All Figures

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{3592f01a.ps}\hspace*{3mm} \includegraphics[width=6.4cm,clip]{3592f01b.ps} \end{figure}$ Figure 1: Entropy (in units of $k_{\rm B}$ per nucleon) in Model T310 at a time of 420 ms after core bounce. The white contour line encloses the region where the $\rm {^{56}Ni}$ mass fraction is $\geq$ $20\%$ . a) Calculation performed with the original PROMETHEUS code showing odd-even decoupling. Note the deformation of the shock. b) Calculation performed with HERAKLES.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3592f02.ps} \end{figure}$ Figure 2: Spacetime plot for the evolution of the logarithm of the density for our one-dimensional explosion, Model O310. The supernova shock is visible as the outermost discontinuity that extends diagonally through the plot. Around 500 ms a reverse shock forms in the inner ejecta that originates from the (hardly visible) slight deceleration of the main shock in the oxygen core. The reverse shock separates the ejecta from the neutrino-driven wind.
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In the text

$\begin{figure} \par\includegraphics[width=14.7cm,clip]{3592f03.ps} \end{figure}$ Figure 3: Snapshots of the density, entropy, velocity and electron fraction distribution in Model O310, 20 ms (heaviest line), 220 ms, 420 ms, 620 ms and 820 ms after core bounce.
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In the text

$\begin{figure} \par\includegraphics[width=14.9cm,clip]{3592f04.ps} \end{figure}$ Figure 4: Evolution of density, temperature, entropy and electron fraction as functions of the enclosed mass for Model O310 between t = 20 ms and t = 820 ms post-bounce. The positions of the Fe/Si and Si/O interfaces, and the $Y_{\rm e}$ discontinuity (see text) are indicated by dotted vertical lines.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3592f05.ps} \end{figure}$ Figure 5: Chemical composition of Model O310 versus mass at t = 820 ms. X denotes the neutronization tracer nucleus.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3592f06.ps} \end{figure}$ Figure 6: Density and pressure profiles of Model O310 at t = 820 ms. The position of the $Y_{\rm e}$ discontinuity and of the Si/O interface are indicated by dotted vertical lines. Note the dense shell at $r = 1.1 \times 10^{9}$ cm, and the density and pressure gradients of opposite signs for $1.05\times10^{9}~{\rm cm} \leq r \leq 1.35 \times 10^{9}~ {\rm cm}$ .
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In the text

$\begin{figure} \par\includegraphics[width=17cm,clip]{3592f07.ps} \end{figure}$ Figure 7: Fractional mass of different elements contained within the velocity interval $[v_{\rm r},v_{\rm r}+{\rm d}v_{\rm r}]$ as a function of the radial velocity $v_{\rm r}$ in Model T310. The resolution is ${\rm d}v_{\rm r} = 350~{\rm km~s^{-1}}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{3592f08a.ps}\hspace*{4mm} \includegraphics[width=9.9cm,clip]{3592f08b.ps} \end{figure}$ Figure 8: a) Evolution of the density in our one-dimensional type II supernova simulation Model $\overline {\rm T310}$ (left). The dotted lines indicate the positions of the Si/O, (C+O)/He and He/H interfaces 0.82 s after core bounce. b) Shock velocity as a function of shock radius in Model $\overline {\rm T310}$ , and radial dependence of $\rho r^3$ for our progenitor model (right). Note the deceleration of the shock after it has crossed the (C+O)/He interface at $\log~ (r/{\rm cm}) = 9.55$ and the He/H interface at $\log~ (r/{\rm cm}) = 10.85$ . The increase of the shock velocity for $\log~ (r/{\rm cm}) \geq 12.2$ is due to the steep drop of the density in the atmosphere of the star.
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In the text

$\begin{figure} \par\includegraphics[width=16.3cm,clip]{3592f09.ps} \end{figure}$ Figure 9: Structure of Model $\overline {\rm T310}$ , a) 20 s (left), and b) 300 s after bounce (right). Shown are (from top) the density, pressure, velocity, sound speed, and mass fractions as functions of radius. Note the unstable regions (shaded in grey) near the Si/O, (C+O)/He and He/H composition interfaces, where the density and pressure gradients have opposite signs. At t=300 s, the density gradient at the inner edge of the dense shell that has formed below the He/H interface is in the process of steepening into a reverse shock (compare also Fig. 8a). Note also the enormous drop of the velocity in the layers that are enriched in $\rm {^{56}Ni}$ , from 6000 km s^-1 at 20 s to 1300 km s^-1 at 300 s.
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In the text

