All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{1095fg01.eps} \end{figure}$ Figure 1: HR-diagram for 20 $M_{\odot }$ models: solid, dashed, dotted-dashed and dotted lines correspond respectively to $v_{\rm {ini}}= 0$ , 100, 200 and 300 km s^-1. We also indicate the position of the progenitor of SN 1993J.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1095fg02.eps} \end{figure}$ Figure 2: 3D HR diagram with central helium mass fraction as the third dimension for non-rotating and rotating 20 $M_{\odot }$ models.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1095fg03.eps} \end{figure}$ Figure 3: $T_{\rm {eff}}$ vs. central helium mass fraction for 20 $M_{\odot }$ models: solid, dashed, dotted-dashed and dotted lines correspond respectively to $v_{\rm {ini}}= 0$ , 100, 200 and 300 km s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg04.eps} \end{figure}$ Figure 4: Burning lifetimes as a function of the initial mass and velocity. Solid and dotted lines correspond respectively to rotating and non-rotating models. Long-dashed and dotted-dashed lines are used for rotating and non-rotating Ne-burning lifetimes to point out that they are to be considered as estimates (see text).
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg05.eps} \end{figure}$ Figure 5: $\Omega$ variations as a function of the radius inside 15 $M_{\odot }$ models: the dashed line is a profile from a model without dynamical shear and the solid line from a model with dynamical shear and ${\rm Ri}_{\rm c}=1$ during core O-burning. The long and short arrows indicate the zones where ${\rm Ri}<1$ in the model without and with dynamical shear respectively. Note that the profiles do not differ significantly.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg06.eps} \end{figure}$ Figure 6: Angular velocity as a function of the lagrangian mass coordinate, m_r inside the 25 $M_{\odot }$ model ( $v_{\rm {ini}}= 300$ km s^-1) at various evolutionary stages.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg07.eps} \end{figure}$ Figure 7: Local specific angular momentum profiles for the 25 $M_{\odot }$ model ( $v_{\rm {ini}}= 300$ km s^-1) at different evolutionary stages.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg08.eps}\hspace*{4mm} \includegraphics[width=8.4cm,clip]{1095fg09.eps} \end{figure}$ Figure 8: Log $T_{\rm {c}}$ vs. Log $\rho _{\rm {c}}$ diagrams: left: evolutionary tracks for the 15 and 60 $M_{\odot }$ models. Right: evolutionary tracks zoomed in the advanced stages for the 12, 20 and 40 $M_{\odot }$ models. Solid lines are rotating models and dashed lines are non-rotating models. The ignition points of every burning stage are connected with dotted lines. The additional long dashed line corresponds to the limit between non-degenerate and degenerate electron gas ( $P^{\rm{el}}_{\rm{perfect~gas}}=P^{\rm{el}}_{{\rm degenerate~gas}}$ ).
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg10.eps}\hspace*{2mm} \includegraphics[width=8.5cm,clip]{1095fg11.eps} \end{figure}$ Figure 9: Log of the energy production rate per unit mass at the star center as a function of the time left until core collapse for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models. Nuclear energy production rates during H- and He-burnings are shown in dotted ( $\varepsilon _{\rm H}$ ) and dashed ( $\varepsilon _{\rm He}$ ) lines respectively. The solid line corresponds to the nuclear energy production rate in absolute value during the advanced stages ( $\varepsilon _{\rm C}{-}\varepsilon _{\rm Si}$ ). Black crosses are drawn on top of the line whenever the energy production rate is negative. The thick long dashed line is the energy loss rates due to neutrinos multiplied by -1( $- \varepsilon _{\nu }$ ). Finally the gravitational energy production rate in absolute value is plotted in the dotted-dashed line ( $\varepsilon _{g}$ ). Blue squares are plotted on top when this energy is negative. Note that negative gravitational energy production corresponds to an expansion.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{1095fg12.eps}\hspace*{2mm} \includegraphics[width=8.4cm,clip]{1095fg13.eps} \end{figure}$ Figure 10: Log of the energy production rate per unit mass as a function of $m_r/M_{\rm tot}$ during shell C-burning for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models. The solid line corresponds to the nuclear energy in absolute value during C-burning ( $\varepsilon _{\rm C}$ ). Nuclear energy during H- and He-burnings are shown in dashed ( $\varepsilon _{\rm He}$ ) and dotted ( $\varepsilon _{\rm H}$ ) lines respectively. The long dashed line is the energy loss rates due to neutrinos multiplied by -1( $- \varepsilon _{\nu }$ ). Finally the gravitational energy production rate in absolute value is plotted in the dotted-dashed line ( $\varepsilon _{g}$ ). Blue squares are plotted on top when this energy is negative. Note that negative gravitational energy corresponds to an expansion.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg14.eps}\hspace*{4mm}... ...8.eps}\hspace*{4mm}\includegraphics[width=7.2cm,clip]{1095fg19.eps} \end{figure}$ Figure 11: Kippenhahn diagrams for the non-rotating ( left) and $v_{\rm {ini}}= 300$ km s^-1 ( right) 12 ( top), 15 ( middle) and 20 ( bottom) $M_{\odot }$ models. The black zones correspond to convective regions (see text).
