All Figures

$\begin{figure} \par\includegraphics[angle=-90,width=6.7cm,clip]{5251fig1.ps}\end{figure}$ Figure 1: Examples of main sequence (MS) and post-main sequence (PoMS1 and PoMS2 - see description in text) models satisfying the observational constraints for Procyon A: its position in the HR diagram constrained by effective temperature and the luminosity from Steffen (1985) (dashed box); the VINCI/VLTI (Kervella et al. 2002) radius measurement reduces the possible domain (grey area).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.85cm,clip]{5251fig2.ps}\end{figure}$ Figure 2: Large frequency spacings $\Delta \nu _{n,\ell }$ for degrees $\ell$ = 0 and $\ell$ = 1 for frequencies of Martic et al. (2004) (star) and Eggenberger et al. (2004)(square). The hatched areas indicate the values of mean large frequency spacing $\overline {\Delta \nu }_{\rm obs}$ for the two sets of observations (lower for the Martíc's data).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.1cm,clip]{5251fi3a.ps}\par\includegraphics[angle=-90,width=6.1cm,clip]{5251fi3b.ps}\end{figure}$ Figure 3: Small frequency spacings $\delta \nu _{02}$ and $\delta \nu _{01}$ for the frequencies of Martic et al. (2004) and Eggenberger et al. (2004). The same symbols as in Fig. 2.
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In the text

$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fig4.ps}\end{figure}$ Figure 4: Initial chemical composition of our models for Procyon A satisfying the constraints of Table 1. Grey open symbols indicate MS models, dark filled symbols PoMS models. Diamond 1.36 $M_\odot$ , circle 1.38 $M_\odot$ , triangle 1.42 $M_\odot$ , stars 1.44 $M_\odot$ , square 1.45 $M_\odot$ , diamond 1.46 $M_\odot$ , cross 1.48 $M_\odot$ . The two full lines indicate the minimum and maximum values of $Y_{\rm i}$ resulting from the constraint of the galaxy chemical evolution given in Table 1. The dotted line corresponds to a stronger constraint ${\Delta Y/\Delta Z}\le 3$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fig5.ps}\end{figure}$ Figure 5: Initial helium versus age. Same models and symbols as in Fig. 4.
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In the text

$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fig6.ps}\end{figure}$ Figure 6: Frequencies $\nu _{G \ell }$ of the highest-frequency gravity modes for $\ell$ = 2 and 3 versus the characteristic period P₀. The two regions where points are lacking correspond to the turning point of the evolutionary track in the HR diagram. There the models stay a very short time. Same models and symbols as in Fig. 4.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{5251fi7a.ps}\includegraphics[width=7.4cm,clip]{5251fi7b.ps}\end{figure}$ Figure 7: Left panel: propagation diagram: variation of the Brunt-Väissälä frequency N (full line) and of the Lamb frequency S $_\ell$ ( $\ell$ = 1, 2, 3 dashed lines) in $\mu$ Hz as a function of the stellar normalized radius rfor a PoMS model with mass 1.38 $M_\odot$ . Right panel: frequency versus logarithm of the non-dimensioned kinetic energy E of the mode for consecutive modes of degree $\ell$ = 0 (dotted), 1 (full), 2 (dashed), 3 (fancy) of the same model. The values of the highest frequency gravity modes for $\ell$ = 2 and $\ell$ = 3 are given by the horizontal lines in the left panel and by the arrows in the right panel. The heavy lines indicate the regions where these modes are propagative. Most of their amplitude is located in the core (see also Fig. 8 (1)).
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In the text

$\begin{figure} \par\includegraphics[width=7.65cm,clip]{5251fig8.ps}\end{figure}$ Figure 8: Kinetic energy density as a function of the radius for different type of modes $\ell$ = 2 of the same PoMS model as in Fig. 7: (1) gravity mode $\nu \sim 1144~\mu$ Hz, (2) acoustic mode p20 $\nu \sim 1176~\mu$ Hz, (3) and (4) two consecutive mixed modes $\nu \sim 994$ and 998 $\mu$ Hz in between the pure acoustic modes p12 and p14.
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In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{5251fig9.ps}\end{figure}$ Figure 9: Large frequency spacing normalized to the observed radius of Procyon A as a function of the mass. Its increase with respect to the mass is larger for PoMS than for MS models. Open (filled) symbols for MS (PoMS) models.
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In the text

