution of the sub-arcsecond environment of IRC +10216 is the knowledge of the position of the central star in the images. As we have suggested in the previous modeling (Paper III), the brightest compact peak A seen in all images is not the direct light from the central star. The star is most likely located at the position of the fainter peak B, whereas component A is the radiation emitted and scattered in the optically thinner conical cavity of the optically thick bipolar dust shell. The even fainter components C and D in the H and K images were identified with smaller-scale deviations of the density distribution of the circumstellar environment from axial symmetry (Figs. 1 and 2 in Paper III). These inhomogeneities are less opaque than other, more regular regions of the compact dense shell.

An alternative interpretation of the morphology of our images of IRC +10216 would be that components A and B are the lobes of a bipolar nebula and that the star is located in the dark region between them. However, this interpretation disagrees with our radiative transfer modeling presented in Paper III. A reason for this is that the optically thick dust which would form the bipolar lobes cannot exist so close to the star, at half the distance between the components. Thus, the star is probably located either at A or B. The fan-shaped morphology of component A in the J- and H-band images, as well as other evidence presented in Papers II and III, strongly suggest that the star is located at the position of B.

Having defined the stellar position at component B, we can now interpret the evolving appearance of IRC +10216 in terms of an increased mass-loss rate during the last $\sim$ 30 years. One of the main features of the entire 8-epoch sequence of imaging is the relative fading of the stellar component B (Figs. 1 and 2). Other changes seen in the images are the increasing distances of components A, C, D from the star (Fig. 4) and their greatly varying shapes. Our radiative transfer modeling (Paper III) has shown that the observed components are cavities in the dense opaque shell; therefore, the observed motion requires an additional discussion (Sect. 3.2.4).

3.2.2 The near-IR images and model cavities

In order to better visualize the relative location of the components, we have shown the structure (conical cavities) of our model (Paper III) in the observed images by dashed lines in Figs. 3 and 5. The lines intersecting at the position of the central star and making an angle of 46 $\hbox{$^\circ$ }$ between them, outline the biconical geometry of the cavities.

The April 1996 J-band image in Fig. 3 best exhibits the bipolar geometry of IRC +10216. Clearly visible at this wavelength are the fan shape of the brightest component A and even the scattered light from the opposite (northern) cavity on the far side of the dense shell. Faint direct stellar light is visible near the origin of the conical cavities. The star (component B) appears much brighter in the January 1997 H-band image (Fig. 3), whereas the fan shape of the cavity (component A) is less prominent but still well visible at this wavelength. The H and K images in 1997 agree very well with our model presented in Paper III. The March 2001 H and K images are qualitatively similar to the older images obtained in 1997, but distorted by the appearance of several fainter structures close to component D and by merging of the bright component A with component C. The faint direct stellar light has become more difficult to identify in H and it has been buried in the enhanced dust emission from all the other components in the March 2001 K-band image.

The most recent J image of IRC +10216 with a 3 times higher resolution (50 mas, Fig. 2) shows in much greater detail the fine structure of the envelope. The image reveals a rather isolated, faint peak at the position of the central star (marked in Fig. 2). The following evidence suggests that this peak is indeed the direct light from the star, not just a clump that happened to be there: (1) its position angle relative to A (PA $\approx 20$ $\hbox{$^\circ$ }$ ) is the same as in all the images where the star (component B) is clearly visible, (2) the H image at the same epoch shows a (less isolated) peak at the same position, (3) the distance of approximately 347 mas between the peak and the component A is consistent with the fit of Fig. 4.

One might think that the faint stellar peak should be much better visible in K band (Fig. 2), where optical depths are significantly lower compared to J. However, the greatly enhanced hot dust emission in K band may well make it completely invisible. In fact, from the continuum of the model stellar atmosphere used in Paper III, we estimate that the stellar brightness in J and K bands is approximately the same. The dust model of Paper III would predict that the star is a factor of $\sim$ $1.8 \times 10^3$ brighter in K than in J band, whereas our new model of IRC+10216 (Men'shchikov et al., submitted), computed specifically for the latest epoch of March 2001, predicts a larger factor of $\sim$ $1.3 \times 10^4$ . On the other hand, from the calibrated color images of Fig. 5 we know that the nebula becomes much brighter between J and K (and thus redder), by a factor of $\sim$ $1.4 \times 10^4$ . Therefore, it is unlikely that in K the stellar peak is visible better than in J band.

