All Figures

$\begin{figure} \par\includegraphics[angle=-90,width=11.8cm,clip]{h4695_Fig01.ps} % \end{figure}$ Figure 1: The Hertzsprung-Russell diagram with the evolutionary tracks of hydrogen-burning AGB remnants, computed consistently by Blöcker (1995b) for different initial masses (3 $M_{\odot }$ to 7 $M_{\odot }$ ) through all relevant phases including mass loss. The two lowest-mass tracks (0.565 and 0.546 $M_{\odot }$ ) are from Schönberner (1983) and have initial masses of 1 and 0.8 $M_{\odot }$ , resp. The isochrones are labeled in units of 10³ years, and the zero points of the post-AGB ages are at the beginnings of the tracks in the right upper corner of the diagram. They correspond to the (fundamental) radial pulsation period of 50 days for the Blöcker models, and to $T_{\rm eff} = 5000\ {\rm K}$ for the Schönberner models.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig02.ps} \end{figure}$ Figure 2: Initial AGB wind-envelope structures: heavy particle densities (thick), electron densities (dotted), and flow velocities (thin) as a function of radius. Envelope and stellar parameters are given in the individual panels. Top: example of an AGB model with constant mass-loss rate and wind speed (T YPE A). Middle panels: density structures caused by mass-loss variations close to the tip of the AGB, assuming a constant wind speed of 10 km s^-1 (see Blöcker 1995a, Fig. 7 therein, and Calonaci 2000 for details). The density modulations are signatures of the last thermal pulses on the AGB (T YPE B). Bottom: density and velocity profiles resulting from full hydrodynamical simulations along the upper AGB (Steffen et al. 1998). The large density trough at $\sim$ $10^{18}~ {\rm cm}$ is due to the last thermal pulse 40 000 years before the star left the AGB (T YPE C).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=11.7cm,clip]{h4695_Fig03a.ps... ...3mm} \includegraphics[angle=-90,width=11.7cm,clip]{h4695_Fig03b.ps} \end{figure}$ Figure 3: Top panels: evolutionary path for the 0.605 $M_{\hbox {$\odot $ }}$ post-AGB model with ages indicated (left), and the corresponding photon and wind luminosity, $\dot{M}\cdot V^2/2$ (dashed line) vs. time (right). Bottom panels: mass-loss rate (left) and wind velocity (right).
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{h4695_Fig04.ps} \end{figure}$ Figure 4: Position-time diagram for sequence 3 of Table 1 where at each time the logarithm of the normalized density $\rho (r,t)/\rho _{\rm max}(t)$ is displayed. High-density regions are bright, low-density regions dark. The degree of hydrogen ionization is indicated by the black contour lines. The white line delineates the radial position of the inner shock which thermalizes the central-star wind. The following regions can clearly be distinguished (from right to left): the undisturbed AGB matter, either neutral or ionized (halo), "shell'' and "rim'' of the planetary nebula proper, the hot, shocked central-star wind (so-called hot bubble), bounded by the inner shock and the contact discontinuity, the latter being the interface which separates the hot bubble from the PN, and the undisturbed central-star wind. See text for a more thorough discussion of the different structures and how they evolve with time.
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In the text

$\begin{figure} \par\includegraphics[width=16.8cm,clip]{h4695_Fig05.ps} \end{figure}$ Figure 5: Radial run of heavy particle density (solid), electron density (dashed), velocity, temperature (solid) and (thermal) pressure (dashed) for sequence No. 3 at t=748 yr, with stellar parameters of $T_{\rm eff} = 10~051~{\rm K}$ and $L = 6~310~{L}_{\odot}$ (proto-planetary nebula stage).
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In the text

$\begin{figure} \par\includegraphics[width=16.6cm,clip]{h4695_Fig06.ps} \end{figure}$ Figure 6: Same as in Fig. 5 but for t=1 286 yr, and $T_{\rm eff} = 20~681~{\rm K}$ , $L = 6~310~{L}_{\odot}$ (ionization phase). The very thin shell of shocked central-star wind material with $\simeq$ $20~000~{\rm K}$ shown in Fig. 5 at $0.26\times 10^{17}$ cm has changed now to a more extended hot bubble with $\simeq$ $2\times 10^{6}~{\rm K}$ .
