All Figures

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{veqX.eps}} \end{figure}$ Figure 1: Evolution of the rotational velocities for star models of different initial masses between 120 and 9 $M_{\odot }$ with account taken of anisotropic mass loss during the MS phase. The rapid decrease near the end of the MS evolution is due to the bi-stability limit in the mass loss rates. The location of the end of the MS phase corresponds to the vertical decrease of the velocity.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{omcX.eps}} \end{figure}$ Figure 2: Evolution of the fraction $\frac{\Omega}{\Omega_{{\rm c}}}$ of the angular velocity to the critical angular velocity at the surface of star models of different initial masses between 120 and 9 $M_{\odot }$ with account taken of anisotropic mass loss during the MS phase.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{vrotwr1.eps}} \end{figure}$ Figure 3: Evolution as a function of the actual mass of the rotation period, the rotational velocity and the ratio of the angular velocity to the critical value during the WR stage of massive stars. The continuous line corresponds to the so-called eWNL phase (see text), the dotted and short-dashed lines show the evolution during the eWNE and WC phases respectively. The long-dashed lines in the panels for the velocities show the evolution of the polar radius, (in this case the unity on the ordinates are $R/R_{\odot }$ ). Left: the WR phase of a star with an initial mass of 85 $M_{\odot }$ with $v_{{\rm ini}}= 300$ km s^-1. Right: the same for an initial mass of 25 $M_{\odot }$ with $v_{{\rm ini}}= 300$ km s^-1.
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In the text

$\begin{figure} \par\resizebox{8.2cm}{!}{\includegraphics[clip]{vrotwr2.eps}} \end{figure}$ Figure 4: Same as Fig. 3 for 60 $M_{\odot }$ stellar models. Left: the WR phase of a star with an initial mass of 60 $M_{\odot }$ and $v_{{\rm ini}}= 300$ km s^-1. Right: for an initial mass of 60 $M_{\odot }$ with $v_{{\rm ini}}= 500$ km s^-1. In the e-version, the red color corresponds to the phase where H is present (eWNL), the black to the phase of an He-star (eWNE) and the blue to the WC phase.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=15.3cm,clip]{hrX.eps} \end{figure}$ Figure 5: Evolutionary tracks for non-rotating (dotted lines) and rotating (continuous lines) models for a metallicity Z = 0.020. The rotating models have an initial velocity $v_{\rm ini}$ of 300 km s^-1, which corresponds to an average velocity during the MS phase of about 180 to 240 km s^-1 (see Table 1).
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{finalX.eps}} \end{figure}$ Figure 6: Relations between the final mass versus the initial mass for solar metallicity models. The cases with and without rotation are indicated. The line with slope one, labeled by $\dot {M}=0$ , would correspond to a case without mass loss. The relation obtained from the models of Schaller et al. (1992) is also shown.
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In the text

$\begin{figure} \par\resizebox{8.15cm}{!}{\includegraphics[clip]{hrkiport.eps}} \end{figure}$ Figure 7: The two upper panels show the evolutionary tracks of a non-rotating and a rotating 60 $M_{\odot }$ stellar model. The bold part of the track corresponds to the O-type star Main-Sequence phase; the dotted part shows the intermediate phase, when present, between the O-type star phase and the WR phase; the thin continuous line is the track during the WR phase. The two lower panels show the evolution as a function of time of the total mass and of the masses of the convective cores during the H- and the He-burning phases.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{wr120X.eps}} \end{figure}$ Figure 8: Evolutionary tracks for a non-rotating (light dotted-line) and a rotating 120 $M_{\odot }$ stellar model at solar metallicity. The circles along the tracks indicate the end ofthe eWNL phase, the squares the end of the eWNE phase, and the triangles, the beginning of the WC phase. The WN/WC stars lie along the portion of the tracks between the squares and the triangles. The crosses indicate the end of the central H-burning phase.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{tma.eps}}\end{figure}$ Figure 9: Lifetimes of WR stars of different initial mass for non-rotating stellar models. The durations of the WR sub-phases are also indicated. There is no transition WN/WC phase.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{tma2.eps}} \end{figure}$ Figure 10: Lifetimes for rotating stellar models in the WR subphases.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{twrviX.eps}} \end{figure}$ Figure 11: Durations of the WR phases and of the WR sub-phases for stars of 60 $M_{\odot }$ with various initial velocities.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{twrX.eps}} \end{figure}$ Figure 12: Lifetimes of Wolf-Rayet stars from various initial masses at solar metallicity. The continuous line shows the results from the present rotating models. The WR lifetimes of the non-rotating models from the present work are shown by the dotted line. The short- and long-dashed curves show the results obtained from the models of Schaller et al. (1992) and Meynet et al. (1994) with normal ( $1 \times \dot{M}$ ) and enhanced mass loss rates ( $2 \times \dot{M}$ ) respectively.
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In the text