3.2.3 Shapes of the near-IR color maps

The high-resolution J-H, J-K, and H-K color images in Fig. 5 observed in March 2001 confirm our interpretation that the bright components A, C, and D are, respectively, the cavity and smaller-scale inhomogeneities in the dense shell, not dense clumps of dust as it might appear from the images alone (Figs. 1-3). In fact, all the bright components coincide with the blue areas in the color images, the cavity A corresponding to the bluest spot. This is a natural consequence of lower optical depths along those directions from the star, with the "hot'' stellar photons being scattered into the direction of the observer. This is illustrated in Fig. 5 by the dashed lines showing the geometry of our model (Paper III). The bluest, optically thinnest spot is located precisely inside the conical cavity. The star, obscured by $\sim$ 40 mag of visual circumstellar extinction, is situated in the red area of the color images, as it was also in the previous epochs (Fig. 16 in Paper III).

3.2.4 Moving dense layer or dust evaporation?

The apparent motion of the components A, C, and D (Fig. 1) could be attributed either to the real radial expansion of the opaque dense layer with several "holes'' in the dense dust formation zone or to a displacement of the dust formation radius due to evaporation of recently formed dust by a hotter environment. Here, we analyze both processes and argue that the temperature-induced displacement of the dust formation zone is acting in IRC +10216. For simplicity, we consider a single dust formation radius corresponding to the formation of carbon dust (cf. Paper III).

One can explain the observed decreasing brightness of the star by assuming a monotonically increasing mass-loss rate and, hence, higher densities and optical depths of the wind in the dust formation zone. Higher mass loss and continuing condensation of new dust in the wind out of the gas phase increase the temperatures of the outflowing gas and dust due to backwarming. Increasing temperatures affect the location of the inner dust boundary of the envelope via dust sublimation, causing its displacement with a velocity that has nothing to do with the outflow motion of the envelope.

Crucial to distinguishing between the real motion of a dense layer and the temperature-induced shift of the dust formation zone are estimates of the apparent velocities of the components A, C, and D relative to the star. For the assumed distance of 130 pc, the linear fit in Fig. 4 gives for the brightest component A a velocity $v_{\rm A} \approx 18$ km s^-1 in the plane of sky. On the basis of our model (Paper III), one can derive for the component a deprojected radial velocity $v_{\rm r{\rm A}} \approx 19$ km s^-1.

Since the deprojected radial velocity is higher than the observed (terminal) wind outflow speed in IRC +10216 of $v \approx 15$ km s^-1, it is unlikely that the observed changes reflect just an expansion of a dense layer in which grains are forming. In fact, the standard picture of a stationary stellar wind predicts an acceleration of dust and gas within distances by a factor of $\sim$ 2-5 larger than the dust formation radius (Steffen et al. 1997). Due to the radiation pressure on dust grains, the wind velocity increases in this transition zone, approaching asymptotically the terminal velocity at larger distances. As our model (Paper III) associates the observed components of IRC +10216 with the dust formation zone, we expect that dust and gas are not yet fully accelerated there, i.e. that the radial outflow velocity $v_{\rm r} < 15$ km s^-1.

However, the deprojected velocity $v_{\rm r{\rm A}} \approx 19$ km s^-1 is significantly larger than the expected wind velocity in the dust formation zone. Only if we assume an unlikely lower limit of 100 pc (Becklin et al. 1969), does the deprojected velocity $v_{\rm r{\rm A}}$ approach (from above) $v \approx 15$ km s^-1, which is still too high for the dust formation zone. If, however, the actual distance to IRC +10216 is larger than 130 pc, one would obtain $v_{\rm r} \ga 19$ km s^-1 and an even larger discrepancy.

Moreover, there are reasons to believe that the acceleration depicted by the parabolic fit in Fig. 4 is real and that the actual apparent motion of A is now as fast as $v_{\rm A} \approx 26$ km s^-1. The corresponding deprojected velocity is then $v_{\rm r{\rm A}} \approx 28$ km s^-1, much higher than the expected wind speed, for any realistic distance to IRC +10216. Taken in context with increasing optical depths in the shell, this suggests that the observed motions are caused by the rapid dust evaporation due to backwarming and higher temperatures in the dense environment formed by the increased mass loss.

