All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fig1.ps} \end{figure}$ Figure 1: Temporal variations of the temperature ( top), entropy ( middle) and lepton fraction ( bottom) as functions of the baryon density, for evolutionary times corresponding to t=0.1, 0.5, 1 and 8 s after formation of the PNS. Results are for a $M_{\rm B}=1.6~M_\odot$ star in spherical symmetry.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fig2.ps} \end{figure}$ Figure 2: Equatorial profiles of angular velocity ( top), and density ( bottom) of PNSs from axisymmetric simulations of stellar core collapse (DFM). The four models correspond to a different amount of angular momentum of the iron core, namely, $\vert T/W\vert= 0.9\%$ (solid), 0.5% (dashes), 0.25% (dash-dot), and 0.05% (dash-3 dots). The dotted lines on the upper panel are fits to the simple law (9) with R₀²=50 km².
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0619ome.ps} \end{figure}$ Figure 3: Surfaces of constant angular velocity (projected in a transversal plane) of a differentially rotating star with R₀=100 km, for t=1 s, and rotating with $\Omega = 354$ rad/s. ( $\Omega /\Omega _{\rm K}=0.995$ ). The surface is marked by the thick solid line. Because of relativistic effects, the stationary solution does not show exact cylindrical symmetry.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fig4.ps} \end{figure}$ Figure 4: Temporal evolution of the angular velocity $\Omega /\Omega _{\rm K}$ and the rotation parameter |T/W| for a sequence of rigidly rotating PNSs with constant angular momentum ( $1.5~GM_{\hbox{$\odot$ }}^2 /c$ ) and a fixed baryonic mass of $M_{\rm B} = 1.6~M_{\hbox{$\odot$ }}$ .
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0619fent.ps} \end{figure}$ Figure 5: Iso-enthalpy lines of a differentially rotating star with R₀=100 km, for t=1 s, and rotating with $\Omega = 354$ rad/s. ( $\Omega /\Omega _{\rm K}=0.995$ ). For low differential rotation the structure of the star still looks normal.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0619feto.ps} \end{figure}$ Figure 6: Iso-enthalpy lines of a differentially rotating star with R₀=10 km, for t=1 s, and rotating with $\Omega = 1570$ rad/s. The toroidal shape is clearly visible for all models differentially rotating with R₀ smaller than a certain threshold.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619J.ps} \end{figure}$ Figure 7: Total angular momentum as a function of the central angular velocity for PNSs with fixed baryonic mass of 1.6 $M_\odot$ at evolutionary times of 0.5 ( top), 1.0 ( middle) and 10 s ( bottom), and for different values of R₀: $R_0=\infty$ (solid), 50 km (dash-dot), 20 km (thick dashed), $R_{\rm eq}/2$ (thin dashed), 10 km (dots).
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619TW.ps} \end{figure}$ Figure 8: Rotation parameter, |T/W|, as a function of the central angular velocity for PNS with fixed baryonic mass of 1.6 $M_\odot$ at evolutionary times of 0.5 ( top), 1.0 ( middle) and 10 s ( bottom), and for different values of R₀: $R_0=\infty$ (solid), 50 km (dash-dot), 20 km (thick dashed), $R_{\rm eq}/2$ (thin dashed), 10 km (dots).
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619Ax.ps} \end{figure}$ Figure 9: Axis ratio (polar to equatorial) as a function of the central angular velocity for a PNS with a baryonic mass of 1.6 $M_\odot$ at t=10 s, and for different values of R₀: $R_0=\infty$ (solid), 50 km (dash-dot), 20 km (thick dashed), $R_{\rm eq}/2$ (thin dashed), 10 km (dots).
