Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[angle=-90,width=14cm,clip]{0106fig1.eps} \end{figure}$ Figure 1: Evolution of the equatorial velocities ( upper panels) and of the ratio $\frac{\Omega}{\Omega_{{\rm c}}}$ of the angular velocity to the critical angular velocity ( lower panels) at the surface of star models of different initial masses and metallicities. Values of the initial masses are indicated in the upper left and right panels. The initial masses corresponding to the tracks plotted in the middle panels are the same as those shown in the left panels. The initial rotational velocity of all the models is 300 km s^-1. Empty circles are placed at the stage when the star enters into the Wolf-Rayet phase.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{0106fig2.eps} \end{figure}$ Figure 2: Evolution as a function of the actual mass of the rotation period, of the surface equatorial velocity and of the ratio of the angular velocity to the critical value during the WR stage of rotating stars. The long-dashed lines in the panels for the velocities show the evolution of the radius in solar units. Left: the WR phase of a star with an initial mass of 60 $M_{\odot }$ with $v_{{\rm ini}}= 300$ km s^-1 and Z = 0.004. Right: for an initial mass of 60 $M_{\odot }$ with $v_{{\rm ini}}= 300$ km s^-1and Z = 0.040.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=14cm,clip]{0106fig3.eps} \end{figure}$ Figure 3: Evolutionary tracks for 40 and 120 $M_{\odot }$ rotating models at different metallicities. The initial velocity is 300 km s^-1. The light dotted lines correspond to the non-WR part of the tracks. The tracks during the WR phase are shown by heavy lines (continuous for the 120 $M_{\odot }$ and dashed for the 40 $M_{\odot }$ model). Symbols along the tracks are placed where the indicated surface hydrogen ( $X_{\rm surf}$ ) and helium ( $Y_{\rm surf}$ ) abundances are reached.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{0106fig4.eps} \end{figure}$ Figure 4: Evolution of the mass of the stars as a function of the effective temperature for different initial mass models (from 9 to 40 $M_{\odot }$ ) at various metallicities during the Main-Sequence phase ( $\upsilon _{\rm ini}=300$ km s^-1). The initial mass of the stars is the ordinate of the hottest point of each track (left point). Models at Z= 0.004, 0.008, 0.020 and 0.040 are shown with dotted, short-dashed, continuous and long-dashed lines respectively. One can note the effect of the crossing of the bistability limit around 25 000 K (see text).
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0106fig5.eps} \end{figure}$ Figure 5: Relations between the final and the initial mass for rotating stellar models at various metallicities. The line with slope one, labeled $\dot {M}=0$ , corresponds to the case without mass loss.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{0106fig6.eps} \end{figure}$ Figure 6: Evolution as a function of time of the total mass $M_{\rm Tot}$ and of the mass of the convective cores $M_{\rm cc}$ during the H- and He-burning phases, for a 60 $M_{\odot }$ stellar model with and without rotation at Z = 0.040. The type of the WR star at a given age is given in the upper part of the figure.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.65cm,clip]{0106fig7.eps} \end{figure}$ Figure 7: Lifetimes of Wolf-Rayet stars from various initial masses at four different metallicities. All the models begin their evolution with $\upsilon _{\rm ini}$ = 300 km s^-1 on the ZAMS, the corresponding time-averaged velocities during the MS O-type star phase are given in Table 1.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.65cm,clip]{0106fig8.eps} \end{figure}$ Figure 8: Lifetimes of Wolf-Rayet stars from various initial masses for Z = 0.040 and 0.004 from different sets of models: continuous lines are for the present rotating models with $\upsilon _{\rm ini}$ = 300 km s^-1, the dotted and dashed lines are for the non-rotating stellar models with "normal'' and "enhanced'' mass loss rates computed by Meynet et al. (1994). The black squares indicate the lifetimes obtained for the non-rotating 25, 60 and 120 $M_{\odot }$ models obtained in the present work at Z=0.040.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=14cm,clip]{0106fig9.eps}\end{figure}$ Figure 9: Variation of the durations of the WR subphases as a function of the initial mass at various metallicities. All the models begin their evolution with $\upsilon _{\rm ini}$ = 300 km s^-1.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.65cm,clip]{0106fg10.eps} \end{figure}$ Figure 10: Variation of the number ratios of Wolf-Rayet stars to O-type stars as a function of the metallicity. The observed points are taken from Maeder & Meynet (1994). The dotted line shows the predictions of the models of Meynet et al. (1994) with normal mass loss rates. The continuous and the dashed lines show the predictions of the present rotating and non-rotating stellar models respectively. The black pentagon shows the ratio predicted by Z=0.040 models computed with the metallicity dependence of the mass loss rates during the WR phase proposed by Crowther et al. (2002).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.65cm,clip]{0106fg11.eps} \end{figure}$ Figure 11: 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 continuous and dotted lines show the predictions of the present rotating and non-rotating stellar models respectively. The black pentagon shows the ratio predicted by Z=0.040 models computed with the metallicity dependence of the mass loss rates during the WR phase proposed by Crowther et al. (2002).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{0106fg12.eps} \end{figure}$ Figure 12: Variation of the number ratios of type Ib/Ic supernovae to type II supernovae. The crosses with the error bars correspond to the values deduced from observations by Prantzos & Boissier (2003). The dotted line is an analytical fit proposed by these authors. The continuous and dashed line show the predictions of the present rotating and non-rotating stellar models.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0106fg13.eps} \end{figure}$ Figure 13: Evolution during the MS phase of the N/C ratios (in number) at the surface of rotating stellar models as a function of the effective temperature. The differences in N/C ratios are given with respect to the initial values.