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{h4695_Fig07a.ps}\par\vspace*{4mm} \includegraphics[width=16cm,clip]{h4695_Fig07b.ps} \end{figure}$ Figure 7: Same as in Fig. 5 but for t=2 939 yr, $T_{\rm eff} = 49~225~{\rm K}$ , $L = 6~177~{L}_{\odot}$ ( top), and t=7 138 yr, $T_{\rm eff} = 156~675~{\rm K}$ , $L = 2~038~{L}_{\odot}$ ( bottom), at maximum effective temperature of the track (compression phase). Note the different radial coverage of the top and bottom panels.
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In the text

$\begin{figure} \par\includegraphics[width=16.4cm,clip]{h4695_Fig08.ps} \end{figure}$ Figure 8: Same as in Fig. 5 but for t=9 966 yr and $T_{\rm eff} = 122~019~{\rm K}$ , $L = 244~{L}_{\odot},$ showing a phase after re-ionization has succeeded in reshaping the inner parts of the PN.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig09.ps} \end{figure}$ Figure 9: From top to bottom: heavy particle densities (thick), electron densities (dotted), and flow velocities (thin) for models of the sequences Nos. 2, 3, 4, 5 of Table 1 (C ASE I) at P HASE I when the AGB wind envelopes are still neutral while the central-star winds are already ionized. Model and star parameters are given in the individual frames.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig10.ps} \end{figure}$ Figure 10: From top to bottom: models of the sequences Nos. 2, 3, 4, 5 of Table 1 (T YPE I) at P HASE II when the central star is 3 000 years old and about $T_{\rm eff} = 50~000~{\rm K}$ hot. Now all the matter within the computational regime is fully ionized, except in the model of seq. 4 where the ionization front is still trapped (dashed: electron density). All the optically thin models show well developed double-shell structures. The maximum flow velocities, however, are quite small, around $\simeq$ 20 km s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=8.6cm,clip]{h4695_Fig11.ps} \end{figure}$ Figure 11: From top to bottom: models of the sequences Nos. 2, 3, 4, 5 of Table 1 (C ASE I) at P HASE III when the central star is at the turn-around point (maximum effective temperatures of 156 000 K) after 7100 years of post-AGB evolution.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{h4695_Fig12.ps} \end{figure}$ Figure 12: From top to bottom: models of the sequences Nos. 2, 3, 4, 5 of Table 1 (C ASE I) at P HASE IV after about 10 000 years when the central-star luminosity has approached the beginning of the white-dwarf cooling path, $L=240~{L}_{\odot}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig13a.ps}\par\vspac... ...vspace*{3mm} \includegraphics[width=8.8cm,clip]{h4695_Fig13c.ps} \end{figure}$ Figure 13: Models of sequences Nos. 11 and 12 at three evolutionary stages. Line types are the same as before: particle densities (thick), electron densities (dotted), and flow velocities (thin). Note the different range of the radial scales and the flow velocities. Top: compression phase at $T_{\rm eff} \simeq 50~000~{\rm K}$ (P HASE II). Middle: near the turn-around point at maximum compression (P HASE III). Bottom: recombination/reionization at low central-star luminosities (P HASE IV).