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fJ15.ps} \end{figure}$ Figure 10: Temporal evolution of the central angular velocity $\Omega _{\rm c}$ and of the rotation parameter |T/W| for two sequences of differentially rotating PNSs with R₀=10 km (solid line) and R₀=20 km (dashed line). In both cases we fix the total angular momentum to $1.5~GM_{\hbox{$\odot$ }}^2 /c$ and the baryonic mass to $M_{\rm B} = 1.6~M_{\hbox{$\odot$ }}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619flum.ps} \end{figure}$ Figure 11: Estimated neutrino luminosity ( $-{\rm d}M_{\rm G}/{\rm d}t$ ) as a function of time, consistent with the evolution at fixed baryonic mass of $M_{\rm B} = 1.6~M_{\hbox{$\odot$ }}$ and angular momentum of $1.5~GM_{\hbox{$\odot$ }}^2 /c$ . The two models are differentially rotating with R₀=10 km (solid line) and R₀=20 km (dashed line). The order of magnitude and the exponential decay are similar to the luminosities obtained in simulations with neutrino transport for non-rotating stars.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fig1.ps} \end{figure}$	Figure 1: Temporal variations of the temperature ( top), entropy ( middle) and lepton fraction ( bottom) as functions of the baryon density, for evolutionary times corresponding to t=0.1, 0.5, 1 and 8 s after formation of the PNS. Results are for a $M_{\rm B}=1.6~M_\odot$ star in spherical symmetry.
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$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0619ome.ps} \end{figure}$	Figure 3: Surfaces of constant angular velocity (projected in a transversal plane) of a differentially rotating star with R₀=100 km, for t=1 s, and rotating with $\Omega = 354$ rad/s. ( $\Omega /\Omega _{\rm K}=0.995$ ). The surface is marked by the thick solid line. Because of relativistic effects, the stationary solution does not show exact cylindrical symmetry.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fig4.ps} \end{figure}$	Figure 4: Temporal evolution of the angular velocity $\Omega /\Omega _{\rm K}$ and the rotation parameter \|T/W\| for a sequence of rigidly rotating PNSs with constant angular momentum ( $1.5~GM_{\hbox{$\odot$ }}^2 /c$ ) and a fixed baryonic mass of $M_{\rm B} = 1.6~M_{\hbox{$\odot$ }}$ .
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$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0619fent.ps} \end{figure}$	Figure 5: Iso-enthalpy lines of a differentially rotating star with R₀=100 km, for t=1 s, and rotating with $\Omega = 354$ rad/s. ( $\Omega /\Omega _{\rm K}=0.995$ ). For low differential rotation the structure of the star still looks normal.
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$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0619feto.ps} \end{figure}$	Figure 6: Iso-enthalpy lines of a differentially rotating star with R₀=10 km, for t=1 s, and rotating with $\Omega = 1570$ rad/s. The toroidal shape is clearly visible for all models differentially rotating with R₀ smaller than a certain threshold.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0619J.ps} \end{figure}$	Figure 7: Total angular momentum as a function of the central angular velocity for PNSs with fixed baryonic mass of 1.6 $M_\odot$ at evolutionary times of 0.5 ( top), 1.0 ( middle) and 10 s ( bottom), and for different values of R₀: $R_0=\infty$ (solid), 50 km (dash-dot), 20 km (thick dashed), $R_{\rm eq}/2$ (thin dashed), 10 km (dots).
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0619TW.ps} \end{figure}$	Figure 8: Rotation parameter, \|T/W\|, as a function of the central angular velocity for PNS with fixed baryonic mass of 1.6 $M_\odot$ at evolutionary times of 0.5 ( top), 1.0 ( middle) and 10 s ( bottom), and for different values of R₀: $R_0=\infty$ (solid), 50 km (dash-dot), 20 km (thick dashed), $R_{\rm eq}/2$ (thin dashed), 10 km (dots).
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0619Ax.ps} \end{figure}$	Figure 9: Axis ratio (polar to equatorial) as a function of the central angular velocity for a PNS with a baryonic mass of 1.6 $M_\odot$ at t=10 s, and for different values of R₀: $R_0=\infty$ (solid), 50 km (dash-dot), 20 km (thick dashed), $R_{\rm eq}/2$ (thin dashed), 10 km (dots).
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0619fJ15.ps} \end{figure}$	Figure 10: Temporal evolution of the central angular velocity $\Omega _{\rm c}$ and of the rotation parameter \|T/W\| for two sequences of differentially rotating PNSs with R₀=10 km (solid line) and R₀=20 km (dashed line). In both cases we fix the total angular momentum to $1.5~GM_{\hbox{$\odot$ }}^2 /c$ and the baryonic mass to $M_{\rm B} = 1.6~M_{\hbox{$\odot$ }}$ .
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