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$\begin{figure} \par\includegraphics[width=17.8cm,clip]{H4181F1.eps} \end{figure}$ Figure 1: Ratios of four of the drift/PC model quantities given in Tables 4 and 5 plotted as a function of the respective PC model quantity. From the left the averaged quantities are: a) the mass loss rate $\ensuremath{\langle\dot{M}\rangle}$ ; b) the terminal velocity $\ensuremath{\langle u_{\infty}\rangle}$ ; c) the degree of condensation $\ensuremath{\langle f_{{\rm cond}}\rangle}$ ; and d) the dust/gas density ratio $\ensuremath{\langle\ensuremath{\rho_{{\rm d}}/\rho}\rangle}$ . Note that all plots are logarithmic on the y-axis and of the same scale. Only models where both PC models and drift models have formed a wind are shown. The ratios of constant-opacity models are represented by open circles $\circ$ , and Planck mean models by filled squares $\blacksquare$ , respectively. The two constant-opacity models showing an increased mass loss rate when allowing drift are indicated in all panels with the symbol $\circledcirc$ . The region enclosed by the horizontal lines, $\rm0.9\le ratio \le 1.1$ , indicates an insignificant decrease/increase of the respective ratio. Note that each set of constant-opacity models and Planck mean models tend to form groups; excepting the two " $\circledcirc$ '' models.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H4181F2.eps} \end{figure}$ Figure 2: Model average quantities as a function of the mass loss rate $\ensuremath{\langle\dot{M}\rangle}$ . The panels show: a) and b) the degree of condensation $\ensuremath{\langle f_{{\rm cond}}\rangle}$ ; c) and d) the optical depth of the dust $\ensuremath{\langle\tau_{{\rm d}}\rangle}$ . The panels on the left show PC models (open symbols) and the panels on the right drift models (filled symbols). Furthermore, constant-opacity models are represented by circles, stars, and downwards pointing triangles ( $\circ ,\oplus ,\circledcirc ,\bullet ,\ensuremath {\star } ,\ensuremath {\blacktriangledown }$ ), and Planck mean models by squares and upwards pointing triangles ( $\Box,\boxplus,\ensuremath{\textcolor{mygray}{\blacksquare}} ,\ensuremath{\textcolor{mygray}{\blacktriangle}}$ ). A key to the symbols is given just before Sect. 4.1, and in Tables 4-6. Note that the PC models without a corresponding drift model wind (indicated by $\oplus$ and $\boxplus$ ) all have low mass loss rates. The drift models are as a group better correlated with the mass loss rate in the degree of condensation ( b)) than the PC models are ( a)).
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H4181F3.eps} \end{figure}$ Figure 3: Model average quantities as a function of $\ensuremath{\langle\hat{\alpha}\rangle}$ , a quantity characterizing the strength of the radiation pressure relative to the gravitation. The panels show: a) and b) the mass loss rate $\ensuremath{\langle\dot{M}\rangle}$ and c) and d) the terminal velocity $\ensuremath{\langle u_{\infty}\rangle}$ . The panels on the left show PC models (open symbols) and the panels on the right driftmodels (filled symbols). Furthermore, constant-opacity models are represented by circles, stars, and downwards pointing triangles ( $\circ ,\oplus ,\circledcirc ,\bullet ,\ensuremath {\star } ,\ensuremath {\blacktriangledown }$ ), and Planck mean models by squares and upwards pointing triangles ( $\Box,\boxplus,\ensuremath{\textcolor{mygray}{\blacksquare}} ,\ensuremath{\textcolor{mygray}{\blacktriangle}}$ ). A key to the symbols is given just before Sect. 4.1, and in Tables 4-6. Note that the PC models without a corresponding drift model (indicated by $\oplus$ and $\boxplus$ ) all are grouped in the lower-left corners in a) and c). The Planck mean and constant-opacity PC models are clearly more separated as groups compared to the corresponding (opacity) groups of the drift models. Also compare c) with Fig. 3 in HD97.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=8.6cm,clip]{H4181F4a.eps} \hspace*{1mm} \includegraphics[width=8.8cm,clip]{H4181F4b.eps} } \end{figure}$ Figure 4: Radial structure of the inner parts of the wind for the drift (solid line) and PC (dash-dot-dotted line) models R10FU2C18. The panels show: a) the gas velocity u; b) the average grain radius $\langle r_{{\rm d}}\rangle$ ; c) the gas density $\rho$ ; d) the degree of condensation $\ensuremath {f_{{\rm cond}}}$ ; e) the drift velocity $\ensuremath {v_{{\rm D}}}$ ; and f) the grain/gas number density ratio $n_{{\rm d}}/n_{{\rm g}}$ . The accumulation of the dust to regions behind shocks in drift models is seen in e.g. the dust/gas number density ratio ( f) and the degree of condensation ( d). Note the larger variations in the dust quantities of the drift model (right panels).
