All Figures

$\begin{figure} \par\includegraphics[width=12cm,clip]{3108-01.eps}\end{figure}$ Figure 1: Top: evolutionary path for the 0.595 $M_{\hbox {$\odot $ }}$ post-AGB model with ages indicated (left), and the corresponding photon and wind luminosity, $L_{\rm wind}=\dot{M}\cdot V^2/2$ (dashed line) vs. time (right). Bottom: mass-loss rate (left) and wind velocity (right). The end of the strong AGB wind sets the zero point of the post-AGB evolution and the beginning of the much weaker post-AGB winds.
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In the text

$\begin{figure} \resizebox{8.8cm}{4cm}{\includegraphics[bb = 2.2cm 23.5cm 16.7cm 29.cm] {3108-02.ps}}\end{figure}$ Figure 2: Initial model used in this paper. Plotted are the density of the heavy particles (thick), of the electrons (dotted), and the flow velocity (thin) against the distance from the central star.
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In the text

$\begin{figure} \par\scalebox{0.90}{\parbox{18cm}{ \includegraphics[width=15.5cm,... ...space*{1.5mm} \includegraphics[width=15.5cm,clip]{3108-03d.eps} } }\end{figure}$ Figure 3: Heavy-particle density (thick), electron density (dotted), and velocity field (thin) together with the [O III] and [N II] surface brightnesses and emission-line profiles of hydrodynamical models at selected positions along the horizontal part of the 0.595 $M_{\odot }$ post-AGB evolutionary track shown in Fig. 1. The line profiles are computed for the central line-of-sight with infinite spectral resolution and are normalized to their maximum value. The circular aperture has a radius of $1\times 10^{16}$ cm. In the structure and surface-brightness panels, the positions of the leading shock fronts of rim and shell are indicated by thick vertical lines, while the thin horizontal lines (solid and dashed) correspond to the thin vertical lines in the profile panels. They indicate the typical flow velocities within the individual shells as the result of the Gaussian decomposition of the total emission-line profiles. The stellar parameters along the 0.595 $M_{\odot }$ track from Fig. 1 are as follows: t=3 364 yr, $T_{\rm eff}=39~297$ K, L=5 545 $L_{\odot }$ (top); t=4 538 yr, $T_{\rm eff}=54~526$ K, L=5 417 $L_{\odot }$ (next to top); t=7 027 yr, $T_{\rm eff}=98~393$ K, L=4 650 $L_{\odot }$ (next to bottom); t=9 104 yr, $T_{\rm eff}=139~923$ K, L=2 844 $L_{\odot }$ (bottom). Note the different radial extents of the structure and surface-brightness plots.
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In the text

$\begin{figure} \resizebox{17cm}{!} {\includegraphics*[bb= 0 0 581 390]{3108-04.eps}}\end{figure}$ Figure 4: Detailed illustration of how the kinematical properties of our model PN from Fig. 3 develop with time while the central star evolves across the HR diagram as shown in Fig. 1. Material velocities are indicated by V, motions of structures by $\dot{R}$ , with R indicating their radial position. All velocities are measured in the rest frame of the central star. The dotted vertical lines correspond to the models selected for the presentation in Fig. 3. On the left, the properties of the shell are given, on the right those of the rim. The following variables are displayed:
Top, left: for the shell, the velocities (in the stellar rest frame) of the shock front, $\dot{R}_{\rm shell}$ , the postshock flow, $V_{\rm post}$ , and those as measured by decomposition of the synthetic line profiles of [N II] and [O III] resp., are given. The subscript "post'' refers to the maximum velocity reached after the passage of the shell's shock front, corresponding to the end of the shock's relaxation zone (see also Fig. 3). However, during the optically-thick stage, t < 4000 yr, shock and ionization front are so close that the electron temperature immediately behind the shock front is fully determined by photo-ionization, and the shock relaxation zone does not exists. Also in this case "post'' refers to the maximum speed of the flow behind the shock front.
Top, right: corresponding velocities for the rim, except that instead of the post-shock velocity we plotted its pre-shock velocity, $V_{\rm pre}$ , and added also the speed of the contact discontinuity, $\dot{R}_{\rm cd}$ .
Middle: mach numbers of the resp. shocks, $M=(\dot{R}-V_{\rm pre})/C_{\rm s}$ , with $C_{\rm s}$ being the (isothermal) sound speed ahead of the shock, and the ratios between shock speed and corresponding gas velocity as measured by means of a "Doppler'' split emission line, $F = \dot{R}/V$ .
Bottom: kinematic ages, $t_{\rm kin}$ , determined from various combinations of shock positions and velocities vs. the "true'' evolutionary age. The dashed line is the 1:1 relation.
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In the text