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg20.eps}\hspace*{4mm}... ...4.eps}\hspace*{4mm}\includegraphics[width=7.2cm,clip]{1095fg25.eps} \end{figure}$ Figure 12: Kippenhahn diagram for the non-rotating ( left) and $v_{\rm {ini}}= 300$ km s^-1 ( right) 25 ( top), 40 ( middle) and 60 ( bottom) $M_{\odot }$ models. The black zones correspond to convective regions (see text).
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg26.eps} \end{figure}$ Figure 13: Variations of the abundance (in mass fraction) as a function of the lagrangian mass coordinate, m_r, at the end of central Si-burning for the rotating 60 $M_{\odot }$ . Note that the ⁴⁴Ti abundance (dotted-long dashed line) is enhanced by a factor 1000 for display purposes.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg27.eps}\hspace*{4mm}... ...1.eps}\hspace*{4mm}\includegraphics[width=7.2cm,clip]{1095fg32.eps} \end{figure}$ Figure 14: Variation of the abundances in mass fraction as a function of the lagrangian mass at the end of central hydrogen ( top), helium ( middle) and carbon ( bottom) burnings for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg33.eps}\hspace*{4mm}... ...7.eps}\hspace*{4mm}\includegraphics[width=7.2cm,clip]{1095fg38.eps} \end{figure}$ Figure 15: Variation of the abundances in mass fraction as a function of the lagrangian mass at the end of central neon ( top), oxygen ( middle) and silicon ( bottom) burnings for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models. Note that the abundance of ⁴⁴Ti (dotted-long dashed line) is enhanced by a factor 1000 for display purposes.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg39.eps} \end{figure}$ Figure 16: Core masses as a function of the initial mass and velocity at the end of core Si-burning.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg40.eps}\hspace*{2mm} \includegraphics[width=8.3cm,clip]{1095fg41.eps} \end{figure}$ Figure 17: Profiles of the radius, r, density, $\rho$ , temperature, Tand pressure P at the end of core Si-burning for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models. The pressure has been divided by 10¹⁰ to fit it in the diagram.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg42.eps} \end{figure}$ Figure 18: Variation of the He core masses, $M_\alpha$ (light lines), and of the CO core masses, $M_{\rm CO}$ (heavy lines), at the pre-supernova stage in different initial mass models. Only non-rotating models are shown. The different types of line correspond to results obtained by different groups: HMM labels our results, W86 those of Woosley & Weaver (1986), RHW those of Rauscher et al. (2002), LSC those of Limongi et al. (2000) and HLW those of Heger et al. (2000).
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg43.eps} \end{figure}$ Figure 19: $M_{\rm {iron}}$ (and $M_{\rm {Si}}$ ) as a function of $M_\alpha$ for non-rotating models from different authors (see Table 4). The labels are the same as in Fig. 18. The light lines show the variation of $M_{\rm {Si}}$ , the heavy lines those of $M_{\rm {iron}}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg44.eps} \end{figure}$ Figure 20: $M_{\rm {iron}}$ (and $M_{\rm {Si}}$ ) as a function of $M_{\rm CO}$ for non-rotating models from different authors (see Table 4). The labels are the same as in Fig. 18. The light lines show the variation of $M_{\rm {Si}}$ , the heavy lines those of $M_{\rm {iron}}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1095fg45.eps} \end{figure}$ Figure 21: Comparison of different ¹²C $(\alpha ,\gamma )^{16}$ O reaction rates according to various authors: CF85 labels the rate given by Caughlan et al. (1985), CF88, the rate of Caughlan & Fowler (1988), BU96 the rate of Buchmann (1996) and K02 the one of Kunz et al. (2002). All the rates are normalised to the rate given by NACRE (Angulo et al. 1999).
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg46.eps} \end{figure}$ Figure 22: Comparison of the final local specific angular momentum profiles for different 20 $M_{\odot }$ models. Models with different initial velocities, $\upsilon _{\rm {ini}}= 100$ , 200 and 300 km s^-1 are drawn with dotted, solid and thick solid lines respectively. We can see the convergence of the final of the final angular momentum of the core above $\upsilon _{\rm {ini}}= 200$ km s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg47.eps} \end{figure}$ Figure 23: Comparison of the final local specific angular momentum profiles for different 20 $M_{\odot }$ models all with the same initial rotational velocity, $\upsilon _{\rm {ini}}= 200$ km s^-1. The thick solid line (HMM) corresponds to our model. The models from Heger et al. (2000) are drawn with a dotted-dashed line for model E20 (no $\mu$ -barrier) and with a dashed line for model E20B ( $\mu$ -barrier with $f_{\mu }=0.05$ ). Finally, model m20b5 from Heger et al. (2003) including the effect of the magnetic fields according to Spruit (2002) is drawn with the dotted line.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1095fg01.eps} \end{figure}$	Figure 1: HR-diagram for 20 $M_{\odot }$ models: solid, dashed, dotted-dashed and dotted lines correspond respectively to $v_{\rm {ini}}= 0$ , 100, 200 and 300 km s^-1. We also indicate the position of the progenitor of SN 1993J.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1095fg02.eps} \end{figure}$	Figure 2: 3D HR diagram with central helium mass fraction as the third dimension for non-rotating and rotating 20 $M_{\odot }$ models.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1095fg03.eps} \end{figure}$	Figure 3: $T_{\rm {eff}}$ vs. central helium mass fraction for 20 $M_{\odot }$ models: solid, dashed, dotted-dashed and dotted lines correspond respectively to $v_{\rm {ini}}= 0$ , 100, 200 and 300 km s^-1.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg04.eps} \end{figure}$	Figure 4: Burning lifetimes as a function of the initial mass and velocity. Solid and dotted lines correspond respectively to rotating and non-rotating models. Long-dashed and dotted-dashed lines are used for rotating and non-rotating Ne-burning lifetimes to point out that they are to be considered as estimates (see text).
