All Figures

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f01a.eps} \end{figure}$ Figure 1: The initial magnetic field configuration of the models of series AaBbGg-D3M13. Besides the field lines the distribution of the magnetic pressure (color coded) is displayed. $P_{{\rm mag}}$ is largest near the center of the field generating current loop located at a radius of $r_{{\rm mag}}^{D3} = 400~{\rm km}$ in the equatorial plane, and drops rapidly with increasing radius for $r > r_{{\rm mag}}^{D3}$ .
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.15cm,clip]{4306f02a.eps} \incl... ...{4306f02e.eps} \includegraphics[width=5.15cm,clip]{4306f02f.eps} } \end{figure}$ Figure 2: The evolution of the maximum density ( top panels) and the GW amplitude ( bottom panels) of three weak-field models: the standard type-I model A1B3G3-D3M10 ( left panels), the type-II model A2B4G1-D3M10 ( middle panels), and the type-III model A3B3G5-D3M10 ( right panels). The bottom panels show the total GW amplitude $A^{{\rm E}2}_{20}$ (solid lines) together with the partial amplitudes $A^{{\rm E}2}_{20; {\rm hyd}}$ (dashed lines), $A^{{\rm E}2}_{20; {\rm mag}}$ (dash-dotted lines; here almost zero), and $A^{{\rm E}2}_{20; {\rm grav}}$ (dash-dot-dot-dot line).
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In the text

$\begin{figure} \par\includegraphics[width=3.5cm,clip]{4306f03a.eps}\hspace*{2mm}... ...eps}\hspace*{2mm} \includegraphics[width=3.5cm,clip]{4306f03d.eps} \end{figure}$ Figure 3: The evolution of the magnetic energy parameters $\beta _{{\rm mag}}$ (total energy, solid line), $\beta _{\phi }$ (toroidal field energy, dashed line), and $\beta _{{\rm mag}}-\beta _{\phi }$ (poloidal field energy, dotted line) of models A1B3G3-D3M10 ( upper left panel), A3B3G5-D3M10 ( upper right panel), A2B4G1-D3M10 ( lower left panel), and A4B5G5-D3M10 ( lower right panel), respectively. Note that in the upper left panel $\beta _{{\rm mag}} \approx \beta _{\phi }$ and, thus, both lines are almost indistinguishable.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f04a.eps} \end{figure}$ Figure 4: Magnetic pressure (color shaded), velocity field (arrows), and magnetic field lines of model A1B3G3-D3M10 at $t=51.44~{\rm ms}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f05a.eps} \end{figure}$ Figure 5: Same as Fig. 5, but for model A4B5G5-D3M10 at $t= 36.13~{\rm ms}$ .
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.45cm,clip]{4306f06a.eps} \incl... ...{4306f06e.eps} \includegraphics[width=5.45cm,clip]{4306f06f.eps} } \end{figure}$ Figure 6: The dynamics and the GW signal of model A1B3G3-D3M12. The upper left and middle panels provide a comparison of the evolution of the rotational energy parameter $\beta _{{\rm rot}}$ and the maximum density of this model (solid lines) with those of model A1B3G3-D3M10 (dashed lines). The upper right panel displays the evolution of $\beta _{{\rm mag}}$ (solid line), $\beta _{\phi }$ (dashed line), and $\beta _{{\rm mag}}-\beta _{\phi }$ (dotted line), respectively. The GW signal is shown in the lower panels: total amplitude (solid line, left; the dashed line gives the total amplitude of model A1B3G3-D3M10), $-A^{{\rm E}2}_{20;{\rm hyd}}$ (solid line, middle), $A^{{\rm E}2}_{20; {\rm grav}}$ (dashed line, middle), and $A^{{\rm E}2}_{20; {\rm mag}}$ ( right). The corresponding variables of model A1B3G3-D3M10 are shown in Fig. 2.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{4306f07a.eps} \end{figure}$ Figure 7: Snapshot of the inner regions of model A1B3G3-D3M12 at $t=76.94~{\rm ms}$ showing the magnetic pressure (color shaded), the bipolar flow field (vectors), and the magnetic field lines, respectively.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.45cm,clip]{4306f08a.eps} \incl... ...{4306f08e.eps} \includegraphics[width=5.45cm,clip]{4306f08f.eps} } \end{figure}$ Figure 8: The dynamical evolution and the GW signal of model A1B3G3-D3M13. The upper panels display the temporal evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left), the maximum density $\rho _{{\rm max}}$ ( middle), and the magnetic energy parameters ( right; $\beta _{{\rm mag}}$ (solid line), $\beta _{\phi }$ (dashed line), and $\beta _{{\rm mag}}-\beta _{\phi }$ (dotted line)), respectively. The GW signal of the model is shown in the lower panels: total amplitude (solid line, left; the dashed line gives the contribution of the layers with $r \le 59.4$ km), $-A^{{\rm E}2}_{20;{\rm hyd}}$ (solid line, middle), $A^{{\rm E}2}_{20; {\rm grav}}$ (dashed line, middle), and $A^{{\rm E}2}_{20; {\rm mag}}$ ( right).