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig14a.ps}\par\vspac... ...pace*{3mm} \includegraphics[width=8.8cm,clip]{h4695_Fig14c.ps} %\end{figure}$ Figure 14: Models of sequences Nos. 21 and 22 at three evolutionary phases. Top: $T_{\rm eff}\simeq$ 30 000 K, middle: $T_{\rm eff}\simeq$ 50 000 K (P HASE II), and bottom: $T_{\rm eff}\simeq$ 121 000 K (turn-around point, P HASE III). Line types have the same meaning as in the previous figures.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig15.ps} \end{figure}$ Figure 15: Nebular structures at $T_{\rm eff}=50~000$ K, (P HASE II) for the same AGB starting T YPE A envelope but different central-star masses, from M=0.940 ( top), M=0.836 ( middle) to M=0.696 $M_{\odot }$ ( bottom), corresponding to sequences Nos. 14, 12, 10 of Table 1 (C ASE II).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig16.ps} \end{figure}$ Figure 16: P HASE II as in Fig. 15, but for lower stellar masses, from M=0.696 ( top), M=0.625 ( middle) to $M=0.605~{M}_\odot$ ( bottom), corresponding to sequences Nos. 10, 8, 5 of Table 1. Note the different radial coverage. The top frame contains the same model as the bottom frame of Fig. 15 for comparison. Note also that the bottom frame of this figure is the same as in Fig. 10.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig17.ps} \end{figure}$ Figure 17: Position-time diagram of seq. No. 8 ( $M = 0.625~{M}_{\odot}$ ) with the logarithm of the normalized density $\rho (r,t)/\rho _{\rm max}(t)$ coded as grey scales: highest densities white, lowest densities black. The black contour lines indicate the degree of hydrogen ionization, the white line marks the position of the fast wind shock. The inward hook in the position of this shock at 3600 years is due to the rapid fading of the central star.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig18.ps} \end{figure}$ Figure 18: Same as in Fig. 17, but for seq. No. 9 ( $M = 0.696~{M}_{\odot}$ ). Due to the fast fading of this central-star model, the reverse shock of the fast wind jumps inwards after only 1 000 years of post-AGB evolution.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig19.ps} \end{figure}$ Figure 19: Same as in Fig. 17, but for seq. No. 7 ( $M = 0.625~{M}_{\odot}$ ). Here the white-dwarf evolution begins at 3000 years after the model has left the tip of the AGB.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig20.ps} \end{figure}$ Figure 20: Same as in Fig. 17, but for seq. 6, the detailed hydrodynamic treatment of the AGB wind envelope for $M=0.605~{M}_\odot$ . In this particular case we have plotted the logarithm of density times radius squared, $\rho(r,t)~r^2/\rho_{\rm max}(t)~r^2$ , in order to highlight the low-density structures in the halo.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{h4695_Fig21a.ps}\vspace*{3... ...s}\vspace*{3mm} \includegraphics[width=8.4cm,clip]{h4695_Fig21d.ps} \end{figure}$ Figure 21: Density and velocity structure for various snapshots along sequence No. 6 shown in Fig. 20. The stellar parameters are given in the individual panels. The models selected are for a still optical thick case ( top), for the turn-around position ( next to top), during the recombination phase ( next to bottom), and for a very late, reionized stage ( bottom).