$\begin{figure} \includegraphics[width=8.5cm,clip]{3108-05.eps}\end{figure}$ Figure 5: Radial displacements of shell, rim and contact surface of a model PN as a function of time. Plotted are $R_{\rm shell}$ , $R_{\rm rim}$ , and $R_{\rm cd}$ from Fig. 4. The dotted curves represent fits to $R_{\rm rim}$ and $R_{\rm cd}$ of the form R=R₀+c (t-t₀)^b (see text). The parameters for $R_{\rm rim}$ are R₀= 0.031 pc, t₀=3016 yr, $c=6.70\times10^{-7}~ {\rm pc}/{\rm yr}^b$ , and b=1.40, and those for $R_{\rm cd}$ are R₀=0.016 pc, t₀=2039 yr, $c=2.93\times10^{-9}~ {\rm pc}/{\rm yr}^b$ , and b=1.95.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{3108-06.eps}\end{figure}$ Figure 6: Comparison of different kinematical ages derived from the shell radius. They are computed from our hydrodynamical models and plotted as a function of their real evolutionary age. The curves for $R_{\rm shell}/V_{\rm shell}$ are the same as in Fig. 4 and are given for comparison. The dashed line indicates the 1:1 correspondence.
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In the text

$\begin{figure} \par\includegraphics[width=3.75cm,clip]{3108-07a.eps}\hspace*{5mm... ...}\hspace*{5mm} \includegraphics[width=3.75cm,clip]{3108-07d.eps}\par\end{figure}$ Figure 7: Top: normalized surface brightness distributions in [O III] of three selected planetary nebulae from HST monochromatic images (F502N), with effective temperatures of their central stars increasing from left to right (cf. Table 1). For NGC 3242 the He II image (F469N) is added. The cuts are taken along or close to the minor axes and scaled to the model sizes. Bottom: normalized surface-brightness distributions in [O III] 5007 Å (and additionally in He II 4686 Å in the case of NGC 3242) for selected hydrodynamical models that match the observations as closely as possible. The positions of the models along the track shown in Fig. 1 are ( from left to right) at $T_{\rm eff} = 67~250, 74~287, \mbox{and}\ 88~628$ K.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{3108-08.eps}\end{figure}$ Figure 8: Spectroscopic expansion velocities of the objects from Table 1 compared with predictions from the models used in Fig. 7. The dashed line is the 1:1 relation.
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In the text

$\begin{figure} \includegraphics*[bb= 20 5 453 430, width=8.5cm,clip]{3108-09.eps}\end{figure}$ Figure 9: Top: radial H $\beta$ surface-brightness profiles, normalized to maximum emission, of selected hydrodynamical models with a massive central star of 0.696 $M_{\odot }$ (sequence No. 10 in Paper I) plotted as a double logarithmic presentation. The corresponding model structures (except that with t= 900 yr) are shown in Fig. A.2. Bottom: normalized cut of the HST P $\alpha$ image (F187N) along the large semi-major axis (orientation "OA'' of Latter et al. 2000, thick line) compared with the scaled H $\beta$ surface-brightness profile of the 584 yr old model from the top panel (dotted line). The stellar parameters of this particular model are $M = 0.696~\mbox{$M_{\odot}$ },\ L = 9875~\mbox{$L_{\odot}$ },\ T_{\rm eff}= 155~504~{\rm K}$ . We have not corrected for the small effects caused by the different temperature dependence of the Balmer and Paschen line emissivities.
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In the text

$\begin{figure} \includegraphics[width=8.5cm,clip]{3108-10.eps} % \end{figure}$ Figure 10: Kinematic expansion time scales, $t_{\rm kin} = R_{\rm rim}/\dot{R}_{\rm rim}$ , as defined by the motion of the rim shocks of evolving model PNe, against the effective temperatures of their central stars. The sequence with the the 0.595 $M_{\odot }$ model used throughout this paper is supplemented by sequences with other central stars taken from Paper I (Table 1 therein): 0.605 $M_{\odot }$ (No. 6), 0.625 $M_{\odot }$ (No. 8), and 0.696 $M_{\odot }$ (No. 10). Dotted portions belong to the cooling part of the stellar tracks. Selected post-AGB ages (in 10³ yr) are indicated along the curves by small circles. The observational data points, $\theta_{\rm rim}/\dot{\theta}_{\rm rim}$ , are those listed in Table 2.
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In the text