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f09a.eps} \end{figure}$ Figure 9: Snapshot of model A1B3G3-D3M13 at $t=50.19~{\rm ms}$ , when the maximum density reaches the first post-bounce minimum. In the left panel the flow field (vectors) and the magnetic field (field lines) are displayed together with the magnetic pressure (color-coded). The right panel shows the color-coded velocities of in-flowing (i.e. v_r>0) and out-flowing matter (i.e. v_r<0), respectively.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f10a.eps} \end{figure}$ Figure 10: Same as Fig. 9, but at $t=60.40~{\rm ms}$ . Note that the length scales are changed compared to Fig. 9.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f11a.eps} \end{figure}$ Figure 11: Same as Fig. 9, but at $t=68.51~{\rm ms}$ . Note that the length scales of the plot are changed compared to Figs. 9 and 10.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f12a.eps} \end{figure}$ Figure 12: The hydrodynamic plus gravitational parts of the GW amplitude of model A1B3G3-D3M13 at $t=68.5~{\rm ms}$ . Positive contributions to the integrand in the formula for the hydrodynamic plus gravitational amplitude are displayed by colors. The bipolar outflow shows up in the large positive parts near the axis.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f13a.eps} \end{figure}$ Figure 13: Snapshot of model A3B3G5-D3M13 at $t=49.46~{\rm ms}$ showing the velocities of inflows (blue colors) and outflows (red colors).
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,clip]{4306f14a.eps} \inclu... ...]{4306f14e.eps} \includegraphics[width=5.6cm,clip]{4306f14f.eps} } \end{figure}$ Figure 14: The dynamical evolution and the GW signal of model A3B3G5-D3M13. The upper panels display the temporal evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left), the maximum density $\rho _{{\rm max}}$ ( middle), and the magnetic energy parameters ( right; $\beta _{{\rm mag}}$ (solid line), $\beta _{\phi }$ (dashed line), and $\beta _{{\rm mag}}-\beta _{\phi }$ (dotted line)), respectively. The GW signal of the model is shown in the lower panels: total amplitude (solid line, left), $-A^{{\rm E}2}_{20;{\rm hyd}}$ (solid line, middle), $A^{{\rm E}2}_{20; {\rm grav}}$ (dashed line, middle), and $A^{{\rm E}2}_{20; {\rm mag}}$ ( right).
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,clip]{4306f15a.eps} \inclu... ...]{4306f15e.eps} \includegraphics[width=5.6cm,clip]{4306f15f.eps} } \end{figure}$ Figure 15: The evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left panels), of the maximum density ( middle panels) and the GW signal ( right panels) of models A3B3G3-D3M10 ( top panels), and A3B3G3-D3M12 ( bottom panels), respectively.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,clip]{4306f16a.eps} \inclu... ...{4306f16e.eps} \includegraphics[width=5.6cm,clip]{4306f16f.eps} } \end{figure}$ Figure 16: The dynamical evolution and the GW signal of model A3B3G3-D3M13. The upper panels display the temporal evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left), the maximum density $\rho _{{\rm max}}$ ( middle), and the magnetic energy parameters ( right; $\beta _{{\rm mag}}$ (solid line), $\beta _{\phi }$ (dashed line), and $\beta _{{\rm mag}}-\beta _{\phi }$ (dotted line)), respectively. The GW signal of the model is shown in the lower panels: total amplitude (solid line, left; the dashed line gives the contribution of the layers with $r \le 55.6$ km), $-A^{{\rm E}2}_{20;{\rm hyd}}$ (solid line, middle), $A^{{\rm E}2}_{20; {\rm grav}}$ (dashed line, middle), and $A^{{\rm E}2}_{20; {\rm mag}}$ ( right).
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.4cm,clip]{4306f17a.eps} \inclu... ...]{4306f17e.eps} \includegraphics[width=5.4cm,clip]{4306f17f.eps} } \end{figure}$ Figure 17: The dynamical evolution and the GW signal of model A2B4G1-D3M13. The upper panels display the temporal evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left), the maximum density $\rho _{{\rm max}}$ ( middle), and the magnetic energy parameters ( right; $\beta _{{\rm mag}}$ (solid line), $\beta _{\phi }$ (dashed line), and $\beta _{{\rm mag}}-\beta _{\phi }$ (dotted line)), respectively. The GW signal of the model is shown in the lower panels: total amplitude (solid line, left), $-A^{{\rm E}2}_{20;{\rm hyd}}$ (solid line, middle), $A^{{\rm E}2}_{20; {\rm grav}}$ (dashed line, middle), and $A^{{\rm E}2}_{20; {\rm mag}}$ ( right).