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{3592f10.ps} \end{figure}$ Figure 10: Logarithm of the total, time-integrated, linear growth rate in the unstable layers near the Si/O and (C+O)/He composition interfaces of Model $\overline {\rm T310}$ at different times. The linear growth rates increase with time and reach amplification factors $\geq$ 10¹² within the first 300 s (i.e. five minutes) of the explosion.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3592f11.ps}\end{figure}$ Figure 11: Logarithm of the total, time-integrated, linear growth rate in the unstable layers near the Si/O, (C+O)/He and He/H composition interfaces of Model $\overline {\rm T310}$ at different times. Comparing the amplitudes of the growth rates at the Si/O and (C+O)/He interfaces with those given in Fig. 10 one can see that these have saturated after 300 s (in fact the curves for 300 s, 1600 s, and 3000 s are not visible individually because they are identical within plotting accuracy). Note, however, that the rate for the instability at the He/H interface is still increasing between 300 s and 3000 s.
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In the text

$\begin{figure} \par\begin{tabular}{ccc} \includegraphics[width=5.5cm,height=11.2... ...[width=5.5cm,height=11.2cm,clip]{f12f_cmyk_600dpi.eps}\end{tabular} \end{figure}$ Figure 12: Logarithm of the density (top) and of the partial densities (bottom) of $\rm {^{16}O}$ (blue), $\rm {^{28}Si}$ (green), and $\rm {^{56}Ni}$ (red) in Model T310a at selected early epochs. Data values are coded according to the color bars given for each frame. In case of the partial densities, colors other than red, green and blue (resulting from the superposition of these color channels) indicate mixing of the composition. From left to right a) t = 4 s, b) t = 10 s, c) t = 20 s. Note the change of the radial scale. The supernova shock is visible as the outermost circular discontinuity in the density plots.
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In the text

$\begin{figure} \par\begin{tabular}{ccc} \includegraphics[width=5.5cm,height=11.2... ...[width=5.5cm,height=11.2cm,clip]{f13f_cmyk_600dpi.eps}\end{tabular} \end{figure}$ Figure 13: Same as Fig. 12. a) t = 100 s (left), b) t = 300 s (middle), c) t = 1500 s (right). Note the change of the radial scale.
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In the text

$\begin{figure} \par\begin{tabular}{ccc} \includegraphics[width=5.5cm,height=11.2... ...s[width=5.5cm,height=11.2cm,clip]{f14f_cmyk_600dpi.eps}\end{tabular}\end{figure}$ Figure 14: Same as Fig. 12. a) t = 5000 s (left), b) t = 10 000 s (middle), c) t = 20 000 s (right). Note the change of the radial scale. The circular orange/black boundary in the upper right panel corresponds to the outer edge of the computational domain, which the supernova shock has crossed long before.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{3592f15.ps} \end{figure}$ Figure 15: Evolution of the extent of mixing in Model T310a. Left: initial composition. Right: composition 20 000 s after core bounce. The neutronization tracer is denoted with "X''. Note that all heavy elements are confined to the helium core (i.e. to the innermost $4.2~{M_{\odot}}$ of the star) even as late as 20 000 s after core bounce.
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In the text

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{3592f16.ps} \end{figure}$ Figure 16: Logarithm of the fractional mass of different elements that is contained within the velocity interval $[v_{\rm r},v_{\rm r}+{\rm d}v_{\rm r}]$ as a function of the radial velocity $v_{\rm r}$ in Model T310a at various epochs. The resolution is ${\rm d}v_{\rm r} \approx 130~{\rm km~s^{-1}}$ . Note the different scales for the radial velocity in the left and right panels.
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In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{3592f17.ps} \end{figure}$ Figure 17: Same as Fig. 16 but for Model T310b and times of 300 s, 1500 s and 3000 s after bounce.
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{3592f18.ps} \end{figure}$ Figure 18: Logarithm of the density in Model T310b at a time of 1500 s after bounce.
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In the text

