All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4438F1.eps} \end{figure}$ Figure 1: The sticking coefficient $\alpha$ (Eq. (13)) drawn as a function of the drift velocity $\ensuremath{v_{\mathrm{D}}}$ for each of the four hydrocarbon species (upper panel). These species that are all involved in the grain growth rate chemistry are: C (dash-dot-dotted line), $\ensuremath{\mbox{C}_2}$ (dash-dotted line), $\ensuremath{\mbox{C}_2\mbox{H}}$ (dotted line), and $\ensuremath{\mbox{C}_2\mbox{H}_2}$ (solid line). In addition the new/old ratio of the term $\ensuremath{\tilde{w}}\alpha$ is shown in the lower panel. The figure shows that $\alpha$ ( $\ensuremath{\mbox{C}_2\mbox{H}_2}$ ) drops at a much lower drift velocity compared to the other three species, also note the steeply increasing grain formation efficiency (for all species) even at low drift velocities. The relative velocity $\ensuremath{\tilde{w}}$ is calculated using a gas temperature of $\ensuremath{T_{\mathrm{g}}} =1200~$ K. Note, however, that $\ensuremath{\tilde{w}}$ is mostly dependent on the drift velocity when this is high.
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In the text

$\begin{figure} \par\includegraphics{H4438F2a.eps}\hspace*{1mm} \includegraphics... ...aphics{H4438F2c.eps}\hspace*{1mm} \includegraphics{H4438F2d.eps} \end{figure}$ Figure 2: Evolutionary sequence of the radial structure of the drift model P13C16U6-dvs covering five instants of one complete dust formation cycle. The first column shows the dust formation at an arbitrarily selected time defined as (t₀+)0.00 P (in units of the stellar pulsation period). The three following columns are shown at 0.57 P, 1.12 P, and 1.63 P, respectively. The structure of the repeated dust formation cycle at 2.00 P is shown by a solid line in the first column, illustrating the aperiodicity of dust formation in the current model. From the top the panels in each column show: a) the gas velocity u; b) the gas density $\rho$ ; c) the gas temperature $\ensuremath{T_{\mathrm{g}}}$ ; d) the drift velocity $\ensuremath{v_{\mathrm{D}}}$ ; e) the degree of condensation $\ensuremath{f_{\mathrm{cond}}}$ ; f) the dust/gas density ratio $\ensuremath{\rho_{\mathrm{d}}/\rho}$ ; and g) the net growth rate $\tau ^{-1}$ . All panels are shown at the same scale in all four columns. The process illustrated in this figure shows that a nonzero drift velocity allows for the formation of narrow features in the dust already in the inner parts of the wind, cf. Sect. 4.1.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,height=13cm]{H4438F3a.eps}... ...e{0.2cm} \includegraphics[width=5.6cm,height=13cm]{H4438F3b.eps} }\end{figure}$ Figure 3: Illustration of the effects of drift in the inner parts of the stellar wind of model P13C16U6-d__ (solid line) and P13C16U6-dvs (dotted filled line). The panels show: a) the gas velocity u; b) the drift velocity $\ensuremath{v_{\mathrm{D}}}$ ; c) the dust density $\ensuremath{\rho_{\mathrm{d}}}$ ; d) the average grain radius $\ensuremath{\langle r_{\mathrm{d}}\rangle}$ ; e) the gas temperature $\ensuremath{T_{\mathrm{g}}}$ ; f) the chemical growth (without sputtering) $\tau_{{\rm gr,c}}^{-1}(\mbox{C}_2\mbox{H})$ normalized to the net growth rate (excepting non-thermal sputtering) $\tau _{{\rm G}}^{-1}$ ; g) the nucleation rate J_*; h) the chemical growth (without sputtering) $\tau_{{\rm gr,c}}^{-1}(\mbox{C}_2\mbox{H}_2)$ , also normalized (see f); i) the net growth rate excepting non-thermal sputtering $\tau _{{\rm G}}^{-1}$ (Eq. (19)); and j) the non-thermal sputtering $\tau ^{-1}_{{\rm sp,n}}$ (Eq. (14)). All plots are drawn as a function of the stellar radius R_* (lower axis), alternatively in astronomical units (upper axis). The dots on the contour represent individual grid points, a majority of which are located to the shocked regions. The gray horizontal lines are guides. Acetylene is normally the main growth species ( h) in the outer cool and dilute regions of the wind (modeled here). However, when the drift velocity is larger than about 10 $\ensuremath{\,\mbox{km}\,\mbox{s}^{-1}}$ ( b) the sticking coefficient $\alpha$ for acetylene quickly drops to zero (see Fig. 1), and the radical $\ensuremath{\mbox{C}_2\mbox{H}}$ takes over this role ( f). Note that non-thermal sputtering (by helium; j) is present when the drift velocity reaches about 30-35 $\ensuremath{\,\mbox{km}\,\mbox{s}^{-1}}$ .
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In the text