$\begin{figure} \par\includegraphics[width=6.55cm,clip]{5251f10a.ps}\vspace*{-0.09cm} \includegraphics[width=6.55cm,clip]{5251f10b.ps}\end{figure}$ Figure 10: Large frequency spacings for $\ell$ = 0 ( up) and 1 ( down) for MS/PoMS models (full/dashed line) compared to Martic (stars) and Eggenberger (square) observations.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{5251fi11.ps}\end{figure}$ Figure 11: Seismic quantity $\varepsilon$ characterizing the model evolutionary stage versus the mean large frequency spacing $\overline {\Delta \nu }$ . Grey open symbols indicate MS models, dark filled symbols PoMS models. Diamond 1.36 $M_\odot$ , circle 1.38 $M_\odot$ , triangle 1.42 $M_\odot$ , stars 1.44 $M_\odot$ , square 1.45 $M_\odot$ , diamond 1.46 $M_\odot$ , cross 1.48 $M_\odot$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fi12.ps}\end{figure}$ Figure 12: Characteristic period P₀ of gravity modes as a function of the seismic quantity $\varepsilon$ characterizing the model evolutionary stage.
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In the text

$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fi13.ps}\end{figure}$ Figure 13: Characteristics $\delta _0$ and S₀of the small frequency spacings $\delta \nu _{02}$ . The dashed box indicates the location of PoMS1 models. Same models and symbols as in Fig. 11.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5251fi14.ps}\end{figure}$ Figure 14: Variation in the small frequency spacing $\delta \nu _{02}$ with the frequency for the same MS/PoMS models (full/dashed line) as in Fig. 10. The dashed line with the highest peak in the high-frequency range ( $\nu \leq 800~\mu$ Hz) corresponds to the PoMS model with the lower negative value of the slope S₀ (model at the upper left corner in Fig. 13). If we perform a least-square linear fit removing the point at the peak, we obtain a slope $S_0\sim -7$ $\times$ $10^{-4}~\mu$ Hz, instead of -0.125 $\mu$ Hz. This would move the corresponding point towards a region in continuity with MS models in Fig. 13.
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In the text