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{h4695_Fig22.ps} \end{figure}$ Figure 22: Expansion properties of the "rim'' for seq. No. 6 (hydrodynamical simulation). Shown are the speeds of the contact discontinuity (dotted) and of the leading shock front (dashed) vs. time, together with the "Doppler'' velocity (thick). The latter is the mean flow velocity within the "rim'', weighted along the central line of sight by density squared and corresponds to the value one would derive from the Doppler split of emission lines. The somewhat erratic velocity changes of the shock front are due to numerical problems in finding the exact shock position. Below 3000 yrs the resp. velocities are not plotted because the whole model is optically thick and the double-shell structure not well developed.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig23a.ps}\hspace*{3mm} \includegraphics[width=8cm,clip]{h4695_Fig23b.ps} \end{figure}$ Figure 23: Surface-brightness in H $\alpha$ of selected models of the sequences Nos. 2, 3, 5, and 6 (from top to bottom, cf. also Table 1), for $T_{\rm eff} \simeq 50~000~{\rm K}$ (P HASE II, left) and $T_{\rm eff} \simeq 156~000~{\rm K}$ (P HASE III, right). The corresponding model structures are shown in Figs. 10, 11, and 21, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=11.8cm,clip]{h4695_Fig24.ps} \end{figure}$ Figure 24: "Shell'' radii, $R_{\rm o}$ , over "rim'' radii, $R_{\rm i}$ , vs. "rim'' radii for double-shell PNe as adapted from Chu et al. (1987) (filled circles). The data set is supplemented by southern objects collected by Stanghellini & Pasquali (1995) (small asterisks), and by 4 LMC objects drawn from the list of Shaw et al. (2001) (large asterisks). The theoretical predictions as taken from our different hydrodynamical simulations are shown for comparison. The parameters of the sequences are given in the legend: central-star mass, mass-loss rate (in $M_{\odot }$ /yr), and AGB-wind velocity (in km s^-1).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=11.7cm,clip]{h4695_Fig03a.ps... ...3mm} \includegraphics[angle=-90,width=11.7cm,clip]{h4695_Fig03b.ps} \end{figure}$	Figure 3: Top panels: evolutionary path for the 0.605 $M_{\hbox {$\odot $ }}$ post-AGB model with ages indicated (left), and the corresponding photon and wind luminosity, $\dot{M}\cdot V^2/2$ (dashed line) vs. time (right). Bottom panels: mass-loss rate (left) and wind velocity (right).
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$\begin{figure} \par\includegraphics[width=16.8cm,clip]{h4695_Fig05.ps} \end{figure}$	Figure 5: Radial run of heavy particle density (solid), electron density (dashed), velocity, temperature (solid) and (thermal) pressure (dashed) for sequence No. 3 at t=748 yr, with stellar parameters of $T_{\rm eff} = 10~051~{\rm K}$ and $L = 6~310~{L}_{\odot}$ (proto-planetary nebula stage).
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$\begin{figure} \par\includegraphics[width=16.6cm,clip]{h4695_Fig06.ps} \end{figure}$	Figure 6: Same as in Fig. 5 but for t=1 286 yr, and $T_{\rm eff} = 20~681~{\rm K}$ , $L = 6~310~{L}_{\odot}$ (ionization phase). The very thin shell of shocked central-star wind material with $\simeq$ $20~000~{\rm K}$ shown in Fig. 5 at $0.26\times 10^{17}$ cm has changed now to a more extended hot bubble with $\simeq$ $2\times 10^{6}~{\rm K}$ .
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$\begin{figure} \par\includegraphics[width=16cm,clip]{h4695_Fig07a.ps}\par\vspace*{4mm} \includegraphics[width=16cm,clip]{h4695_Fig07b.ps} \end{figure}$	Figure 7: Same as in Fig. 5 but for t=2 939 yr, $T_{\rm eff} = 49~225~{\rm K}$ , $L = 6~177~{L}_{\odot}$ ( top), and t=7 138 yr, $T_{\rm eff} = 156~675~{\rm K}$ , $L = 2~038~{L}_{\odot}$ ( bottom), at maximum effective temperature of the track (compression phase). Note the different radial coverage of the top and bottom panels.
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$\begin{figure} \par\includegraphics[width=16.4cm,clip]{h4695_Fig08.ps} \end{figure}$	Figure 8: Same as in Fig. 5 but for t=9 966 yr and $T_{\rm eff} = 122~019~{\rm K}$ , $L = 244~{L}_{\odot},$ showing a phase after re-ionization has succeeded in reshaping the inner parts of the PN.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig09.ps} \end{figure}$	Figure 9: From top to bottom: heavy particle densities (thick), electron densities (dotted), and flow velocities (thin) for models of the sequences Nos. 2, 3, 4, 5 of Table 1 (C ASE I) at P HASE I when the AGB wind envelopes are still neutral while the central-star winds are already ionized. Model and star parameters are given in the individual frames.