We believe that a reasonable interpretation of the observed changes in IRC +10216 would be the following picture. During the recent period of increasing mass-loss which started $\sim$ 20-30 years ago, a compact dense shell has formed around the star. The mass-loss rate was recently as high as $\dot{M} \approx 10^{-4}~M_\odot$ yr^-1 (Paper III) and the innermost regions of the dust shell are expanding outward at a local wind velocity $v \la 10$ km s^-1. Dust formation continues in the expanding material, thus increasing its optical depth and obscuring the central star. The optical depths in the polar regions remain significantly smaller than in the other regions of the dense shell, making the cavity (A) and the other components relatively brighter than at previous epochs. As the dense, increasingly optically thick dusty shell expands, steeply rising temperatures inside it (due to the backwarming from the steepening density front) inhibit further dust condensation and evaporate outflowing grains. In effect, these processes have been shifting recently the dust formation radius outward with an average velocity $v_{\rm r} \approx 19$ km s^-1 (or as high as $\sim$ 30 km s^-1 in 2001, if the apparent acceleration measured in this work is real). One can predict that the star will remain obscured until $\dot{M}$ starts to drop back to lower values. In a few years from that moment, we could probably be witnessing the star (B) reappearing whereas the cavities becoming relatively fainter.

3.3 Dust formation models and the fading of B

In Fig. 6 the resulting temporal evolution of the gas box is depicted for the following parameters: T₀ = 3000 K at a radius $R_{0} = 3.15 \times 10^{13}~$ cm (corresponding to the Stefan-Boltzmann radius for T₀ and a stellar luminosity of $15~000~L_{\odot}$ ), $\alpha = 0.5$ (i.e. an optically thin temperature distribution), $\dot{M} = 10^{-4}~M_{\odot}$ yr^-1 (reflecting a presently increased mass-loss rate of IRC +10216), a constant outflow velocity of v = 15 km s^-1, and a carbon abundance (by number) of $\epsilon_{\rm C} = 1.5 ~ \epsilon_{\rm O}$ .

In the upper panel of Fig. 6 the prescribed time evolution of gas temperature (Eq. (1)) and density (Eq. (2)) in the gas box are shown. The second panel depicts the nucleation rate J_*, i.e. the number of seed particles formed per second and hydrogen nucleus (solid line) and the number of dust grains per hydrogen nucleus (dash-dotted line). In the third panel, the degree of condensation, i.e. the fraction of condensible material that is actually condensed is shown (solid line). The dash-dotted line indicates the optical depth at 2.2 $\mu$ m (measured from the star), that would build up in a stationary situation. To calculate the dust extinction coefficient, we assume the small particle limit of Mie theory. This is justified, since the mean particle radius $\langle a \rangle$ reached after 15 P is $5\times10^{-2}~\mu$ m, giving a maximum size parameter $x = 2 \pi \langle a \rangle / \lambda = 0.14$ at the considered wavelength of $\lambda = 2.2~\mu$ m. The optical properties of the grains are described by the complex refractive index of amorphous carbon tabulated in Preibisch et al. (1993). In the lower panel we plot the normalized intensity at 2.2 $\mu$ m that would emerge along the line of sight from the increasingly obscured radiation source (solid line). This intensity is calculated from the formal solution of the radiative transfer equation:

Here we assume thermal emission of the dust grains (B is the Kirchhoff-Planck function) and normalize the intensity to I₀ = B(T₀).

For comparison, we also plotted in the lower panel of Fig. 6 the observed intensity of component B, normalized to its intensity in our 1997 speckle image (crosses). The intensity of component B fades from its maximum value to 17% of this value within about 1400 d, corresponding to 2.2 pulsation periods of IRC +10216. This time interval is indicated in the lower panel of Fig. 6 by the vertical dashed lines. The comparison shows that dust condensation in front of the star in fact can reproduce the observed time scale of the fading of component B for realistic values of the parameters characterizing our simple toy model.

In Table 2 the timescale $\tau$ of the intensity drop to 17% of the initial value is summarized for various parameter combinations. We note a steep dependence of $\tau$ on the C/O ratio, i.e. on the amount of material available for dust formation. Consistent model calculations for dust driven outflows (e.g., Winters et al. 2000b; Arndt et al. 1997; Dominik et al. 1990) show, that the outflow velocity of a carbon-rich dust-driven wind also depends strongly on the C/O ratio. For the observed outflow velocity of IRC +10216 of $\sim$ 15 km s^-1, C/O ratios in the range $(1.20 \la {\rm C/O} \la 1.60)$ are required. Therefore, Table 2 implies, that the present day mass-loss rate of IRC +10216 in fact should have increased considerably above the "canonical'' value of (a few) $10^{-5}~M_{\odot}$ /yr derived from CO rotational line observations probing the outer and therefore, older parts of the circumstellar shell (e.g., Schöier & Olofsson 2001) or from CO infrared line profiles observed about one decade ago (e.g., Winters et al. 2000a).

