All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{0169fg11.eps}\end{figure}$ Figure 1: Theoretical evolutionary track of a 1.25 $M_{\odot }$ star with a metallicity Z=0.02 in the H-R diagram. The core helium flash begins at the the tip of the red giant branch indicated by the arrow.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{0169fg21.eps}\end{figure}$ Figure 2: Temperature distribution as a function of radius. The dashed line gives the distribution obtained from stellar evolutionary calculations, while the solid line shows the mapped and stabilized distribution used as initial condition in the hydrodynamic simulations. CVZ marks the convection zone.
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In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{0169fg22.eps}\hspace*{7mm} \includegraphics[width=7.8cm,clip]{0169fg23.eps}\end{figure}$ Figure 3: Left panel: pressure (in $10^{22}\mbox{\ dyn$~{\rm cm}^{-2}$ }$ ) and density (in 10⁵ g cm^-3) distribution of the mapped and stabilized initial model. The pressure and density distribution of the original stellar evolution model cannot be distinguished from the corresponding profiles of the stabilized model on this scale. Right panel: chemical composition of the initial model.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0169fg24.eps}\end{figure}$ Figure 4: Temporal evolution of the helium luminosity $L_{\rm He}$ (solid) versus the hydrogen luminosity $L_{\rm H}$ (dash-dotted) of model M during the core helium flash.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{0169fg41.eps}\end{figure}$ Figure 5: Evolution of the temperature maximum $T_{\rm max}$ in the one-dimensional models hefl.1d.1 (solid), hefl.1d.2 (dashed), and hefl.1d.3 (dash-dotted), respectively.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{0169fg42.eps}\end{figure}$ Figure 6: Temperature stratification across the helium core in model hefl.1d.3 during the runaway at t₁ = 12 270 s (dotted), t₂ = 12 352 s (dashed), t₃ = 12 392 s (dash-dotted), and t₄ = 12 762 s (dash-dot-dotted), respectively. The solid line corresponds to the initial model (t₀), and the arrow indicates the direction of the flame propagation.
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In the text

$\begin{figure} \par\includegraphics[width=7.55cm,clip]{0169fg51.eps}\hspace*{1.3cm} \includegraphics[width=7.3cm,clip]{0169fg52.eps}\end{figure}$ Figure 7: Left panel: temporal evolution of the horizontally averaged temperature maximum $\langle T \rangle_{\rm max}$ (solid), and the global temperature maximum $T_{\rm max}$ (dotted) in model hefl.2d.3. The dashed line corresponds to the temporal evolution of the maximum temperature in the stellar evolutionary calculations of model M. Right panel: the rms convection velocity $v_{\rm cnv}$ in simulation hefl.2d.3 averaged over 6000 s (solid) versus the convection velocity predicted by the mixing length theory $v_{\rm mlt}$ (dashed).
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In the text

$\begin{figure} \par\includegraphics[width=5.25cm,clip]{0169btmp.eps}\hspace*{0.8... ....eps}\hspace*{1cm} \includegraphics[width=5.1cm,clip]{0169ec12.eps}\end{figure}$ Figure 8: Snapshots of the onset of convection at 1020 s ( upper panels), and of the evolved convection at 29 000 s ( lower panels) in model hefl.2d.3, showing the temperature contrast $\Delta T = \mbox{100}\times (T - \langle T \rangle_{\theta}) / \langle T \rangle_{\theta}$ ( left panels), the velocity field ( middle panels), and the ¹²C contrast $\rm \Delta ^{12}C = \mbox{100}\times (^{12}C - \langle^{12}C \rangle_{\theta}) / \langle^{12}C\rangle_{\theta}$ ( right panels), respectively. $\langle \rangle_{\theta}$ denotes a horizontal average at a given radius.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0169f55a.eps}\hspace*{1.3c... ...eps}\hspace*{1.3cm} \includegraphics[width=7.6cm,clip]{0169f55d.eps}\end{figure}$ Figure 9: Snapshots of various energy fluxes and source terms in model hefl.2d.3 (time averaged from t = 18 000 s to t = 24 000 s): a) convective flux $F_{\rm C}$ (solid), and the energy flux due to the thermal transport $F_{\rm R}$ (dash-dotted); b) kinetic flux $F_{\rm K}$ (solid), acoustic flux F_P (dash-dot-dotted), and sum of the kinetic and convective flux $F_{\rm C}+F_{\rm K}$ (dashed); c) source terms due to work done by buoyancy forces $P_{\rm A}$ , and d) due to volume changes P_P. The vertical lines enclose the nuclear burning zone (T > 10⁸ K).