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$\begin{figure} \par\includegraphics[width=8.6cm,clip]{h4695_Fig11.ps} \end{figure}$	Figure 11: From top to bottom: models of the sequences Nos. 2, 3, 4, 5 of Table 1 (C ASE I) at P HASE III when the central star is at the turn-around point (maximum effective temperatures of 156 000 K) after 7100 years of post-AGB evolution.
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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{h4695_Fig12.ps} \end{figure}$	Figure 12: From top to bottom: models of the sequences Nos. 2, 3, 4, 5 of Table 1 (C ASE I) at P HASE IV after about 10 000 years when the central-star luminosity has approached the beginning of the white-dwarf cooling path, $L=240~{L}_{\odot}$ .
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig14a.ps}\par\vspac... ...pace*{3mm} \includegraphics[width=8.8cm,clip]{h4695_Fig14c.ps} %\end{figure}$	Figure 14: Models of sequences Nos. 21 and 22 at three evolutionary phases. Top: $T_{\rm eff}\simeq$ 30 000 K, middle: $T_{\rm eff}\simeq$ 50 000 K (P HASE II), and bottom: $T_{\rm eff}\simeq$ 121 000 K (turn-around point, P HASE III). Line types have the same meaning as in the previous figures.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig15.ps} \end{figure}$	Figure 15: Nebular structures at $T_{\rm eff}=50~000$ K, (P HASE II) for the same AGB starting T YPE A envelope but different central-star masses, from M=0.940 ( top), M=0.836 ( middle) to M=0.696 $M_{\odot }$ ( bottom), corresponding to sequences Nos. 14, 12, 10 of Table 1 (C ASE II).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{h4695_Fig16.ps} \end{figure}$	Figure 16: P HASE II as in Fig. 15, but for lower stellar masses, from M=0.696 ( top), M=0.625 ( middle) to $M=0.605~{M}_\odot$ ( bottom), corresponding to sequences Nos. 10, 8, 5 of Table 1. Note the different radial coverage. The top frame contains the same model as the bottom frame of Fig. 15 for comparison. Note also that the bottom frame of this figure is the same as in Fig. 10.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig18.ps} \end{figure}$	Figure 18: Same as in Fig. 17, but for seq. No. 9 ( $M = 0.696~{M}_{\odot}$ ). Due to the fast fading of this central-star model, the reverse shock of the fast wind jumps inwards after only 1 000 years of post-AGB evolution.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig19.ps} \end{figure}$	Figure 19: Same as in Fig. 17, but for seq. No. 7 ( $M = 0.625~{M}_{\odot}$ ). Here the white-dwarf evolution begins at 3000 years after the model has left the tip of the AGB.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig20.ps} \end{figure}$	Figure 20: Same as in Fig. 17, but for seq. 6, the detailed hydrodynamic treatment of the AGB wind envelope for $M=0.605~{M}_\odot$ . In this particular case we have plotted the logarithm of density times radius squared, $\rho(r,t)~r^2/\rho_{\rm max}(t)~r^2$ , in order to highlight the low-density structures in the halo.
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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{h4695_Fig21a.ps}\vspace{3... ...s}\vspace{3mm} \includegraphics[width=8.4cm,clip]{h4695_Fig21d.ps} \end{figure}$	Figure 21: Density and velocity structure for various snapshots along sequence No. 6 shown in Fig. 20. The stellar parameters are given in the individual panels. The models selected are for a still optical thick case ( top), for the turn-around position ( next to top), during the recombination phase ( next to bottom), and for a very late, reionized stage ( bottom).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{h4695_Fig23a.ps}\hspace*{3mm} \includegraphics[width=8cm,clip]{h4695_Fig23b.ps} \end{figure}$	Figure 23: Surface-brightness in H $\alpha$ of selected models of the sequences Nos. 2, 3, 5, and 6 (from top to bottom, cf. also Table 1), for $T_{\rm eff} \simeq 50~000~{\rm K}$ (P HASE II, left) and $T_{\rm eff} \simeq 156~000~{\rm K}$ (P HASE III, right). The corresponding model structures are shown in Figs. 10, 11, and 21, respectively.
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