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=8.7cm,clip]{H4181F5a.eps} \hspace*{1mm} \includegraphics[width=8.8cm,clip]{H4181F5b.eps} } \end{figure}$ Figure 5: The temporal evolution at the outer boundary. The panels on the l.h.s. show the constant-opacity drift and PC models R13FU4C14 (solid and dash-dot-dotted lines, respectively), and the panels on the r.h.s. the Planck mean drift and PC models P13FU6C14 (solid and dash-dot-dotted lines, respectively). With the exception of the piston amplitude $\Delta {u}_{\rm p}$ , which is larger in the Planck mean models, all other model parameters are the same. The panels show (from the top): the terminal velocity $u_{\infty }$ ; the mass loss rate $\dot{M}$ ; the degree of condensation $f_{{\rm cond}}$ ; the dust/gas density ratio $\ensuremath {\rho _{{\rm d}}/\rho }$ ; the mean grain radius $\langle r_{{\rm d}}\rangle$ ; and the drift velocity $v_{{\rm D}}$ . Note the much larger variations present in both drift models compared to the PC models, also compare with Fig. 6.
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In the text

$\begin{figure} \par\includegraphics[width=17.9cm,clip]{H4181F6.eps} \end{figure}$ Figure 6: Temporal variations of average properties (q) measured by the fluctuation amplitude $r=\ensuremath {\sigma _{{\rm s}}} /q$ (Sect. 5.2). From the left the figure shows: a) the mass loss rate $\ensuremath{\langle\dot{M}\rangle}$ ; b) the terminal velocity $\ensuremath{\langle u_{\infty}\rangle}$ ; c) the degree of condensation $\ensuremath{\langle f_{{\rm cond}}\rangle}$ ; and d) the dust optical depth $\ensuremath{\langle\tau_{{\rm d}}\rangle}$ . All plots are drawn to the same scale. Filled symbols represent drift models (lower panels) and open symbols PC models (upper panels). constant-opacity models are represented by circles, stars, and downwards pointing triangles ( $\circ ,\oplus ,\circledcirc ,\bullet ,\ensuremath {\star } ,\ensuremath {\blacktriangledown }$ ), and Planck mean models by squares and upwards pointing triangles ( $\Box,\boxplus,\ensuremath{\textcolor{mygray}{\blacksquare}} ,\ensuremath{\textcolor{mygray}{\blacktriangle}}$ ). Furthermore, PC models without a corresponding drift model for the same set of model parameters are indicated with the symbol $\oplus$ or $\boxplus$ . Models for which the drift models have a larger average mass loss rate are indicated with open rings ( $\circledcirc$ ; PC models), and stars ( $\star$ ; drift models). Triangles represent G-models (cf. Sect. 5.1). Note the distinctly smaller scattering and larger variations of the values of the drift models compared to the values of the PC models.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4181F7.eps}} \end{figure}$ Figure 7: Ratios of the average mass loss rates $\ensuremath{\langle\dot{M}\rangle}$ to the mass loss fit $\dot{M}_{{\rm fit}}$ given in Eq. (9) as a function of: a) and c) the effective temperature $T_{{\rm eff}}$ ; and b) and d) the stellar luminosity L. The upper panels show PC model ratios and the lower panels additionally drift model ratios (for comparison). The plot symbols are the same as in Fig. 6. The horizontal lines indicate the mean ratio for each type of model wind. This figure (specifically the shaded region) should be compared with Figs. 1b, c in Wachter et al. (2002). The Planck mean models are drawn in light gray symbols in the upper panels to emphasize that Eq. (9) is derived for constant-opacity PC models; cf. Sect. 5.3.
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In the text

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{H4181F8.eps}} \end{figure}$ Figure 8: Radial structure of the Planck mean model P10FU6C18 (solid line) and the constant-opacity model R10FU2C18 (dash-dot-dotted line). The shown quantities are: a) the gas velocity; b) the gas density; c) the drift velocity; d) the drag force; e) and f) the energy ratios (see Sect. 5.4). This figure illustrates the importance of the heating by drift ( $\ensuremath {q_{{\rm drift}}}$ ) for the energy balance of the respective model. The heating by drift is negligible in most parts of the Planck mean model (lowermost two panels). On the contrary it is comparable in magnitude to the other energy source terms in the constant-opacity model. Even so we do not find any significant effect on the wind structures caused by this term, cf. Sect. 5.4.
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In the text