$\begin{figure} \par\includegraphics[width=8.6cm,clip]{3108-11.eps}\end{figure}$ Figure 11: Detailed illustration of the different possible correction factors $F = \dot{R}/V$ already presented in the middle panels of Fig. 4 and explained in the legend, but now plotted over effective temperature. The corresponding post-AGB ages are given for comparison, too. The thick vertical mark indicates the moment when the ionization front passes the shock, i.e. of the thick/thin transition. The [N II] and [O III] lines give quite different results only below 50 000 K, i.e. during the optically-thick stage of evolution.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{3108-12.eps}\end{figure}$ Figure 12: Same as in Fig. 11, but now for hydrodynamical models with a central star of 0.696 $M_{\odot }$ (sequence No. 10 of Paper I). In this particular case, [N II] traces only the shell, and [O III] only the rim (see also detailed discussion in the Appendix).
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{3108-A1.eps}\end{figure}$ Figure A.1: Same as in Fig. 1 but for a 0.696 $M_{\odot }$ hydrogen-burning post-AGB model from Blöcker (1995b). Note that in this diagram the ages are given in 100 yr instead of 1000 yr!

In the text

$\begin{figure*} \includegraphics[width=15.0cm]{3108-A2a.eps}\vspace*{1.5mm} \inc... ...2c.eps}\vspace*{1.5mm} \includegraphics[width=15.0cm]{3108-A2d.eps}\end{figure*}$ Figure A.2: Same as in Fig. 3 but for a 0.696 $M_{\odot }$ hydrogen-burning post-AGB model from Blöcker (1995b) whose evolutionary properties are illustrated in Fig. A.1. The snapshots are arranged with increasing post-AGB ages, and the corresponding stellar parameters are as follows (from top to bottom): $t=304~{\rm yr},\ T_{\rm eff}= 71~292~{\rm K},\ L = 11~384~\mbox{$L_{\odot}$ }$ ; $t=450~\mbox{yr},\ T_{\rm eff}= 110~618~\mbox{K},\ L= 10~857~\mbox{$L_{\odot}$ }$ ; $t=584~\mbox{yr},\ T_{\rm eff}= 155~504~\mbox{K},\ L= 9~875~\mbox{$L_{\odot}$ }$ ; $t=752~\mbox{yr},\ T_{\rm eff}= 220~105~\mbox{K},\ L= 7~238~\mbox{$L_{\odot}$ }$ . Note the different radial extents of the structure and surface-brightness plots.

In the text

$\begin{figure} \includegraphics*[bb= 0 0 581 390, width=\textwidth]{3108-A3.eps}\end{figure}$ Figure A.3: Same as in Fig. 4 but now for the sequence with the 0.696 $M_{\odot }$ central star illustrated in the two previous figures. The vertical lines indicate the ages of the models shown in Fig. A.2.

In the text

$\begin{figure} \includegraphics[width=8.8cm]{3108-A4.eps}\end{figure}$ Figure A.4: Same as in Fig. 5 but now for the sequence with the 0.696 $M_{\odot }$ central star. The dotted curves represent again fits to $R_{\rm rim}$ and $R_{\rm cd}$ of the form R=R₀+c (t-t₀)^b (the fit for $R_{\rm rim}$ is indistinguishable). The parameters for $R_{\rm rim}$ (for $t\le 400$ yr only, see text), are R₀= 0.0021 pc, t₀=153 yr, $c=1.05\times10^{-5}~{\rm pc}/{\rm yr}^b$ , and b=1.13. For $R_{\rm cd}$ we have R₀=0.0013 pc, t₀=130 yr, $c=1.51\times10^{-6}~{\rm pc}/{\rm yr}^b$ , and b=1.42.

In the text

$\begin{figure} \resizebox{8.8cm}{4cm}{\includegraphics[bb = 2.2cm 23.5cm 16.7cm 29.cm] {3108-02.ps}}\end{figure}$	Figure 2: Initial model used in this paper. Plotted are the density of the heavy particles (thick), of the electrons (dotted), and the flow velocity (thin) against the distance from the central star.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{3108-06.eps}\end{figure}$	Figure 6: Comparison of different kinematical ages derived from the shell radius. They are computed from our hydrodynamical models and plotted as a function of their real evolutionary age. The curves for $R_{\rm shell}/V_{\rm shell}$ are the same as in Fig. 4 and are given for comparison. The dashed line indicates the 1:1 correspondence.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{3108-08.eps}\end{figure}$	Figure 8: Spectroscopic expansion velocities of the objects from Table 1 compared with predictions from the models used in Fig. 7. The dashed line is the 1:1 relation.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{3108-12.eps}\end{figure}$	Figure 12: Same as in Fig. 11, but now for hydrodynamical models with a central star of 0.696 $M_{\odot }$ (sequence No. 10 of Paper I). In this particular case, [N II] traces only the shell, and [O III] only the rim (see also detailed discussion in the Appendix).
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