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg06.eps} \end{figure}$	Figure 6: Angular velocity as a function of the lagrangian mass coordinate, m_r inside the 25 $M_{\odot }$ model ( $v_{\rm {ini}}= 300$ km s^-1) at various evolutionary stages.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg07.eps} \end{figure}$	Figure 7: Local specific angular momentum profiles for the 25 $M_{\odot }$ model ( $v_{\rm {ini}}= 300$ km s^-1) at different evolutionary stages.
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg14.eps}\hspace{4mm}... ...8.eps}\hspace{4mm}\includegraphics[width=7.2cm,clip]{1095fg19.eps} \end{figure}$	Figure 11: Kippenhahn diagrams for the non-rotating ( left) and $v_{\rm {ini}}= 300$ km s^-1 ( right) 12 ( top), 15 ( middle) and 20 ( bottom) $M_{\odot }$ models. The black zones correspond to convective regions (see text).
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg20.eps}\hspace{4mm}... ...4.eps}\hspace{4mm}\includegraphics[width=7.2cm,clip]{1095fg25.eps} \end{figure}$	Figure 12: Kippenhahn diagram for the non-rotating ( left) and $v_{\rm {ini}}= 300$ km s^-1 ( right) 25 ( top), 40 ( middle) and 60 ( bottom) $M_{\odot }$ models. The black zones correspond to convective regions (see text).
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg26.eps} \end{figure}$	Figure 13: Variations of the abundance (in mass fraction) as a function of the lagrangian mass coordinate, m_r, at the end of central Si-burning for the rotating 60 $M_{\odot }$ . Note that the ⁴⁴Ti abundance (dotted-long dashed line) is enhanced by a factor 1000 for display purposes.
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg27.eps}\hspace{4mm}... ...1.eps}\hspace{4mm}\includegraphics[width=7.2cm,clip]{1095fg32.eps} \end{figure}$	Figure 14: Variation of the abundances in mass fraction as a function of the lagrangian mass at the end of central hydrogen ( top), helium ( middle) and carbon ( bottom) burnings for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models.
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{1095fg33.eps}\hspace{4mm}... ...7.eps}\hspace{4mm}\includegraphics[width=7.2cm,clip]{1095fg38.eps} \end{figure}$	Figure 15: Variation of the abundances in mass fraction as a function of the lagrangian mass at the end of central neon ( top), oxygen ( middle) and silicon ( bottom) burnings for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models. Note that the abundance of ⁴⁴Ti (dotted-long dashed line) is enhanced by a factor 1000 for display purposes.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1095fg39.eps} \end{figure}$	Figure 16: Core masses as a function of the initial mass and velocity at the end of core Si-burning.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg40.eps}\hspace*{2mm} \includegraphics[width=8.3cm,clip]{1095fg41.eps} \end{figure}$	Figure 17: Profiles of the radius, r, density, $\rho$ , temperature, Tand pressure P at the end of core Si-burning for the non-rotating ( left) and rotating ( right) 20 $M_{\odot }$ models. The pressure has been divided by 10¹⁰ to fit it in the diagram.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg43.eps} \end{figure}$	Figure 19: $M_{\rm {iron}}$ (and $M_{\rm {Si}}$ ) as a function of $M_\alpha$ for non-rotating models from different authors (see Table 4). The labels are the same as in Fig. 18. The light lines show the variation of $M_{\rm {Si}}$ , the heavy lines those of $M_{\rm {iron}}$ .
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1095fg44.eps} \end{figure}$	Figure 20: $M_{\rm {iron}}$ (and $M_{\rm {Si}}$ ) as a function of $M_{\rm CO}$ for non-rotating models from different authors (see Table 4). The labels are the same as in Fig. 18. The light lines show the variation of $M_{\rm {Si}}$ , the heavy lines those of $M_{\rm {iron}}$ .
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{1095fg45.eps} \end{figure}$	Figure 21: Comparison of different ¹²C $(\alpha ,\gamma )^{16}$ O reaction rates according to various authors: CF85 labels the rate given by Caughlan et al. (1985), CF88, the rate of Caughlan & Fowler (1988), BU96 the rate of Buchmann (1996) and K02 the one of Kunz et al. (2002). All the rates are normalised to the rate given by NACRE (Angulo et al. 1999).
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