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{0169fg56.eps}\hspace*{7mm} \includegraphics[width=7.85cm,clip]{0169fg57.eps}\end{figure}$ Figure 10: Angular averaged ¹²C distribution (dashed) and temperature stratification (thick) at the inner ( left panel) and outer edge ( right panel) of the convection zone in model hefl.2d.3 at $t = 30~000\mbox{\ s}$ . The vertical dotted lines mark the initial boundaries of the convection zone at t = 0 s.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0169fg58.eps}\hspace*{1.3cm} \includegraphics[width=7.4cm,clip]{0169fg59.eps}\end{figure}$ Figure 11: Left panel: evolution of the total energy production rate in solar luminosity $L_{\odot }$ for models hefl.2d.1 (dotted), hefl.2d.2 (dashed), and hefl.2d.3 (dash-dotted), respectively. Right panel: mean temperature distribution near the temperature inversion for models hefl.2d.1 (dotted), hefl.2d.2 (dashed), and hefl.2d.3 (dash-dotted) at a t = 30 000 s, respectively. The initial distribution is shown by the solid line.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0169fg11.eps}\end{figure}$	Figure 1: Theoretical evolutionary track of a 1.25 $M_{\odot }$ star with a metallicity Z=0.02 in the H-R diagram. The core helium flash begins at the the tip of the red giant branch indicated by the arrow.
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{0169fg21.eps}\end{figure}$	Figure 2: Temperature distribution as a function of radius. The dashed line gives the distribution obtained from stellar evolutionary calculations, while the solid line shows the mapped and stabilized distribution used as initial condition in the hydrodynamic simulations. CVZ marks the convection zone.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0169fg24.eps}\end{figure}$	Figure 4: Temporal evolution of the helium luminosity $L_{\rm He}$ (solid) versus the hydrogen luminosity $L_{\rm H}$ (dash-dotted) of model M during the core helium flash.
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$\begin{figure} \par\includegraphics[width=6.9cm,clip]{0169fg41.eps}\end{figure}$	Figure 5: Evolution of the temperature maximum $T_{\rm max}$ in the one-dimensional models hefl.1d.1 (solid), hefl.1d.2 (dashed), and hefl.1d.3 (dash-dotted), respectively.
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$\begin{figure} \par\includegraphics[width=6.9cm,clip]{0169fg42.eps}\end{figure}$	Figure 6: Temperature stratification across the helium core in model hefl.1d.3 during the runaway at t₁ = 12 270 s (dotted), t₂ = 12 352 s (dashed), t₃ = 12 392 s (dash-dotted), and t₄ = 12 762 s (dash-dot-dotted), respectively. The solid line corresponds to the initial model (t₀), and the arrow indicates the direction of the flame propagation.
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$\begin{figure} \par\includegraphics[width=8.1cm,clip]{0169fg56.eps}\hspace*{7mm} \includegraphics[width=7.85cm,clip]{0169fg57.eps}\end{figure}$	Figure 10: Angular averaged ¹²C distribution (dashed) and temperature stratification (thick) at the inner ( left panel) and outer edge ( right panel) of the convection zone in model hefl.2d.3 at $t = 30~000\mbox{\ s}$ . The vertical dotted lines mark the initial boundaries of the convection zone at t = 0 s.
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