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In the text

$\begin{figure} \par\includegraphics[width=13cm,clip]{0106fg14.eps} \end{figure}$ Figure 14: Evolution as a function of the actual mass of the abundances (in mass fraction) of different elements at the surface of rotating 40 $M_{\odot }$ stellar models at various metallicities.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0106fg15.eps} \end{figure}$ Figure 15: 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 initial masses are indicated. Long-short dashed curves show the evolution of Z = 0.004 models, dashed-dotted curves, short-dashed curves and continuous lines show the evolutions for Z = 0.008, 0.020 and 0.040 respectively.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0106fg16.eps} \end{figure}$ Figure 16: Evolution of the ratios (C+O)/He as a function of the luminosity at the surface of 60 and 120 $M_{\odot }$ rotating models for various initial metallicities (see text). Long-short dashed curves show the evolution of Z = 0.004 models, dashed-dotted curves, short-dashed curves and continuous lines show the evolutions for Z = 0.008, 0.020 and 0.040 respectively. 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

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0106fig5.eps} \end{figure}$	Figure 5: Relations between the final and the initial mass for rotating stellar models at various metallicities. The line with slope one, labeled $\dot {M}=0$ , corresponds to the case without mass loss.
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$\begin{figure} \par\includegraphics[width=8.1cm,clip]{0106fig6.eps} \end{figure}$	Figure 6: Evolution as a function of time of the total mass $M_{\rm Tot}$ and of the mass of the convective cores $M_{\rm cc}$ during the H- and He-burning phases, for a 60 $M_{\odot }$ stellar model with and without rotation at Z = 0.040. The type of the WR star at a given age is given in the upper part of the figure.
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$\begin{figure} \par\includegraphics[angle=-90,width=8.65cm,clip]{0106fig7.eps} \end{figure}$	Figure 7: Lifetimes of Wolf-Rayet stars from various initial masses at four different metallicities. All the models begin their evolution with $\upsilon _{\rm ini}$ = 300 km s^-1 on the ZAMS, the corresponding time-averaged velocities during the MS O-type star phase are given in Table 1.
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$\begin{figure} \par\includegraphics[angle=-90,width=14cm,clip]{0106fig9.eps}\end{figure}$	Figure 9: Variation of the durations of the WR subphases as a function of the initial mass at various metallicities. All the models begin their evolution with $\upsilon _{\rm ini}$ = 300 km s^-1.
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$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{0106fg12.eps} \end{figure}$	Figure 12: Variation of the number ratios of type Ib/Ic supernovae to type II supernovae. The crosses with the error bars correspond to the values deduced from observations by Prantzos & Boissier (2003). The dotted line is an analytical fit proposed by these authors. The continuous and dashed line show the predictions of the present rotating and non-rotating stellar models.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0106fg13.eps} \end{figure}$	Figure 13: Evolution during the MS phase of the N/C ratios (in number) at the surface of rotating stellar models as a function of the effective temperature. The differences in N/C ratios are given with respect to the initial values.
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$\begin{figure} \par\includegraphics[width=13cm,clip]{0106fg14.eps} \end{figure}$	Figure 14: Evolution as a function of the actual mass of the abundances (in mass fraction) of different elements at the surface of rotating 40 $M_{\odot }$ stellar models at various metallicities.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0106fg15.eps} \end{figure}$	Figure 15: 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 initial masses are indicated. Long-short dashed curves show the evolution of Z = 0.004 models, dashed-dotted curves, short-dashed curves and continuous lines show the evolutions for Z = 0.008, 0.020 and 0.040 respectively.
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