$\begin{figure} \par\resizebox{8.7cm}{!}{\includegraphics[angle=-90,clip]{wroX.eps}} \end{figure}$ Figure 13: Variation of the number ratios of Wolf-Rayet stars to O-type stars as a function of the metallicity. The observed points are taken as in Maeder & Meynet (1994). The dotted and continuous lines show the predictions of the models of Schaller et al. (1992) and Meynet et al. (1994) with normal and enhanced mass loss rates respectively. The black square and triangle show the predictions of the present non-rotating and rotating stellar models respectively.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[angle=-90,clip]{massey.eps}} \end{figure}$ Figure 14: Variation of the number ratios of WN to WC stars as a function of metallicity. The black circles are observed points taken from Massey & Johnson (2001 and see references therein), except for the SMC (Massey & Duffy 2001), for NGC 300 (Schild et al. 2002) and for IC10, for which we show the estimate from Massey & Holmes (2002). The black square and triangle show the predictions of the present non-rotating and rotating stellar models respectively.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{nc.eps}} \end{figure}$ Figure 15: Evolution of the N/C ratios (in number) as a function of the effective temperature at the surface of various rotating stellar models. The N/C ratios are normalized to their initial values. The continuous lines show the results for the present rotating models ( $\upsilon _{\rm ini}$ = 300 km s^-1), the dashed-lines show the evolutionary tracks for some models of Paper V. For purpose of clarity, only a part of the 40 $M_{\odot }$ tracks are shown.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{xi60X.eps}} \end{figure}$ Figure 16: Evolution as a function of the actual mass of the abundances (in mass fraction) at the surface of a non-rotating (upper panel) and a rotating (lower panel) 60 $M_{\odot }$ stellar model.
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In the text

$\begin{figure} \par\resizebox{8.75cm}{!}{\includegraphics[angle=-90,clip]{wnc.eps}} \end{figure}$ Figure 17: Evolution of the abundance ratio C/N at the surface of a 40 $M_{\odot }$ stellar model with $\upsilon _{\rm ini}$ = 300 km s^-1 as a function of the ratio C/He. Only the beginning of the WR phase is shown. The equilibrium value of the C/N ratio is around 0.015. Observations as given in the paper by Crowther et al. (1995) are indicated.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{xi40X.eps}} \end{figure}$ Figure 18: Same as Fig. 16 for 40 $M_{\odot }$ stellar models.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{xsl.eps}} \end{figure}$ Figure 19: Evolutionary tracks in the $X_{\rm s}$ versus log $L/L_\odot$ plane, where $X_{\rm s}$ is the hydrogen mass fraction at the surface. The continuous lines are for the rotating models, the dotted or dashed-lines are for the non-rotating models.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{cohe.eps}} \end{figure}$ Figure 20: Evolution of the ratios (C+O)/He as a function of the luminosity at the surface of non-rotating (dashed-lines) and rotating models (continuous lines) for various initial mass models. The correspondence between the (C+O)/He ratios and the different WC subtypes as given by Smith & Maeder 1991 is indicated on the right of the figure.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{veqX.eps}} \end{figure}$	Figure 1: Evolution of the rotational velocities for star models of different initial masses between 120 and 9 $M_{\odot }$ with account taken of anisotropic mass loss during the MS phase. The rapid decrease near the end of the MS evolution is due to the bi-stability limit in the mass loss rates. The location of the end of the MS phase corresponds to the vertical decrease of the velocity.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{omcX.eps}} \end{figure}$	Figure 2: Evolution of the fraction $\frac{\Omega}{\Omega_{{\rm c}}}$ of the angular velocity to the critical angular velocity at the surface of star models of different initial masses between 120 and 9 $M_{\odot }$ with account taken of anisotropic mass loss during the MS phase.
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$\begin{figure} \par\includegraphics[angle=-90,width=15.3cm,clip]{hrX.eps} \end{figure}$	Figure 5: Evolutionary tracks for non-rotating (dotted lines) and rotating (continuous lines) models for a metallicity Z = 0.020. The rotating models have an initial velocity $v_{\rm ini}$ of 300 km s^-1, which corresponds to an average velocity during the MS phase of about 180 to 240 km s^-1 (see Table 1).
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{finalX.eps}} \end{figure}$	Figure 6: Relations between the final mass versus the initial mass for solar metallicity models. The cases with and without rotation are indicated. The line with slope one, labeled by $\dot {M}=0$ , would correspond to a case without mass loss. The relation obtained from the models of Schaller et al. (1992) is also shown.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{tma.eps}}\end{figure}$	Figure 9: Lifetimes of WR stars of different initial mass for non-rotating stellar models. The durations of the WR sub-phases are also indicated. There is no transition WN/WC phase.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{tma2.eps}} \end{figure}$	Figure 10: Lifetimes for rotating stellar models in the WR subphases.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{twrviX.eps}} \end{figure}$	Figure 11: Durations of the WR phases and of the WR sub-phases for stars of 60 $M_{\odot }$ with various initial velocities.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{xi60X.eps}} \end{figure}$	Figure 16: Evolution as a function of the actual mass of the abundances (in mass fraction) at the surface of a non-rotating (upper panel) and a rotating (lower panel) 60 $M_{\odot }$ stellar model.
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$\begin{figure} \par\resizebox{8.75cm}{!}{\includegraphics[angle=-90,clip]{wnc.eps}} \end{figure}$	Figure 17: Evolution of the abundance ratio C/N at the surface of a 40 $M_{\odot }$ stellar model with $\upsilon _{\rm ini}$ = 300 km s^-1 as a function of the ratio C/He. Only the beginning of the WR phase is shown. The equilibrium value of the C/N ratio is around 0.015. Observations as given in the paper by Crowther et al. (1995) are indicated.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{xi40X.eps}} \end{figure}$	Figure 18: Same as Fig. 16 for 40 $M_{\odot }$ stellar models.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{xsl.eps}} \end{figure}$	Figure 19: Evolutionary tracks in the $X_{\rm s}$ versus log $L/L_\odot$ plane, where $X_{\rm s}$ is the hydrogen mass fraction at the surface. The continuous lines are for the rotating models, the dotted or dashed-lines are for the non-rotating models.
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$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{cohe.eps}} \end{figure}$	Figure 20: Evolution of the ratios (C+O)/He as a function of the luminosity at the surface of non-rotating (dashed-lines) and rotating models (continuous lines) for various initial mass models. The correspondence between the (C+O)/He ratios and the different WC subtypes as given by Smith & Maeder 1991 is indicated on the right of the figure.
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