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{4306f18a.eps} \end{figure}$ Figure 18: Model A2B4G1-D3M13 at $t=123.39~{\rm ms}$ when the expansion of the core is maximum just prior to its second collapse. Besides the magnetic pressure (color shaded), the flow field (vectors), and the magnetic field lines are shown.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.15cm,clip]{4306f19a.eps} \incl... ...306f19h.eps} \includegraphics[width=5.15cm,clip]{4306f19i.eps} } \end{figure}$ Figure 19: Evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left) and the maximum density ( middle) of models A4B5G5-D3M10 ( upper row) and A4B5G5-D3M13 ( middle row), respectively. The total GW amplitude of model A4B5G5-D3M10 is shown in the upper right panel, and the evolution of the magnetic energy parameters, $\beta _{{\rm mag}}$ (solid), $\beta _{\phi }$ (dashed), and $\beta _{{\rm mag}}-\beta _{\phi }$ in the middle right panel, respectively. The panels in the bottom row show different contributions to the GW amplitude of model A4B5G5-D3M13: total amplitude ( left), $-A^{{\rm E}2}_{20;{\rm hyd}}$ (solid line, middle), $A^{{\rm E}2}_{20; {\rm grav}}$ (dashed line, middle), and $A^{{\rm E}2}_{20; {\rm mag}}$ ( right).
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f20a.eps} \end{figure}$ Figure 20: Comparison of two snapshots of model A4B5G5-D3M13. The innermost region of the core is displayed at $t=30.98~{\rm ms}$ (at core bounce; left), and at $t=42.54~{\rm ms}$ ( right). The logarithm of the density (color-coded), the velocity (arrow), and the magnetic field lines are displayed, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f21a.eps} \end{figure}$ Figure 21: Model A4B5G5-D3M13 at $t=30.98~{\rm ms}$ (core bounce). The flow field (vectors) and the magnetic field lines are displayed together with the gas pressure (color-coded, left) and the magnetic pressure (color-coded, right), respectively.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{4306f22a.eps} \end{figure}$ Figure 22: Comparison of the evolution of models A1B3G3-D3M12 ( upper panels) and A1B3G3-D3M10 ( lower panels). The left panels display the total magnetic energy (solid lines) of the core, and the total (dashed lines) and poloidal field energy (dash-dotted lines) of the MRI-unstable regions, which are defined according to two different criteria: For the strong-field model A1B3G3-D3M12 all zones are considered where the growth time of the fastest growing mode is less than 10 ms, while for the weak-field model A1B3G3-D3M10 the corresponding magneto-convective limit is used. The energy density $e_{{\rm mag}} = E_{{\rm mag}} / V$ of the poloidal field in the MRI-unstable regions is shown in the right panels. The poloidal field increases rapidly when the MRI grows, which happens in the strong-field model ( top right) shortly after bounce, and in the weak-field model ( bottom right) by magneto-convective modes at later epochs.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f23a.eps} \end{figure}$ Figure 23: The post-shock region of models A3B3G5-D0M12 ( left quadrants) and A3B3G5-D2M12 ( right quadrants) at $t\approx 33.6~{\rm ms}$ about 3 ms after core bounce. Density and magnetic pressure (color-coded) are displayed in the top and bottom quadrants, respectively. Additionally, the flow field (vectors) and the poloidal field lines of the magnetic field are displayed.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,clip]{4306f24a.eps} \inclu... ...]{4306f24e.eps} \includegraphics[width=5.6cm,clip]{4306f24f.eps} } \end{figure}$ Figure 24: The evolution of the maximum density ( top panels) and the GW amplitude ( bottom panels) of models A3B3G3-D0M13 ( left panels), A3B3G3-D3M13 ( middle panels), and A3B3G3-D1M13 ( right panels), respectively. The GW signal of model A3B3G3-D0M13 shows a constant offset from zero, which is subtracted here.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=5.6cm]{4306f25a.eps} \includegra... ...5.6cm]{4306f25b.eps} \includegraphics[width=5.6cm]{4306f25c.eps} } \end{figure}$ Figure B.1: The temporal evolution of the maximum density, the GW signal and the rotational energy parameter $\beta _{{\rm rot}}$ of model A1B3G3-D3M13 comparing simulations with grids of different resolution. Results from a run with the standard grid of 380 logarithmically spaced zones in radius (central resolution of 300 m) and 60 zones uniformly distributed over $0 \leq \theta \leq \pi /2$ are shown by the solid lines, and runs using a coarser grid of 280 zones in radius (central resolution of 600 m) and 30 zones in angle and a finer grid of 580 zones (central resolution of 150 m) and 90 zones in angle are plotted with dotted and dashed lines, respectively.