$\begin{figure} \par\includegraphics[width=16.1cm,clip]{3592f19.ps} \end{figure}$ Figure 19: Same as Fig. 15, but for Model T310b. Left: initial composition. Right: composition 3000 s after core bounce.
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{3592f01a.ps}\hspace*{3mm} \includegraphics[width=6.4cm,clip]{3592f01b.ps} \end{figure}$	Figure 1: Entropy (in units of $k_{\rm B}$ per nucleon) in Model T310 at a time of 420 ms after core bounce. The white contour line encloses the region where the $\rm {^{56}Ni}$ mass fraction is $\geq$ $20\%$ . a) Calculation performed with the original PROMETHEUS code showing odd-even decoupling. Note the deformation of the shock. b) Calculation performed with HERAKLES.
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$\begin{figure} \par\includegraphics[width=14.7cm,clip]{3592f03.ps} \end{figure}$	Figure 3: Snapshots of the density, entropy, velocity and electron fraction distribution in Model O310, 20 ms (heaviest line), 220 ms, 420 ms, 620 ms and 820 ms after core bounce.
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$\begin{figure} \par\includegraphics[width=14.9cm,clip]{3592f04.ps} \end{figure}$	Figure 4: Evolution of density, temperature, entropy and electron fraction as functions of the enclosed mass for Model O310 between t = 20 ms and t = 820 ms post-bounce. The positions of the Fe/Si and Si/O interfaces, and the $Y_{\rm e}$ discontinuity (see text) are indicated by dotted vertical lines.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3592f05.ps} \end{figure}$	Figure 5: Chemical composition of Model O310 versus mass at t = 820 ms. X denotes the neutronization tracer nucleus.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3592f06.ps} \end{figure}$	Figure 6: Density and pressure profiles of Model O310 at t = 820 ms. The position of the $Y_{\rm e}$ discontinuity and of the Si/O interface are indicated by dotted vertical lines. Note the dense shell at $r = 1.1 \times 10^{9}$ cm, and the density and pressure gradients of opposite signs for $1.05\times10^{9}~{\rm cm} \leq r \leq 1.35 \times 10^{9}~ {\rm cm}$ .
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$\begin{figure} \par\includegraphics[width=17cm,clip]{3592f07.ps} \end{figure}$	Figure 7: Fractional mass of different elements contained within the velocity interval $[v_{\rm r},v_{\rm r}+{\rm d}v_{\rm r}]$ as a function of the radial velocity $v_{\rm r}$ in Model T310. The resolution is ${\rm d}v_{\rm r} = 350~{\rm km~s^{-1}}$ .
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$\begin{figure} \par\includegraphics[width=14.8cm,clip]{3592f10.ps} \end{figure}$	Figure 10: Logarithm of the total, time-integrated, linear growth rate in the unstable layers near the Si/O and (C+O)/He composition interfaces of Model $\overline {\rm T310}$ at different times. The linear growth rates increase with time and reach amplification factors $\geq$ 10¹² within the first 300 s (i.e. five minutes) of the explosion.
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$\begin{figure} \par\begin{tabular}{ccc} \includegraphics[width=5.5cm,height=11.2... ...[width=5.5cm,height=11.2cm,clip]{f13f_cmyk_600dpi.eps}\end{tabular} \end{figure}$	Figure 13: Same as Fig. 12. a) t = 100 s (left), b) t = 300 s (middle), c) t = 1500 s (right). Note the change of the radial scale.
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$\begin{figure} \par\begin{tabular}{ccc} \includegraphics[width=5.5cm,height=11.2... ...s[width=5.5cm,height=11.2cm,clip]{f14f_cmyk_600dpi.eps}\end{tabular}\end{figure}$	Figure 14: Same as Fig. 12. a) t = 5000 s (left), b) t = 10 000 s (middle), c) t = 20 000 s (right). Note the change of the radial scale. The circular orange/black boundary in the upper right panel corresponds to the outer edge of the computational domain, which the supernova shock has crossed long before.
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$\begin{figure} \par\includegraphics[width=16cm,clip]{3592f15.ps} \end{figure}$	Figure 15: Evolution of the extent of mixing in Model T310a. Left: initial composition. Right: composition 20 000 s after core bounce. The neutronization tracer is denoted with "X''. Note that all heavy elements are confined to the helium core (i.e. to the innermost $4.2~{M_{\odot}}$ of the star) even as late as 20 000 s after core bounce.
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$\begin{figure} \par\includegraphics[width=14.8cm,clip]{3592f16.ps} \end{figure}$	Figure 16: Logarithm of the fractional mass of different elements that is contained within the velocity interval $[v_{\rm r},v_{\rm r}+{\rm d}v_{\rm r}]$ as a function of the radial velocity $v_{\rm r}$ in Model T310a at various epochs. The resolution is ${\rm d}v_{\rm r} \approx 130~{\rm km~s^{-1}}$ . Note the different scales for the radial velocity in the left and right panels.
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$\begin{figure} \par\includegraphics[width=6.8cm,clip]{3592f17.ps} \end{figure}$	Figure 17: Same as Fig. 16 but for Model T310b and times of 300 s, 1500 s and 3000 s after bounce.
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$\begin{figure} \par\includegraphics[width=6.4cm,clip]{3592f18.ps} \end{figure}$	Figure 18: Logarithm of the density in Model T310b at a time of 1500 s after bounce.
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$\begin{figure} \par\includegraphics[width=16.1cm,clip]{3592f19.ps} \end{figure}$	Figure 19: Same as Fig. 15, but for Model T310b. Left: initial composition. Right: composition 3000 s after core bounce.
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