Once dust has formed in the circumstellar shell, its opacity would lead to a pronounced backwarming and therefore, to a steeper temperature gradient in the dust formation zone. Accordingly, in our simple gas box model, lower temperatures would be reached at the same density. As a result, dust growth becomes more efficient in this region and a reduced C/O ratio is sufficient to recover the observed fading time scale (see Table 2; compare the corresponding entries for $\alpha = 0.5$ with $\alpha = 0.6$ and 0.7).

A more realistic treatment of the dust formation and mass-loss process in IRC +10216 would require the simultaneous solution of the time dependent hydrodynamic equations, taking into account the pulsation of the star, together with the equations describing the dust formation process and the radiative transfer problem. Such a consistent investigation will be presented in a forthcoming paper.

An alternative interpretation of the fading of component B, together with its increasing separation from A, could be based on a scenario, where the star is located in the direction of component A, as argued in previous studies by Weigelt et al. (1998), Haniff & Buscher (1998), and Tuthill et al. (2000). In this case, component B would indicate thermal emission from a dust cloud, ejected from the star in a direction almost perpendicular to the line of sight. The temporal evolution of the brightness of B would then be the result of a competition between the initially increasing thermal emission due to ongoing dust formation in the cloud and decreasing temperature of the cloud as it is moving away from the star. Preliminary results for this scenario, which are based on a consistent model calculation, are presented in Winters et al. (2002). Although the time scale of the fading of component B is reproduced quite well in this model, the calculated intensity ratio between the expanding cloud and the star is smaller than the observed intensity ratio between components B and A by about a factor of 3.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h3683f21.eps}\end{figure}$

Figure 6: Temporal evolution of the gas box. The time coordinate is given in units of P=649 d, the pulsation period of IRC +10216. Upper panel: gas temperature (Eq. (1), solid line, l.h.s. ordinate) and density (Eq. (2), dash-dotted line, r.h.s. ordinate); second panel: dust nucleation rate J_* (solid line, l.h.s. ordinate) and number of dust grains per hydrogen nucleus (dash-dotted line, r.h.s. ordinate); third panel: degree of condensation $f_{\rm cond}$ (solid line, l.h.s. ordinate) and optical depth at 2.2 $\mu$ m (dash-dotted line, r.h.s. ordinate); lower panel: normalized emergent intensity at 2.2 $\mu$ m (solid line) and observed intensity of component B, normalized to its maximum value (crosses). See text for more details.

Table 2: Parameters of the gas box model and resulting fading time scales for an assumed outflow velocity of v=15 km s^-1.
$\alpha$ T₀ $\rho_{0}$ $\dot{M}$ C/O $\tau$

K 10^-13 g/cm³ $M_{\odot}/$ yr 649 d

0.5 2800 2.95 10^-4 1.5 1.83

0.5 2800 2.95 10^-4 1.4 >13

0.5 2800 2.95 10^-4 1.3 $\rightarrow$ $\infty$

0.5 2500 4.68 10^-4 1.5 0.65

0.5 2500 4.68 10^-4 1.4 1.79

0.5 2500 4.68 10^-4 1.3 $\rightarrow$ $\infty$

0.5 2500 0.47 10^-5 2.1 1.58

0.5 2500 0.47 10^-5 2.0 3.05

0.5 2500 0.47 10^-5 1.9 $\rightarrow$ $\infty$

0.5 3000 3.37 10^-4 1.6 1.04

0.5 3000 3.37 10^-4 1.5 2.22

0.5 3000 3.37 10^-4 1.4 $\rightarrow$ $\infty$

0.4 3000 3.37 10^-4 1.6 2.59

0.4 3000 3.37 10^-4 1.5 7.53

0.6 3000 3.37 10^-4 1.5 1.15

0.6 3000 3.37 10^-4 1.4 5.01

0.7 3000 3.37 10^-4 1.5 0.75

0.7 3000 3.37 10^-4 1.4 2.54

0.7 3000 0.34 10^-5 2.1 2.35

0.7 3000 0.34 10^-5 1.9 9.62

0.7 3000 0.34 10^-5 1.5 $\rightarrow$ $\infty$

3 Discussion