$\begin{figure} \par\includegraphics[width=7.05cm,clip]{5251fi15.ps}\end{figure}$ Figure 15: Behavior of the small frequency spacing $\delta \nu _{01}$ . Same symbols as in Fig. 13 (grey/dark for MS/PoMS models), but with different sizes for the PoMS models (dark symbols), the largest full symbols corresponding to the PoMS2 models (central hydrogen less than 0.001). Upper panel: $\delta _1$ versus slope S₁. Lower panel: curvature $\gamma _1$ versus slope S₁. The three groups of points with $S_1 \le 0$ correspond to models with different overshoot parameters, $\zeta =0.2, 0.1$ and 0. from the left to the right.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=7.5cm,clip]{5251f16a.ps}\par\includegraphics[angle=-90,width=7.5cm,clip]{5251f16b.ps}\end{figure}$ Figure 16: MS and PoMS models computed with different values of the additional mixing parameter (cf. Table 2): ${\rm Re}_\nu$ = 0.5 (dotted line), 1. (dashed line), 1.5 (full line). The evolutionary tracks and final position in the HR diagram are very close ( higher panel). The variation in surface metallicity as a function of the age and its final value are very different for MS models ( lower panel).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.7cm,clip]{5251fig1.ps}\end{figure}$	Figure 1: Examples of main sequence (MS) and post-main sequence (PoMS1 and PoMS2 - see description in text) models satisfying the observational constraints for Procyon A: its position in the HR diagram constrained by effective temperature and the luminosity from Steffen (1985) (dashed box); the VINCI/VLTI (Kervella et al. 2002) radius measurement reduces the possible domain (grey area).
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$\begin{figure} \par\includegraphics[angle=-90,width=6.85cm,clip]{5251fig2.ps}\end{figure}$	Figure 2: Large frequency spacings $\Delta \nu _{n,\ell }$ for degrees $\ell$ = 0 and $\ell$ = 1 for frequencies of Martic et al. (2004) (star) and Eggenberger et al. (2004)(square). The hatched areas indicate the values of mean large frequency spacing $\overline {\Delta \nu }_{\rm obs}$ for the two sets of observations (lower for the Martíc's data).
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$\begin{figure} \par\includegraphics[angle=-90,width=6.1cm,clip]{5251fi3a.ps}\par\includegraphics[angle=-90,width=6.1cm,clip]{5251fi3b.ps}\end{figure}$	Figure 3: Small frequency spacings $\delta \nu _{02}$ and $\delta \nu _{01}$ for the frequencies of Martic et al. (2004) and Eggenberger et al. (2004). The same symbols as in Fig. 2.
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$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fig5.ps}\end{figure}$	Figure 5: Initial helium versus age. Same models and symbols as in Fig. 4.
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$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fig6.ps}\end{figure}$	Figure 6: Frequencies $\nu _{G \ell }$ of the highest-frequency gravity modes for $\ell$ = 2 and 3 versus the characteristic period P₀. The two regions where points are lacking correspond to the turning point of the evolutionary track in the HR diagram. There the models stay a very short time. Same models and symbols as in Fig. 4.
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$\begin{figure} \par\includegraphics[width=7.65cm,clip]{5251fig8.ps}\end{figure}$	Figure 8: Kinetic energy density as a function of the radius for different type of modes $\ell$ = 2 of the same PoMS model as in Fig. 7: (1) gravity mode $\nu \sim 1144~\mu$ Hz, (2) acoustic mode p20 $\nu \sim 1176~\mu$ Hz, (3) and (4) two consecutive mixed modes $\nu \sim 994$ and 998 $\mu$ Hz in between the pure acoustic modes p12 and p14.
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$\begin{figure} \par\includegraphics[width=6.8cm,clip]{5251fig9.ps}\end{figure}$	Figure 9: Large frequency spacing normalized to the observed radius of Procyon A as a function of the mass. Its increase with respect to the mass is larger for PoMS than for MS models. Open (filled) symbols for MS (PoMS) models.
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$\begin{figure} \par\includegraphics[width=6.55cm,clip]{5251f10a.ps}\vspace*{-0.09cm} \includegraphics[width=6.55cm,clip]{5251f10b.ps}\end{figure}$	Figure 10: Large frequency spacings for $\ell$ = 0 ( up) and 1 ( down) for MS/PoMS models (full/dashed line) compared to Martic (stars) and Eggenberger (square) observations.
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$\begin{figure} \par\includegraphics[width=6.7cm,clip]{5251fi11.ps}\end{figure}$	Figure 11: Seismic quantity $\varepsilon$ characterizing the model evolutionary stage versus the mean large frequency spacing $\overline {\Delta \nu }$ . Grey open symbols indicate MS models, dark filled symbols PoMS models. Diamond 1.36 $M_\odot$ , circle 1.38 $M_\odot$ , triangle 1.42 $M_\odot$ , stars 1.44 $M_\odot$ , square 1.45 $M_\odot$ , diamond 1.46 $M_\odot$ , cross 1.48 $M_\odot$ .
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$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fi12.ps}\end{figure}$	Figure 12: Characteristic period P₀ of gravity modes as a function of the seismic quantity $\varepsilon$ characterizing the model evolutionary stage.
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$\begin{figure} \par\includegraphics[width=6.85cm,clip]{5251fi13.ps}\end{figure}$	Figure 13: Characteristics $\delta _0$ and S₀of the small frequency spacings $\delta \nu _{02}$ . The dashed box indicates the location of PoMS1 models. Same models and symbols as in Fig. 11.
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