In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f04a.eps} \end{figure}$	Figure 4: Magnetic pressure (color shaded), velocity field (arrows), and magnetic field lines of model A1B3G3-D3M10 at $t=51.44~{\rm ms}$ .
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f05a.eps} \end{figure}$	Figure 5: Same as Fig. 5, but for model A4B5G5-D3M10 at $t= 36.13~{\rm ms}$ .
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$\begin{figure} \par\includegraphics[width=7cm,clip]{4306f07a.eps} \end{figure}$	Figure 7: Snapshot of the inner regions of model A1B3G3-D3M12 at $t=76.94~{\rm ms}$ showing the magnetic pressure (color shaded), the bipolar flow field (vectors), and the magnetic field lines, respectively.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f10a.eps} \end{figure}$	Figure 10: Same as Fig. 9, but at $t=60.40~{\rm ms}$ . Note that the length scales are changed compared to Fig. 9.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f11a.eps} \end{figure}$	Figure 11: Same as Fig. 9, but at $t=68.51~{\rm ms}$ . Note that the length scales of the plot are changed compared to Figs. 9 and 10.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f12a.eps} \end{figure}$	Figure 12: The hydrodynamic plus gravitational parts of the GW amplitude of model A1B3G3-D3M13 at $t=68.5~{\rm ms}$ . Positive contributions to the integrand in the formula for the hydrodynamic plus gravitational amplitude are displayed by colors. The bipolar outflow shows up in the large positive parts near the axis.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4306f13a.eps} \end{figure}$	Figure 13: Snapshot of model A3B3G5-D3M13 at $t=49.46~{\rm ms}$ showing the velocities of inflows (blue colors) and outflows (red colors).
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$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,clip]{4306f15a.eps} \inclu... ...]{4306f15e.eps} \includegraphics[width=5.6cm,clip]{4306f15f.eps} } \end{figure}$	Figure 15: The evolution of the rotational energy parameter $\beta _{{\rm rot}}$ ( left panels), of the maximum density ( middle panels) and the GW signal ( right panels) of models A3B3G3-D3M10 ( top panels), and A3B3G3-D3M12 ( bottom panels), respectively.
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{4306f18a.eps} \end{figure}$	Figure 18: Model A2B4G1-D3M13 at $t=123.39~{\rm ms}$ when the expansion of the core is maximum just prior to its second collapse. Besides the magnetic pressure (color shaded), the flow field (vectors), and the magnetic field lines are shown.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f20a.eps} \end{figure}$	Figure 20: Comparison of two snapshots of model A4B5G5-D3M13. The innermost region of the core is displayed at $t=30.98~{\rm ms}$ (at core bounce; left), and at $t=42.54~{\rm ms}$ ( right). The logarithm of the density (color-coded), the velocity (arrow), and the magnetic field lines are displayed, respectively.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f21a.eps} \end{figure}$	Figure 21: Model A4B5G5-D3M13 at $t=30.98~{\rm ms}$ (core bounce). The flow field (vectors) and the magnetic field lines are displayed together with the gas pressure (color-coded, left) and the magnetic pressure (color-coded, right), respectively.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{4306f23a.eps} \end{figure}$	Figure 23: The post-shock region of models A3B3G5-D0M12 ( left quadrants) and A3B3G5-D2M12 ( right quadrants) at $t\approx 33.6~{\rm ms}$ about 3 ms after core bounce. Density and magnetic pressure (color-coded) are displayed in the top and bottom quadrants, respectively. Additionally, the flow field (vectors) and the poloidal field lines of the magnetic field are displayed.
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$\begin{figure} \par\mbox{\includegraphics[width=5.6cm,clip]{4306f24a.eps} \inclu... ...]{4306f24e.eps} \includegraphics[width=5.6cm,clip]{4306f24f.eps} } \end{figure}$	Figure 24: The evolution of the maximum density ( top panels) and the GW amplitude ( bottom panels) of models A3B3G3-D0M13 ( left panels), A3B3G3-D3M13 ( middle panels), and A3B3G3-D1M13 ( right panels), respectively. The GW signal of model A3B3G3-D0M13 shows a constant offset from zero, which is subtracted here.
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