All Figures

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{0898f01.eps} \end{figure}$ Figure 1: Signal-to-noise ratio ( $A_{\delta _k\nu }/\sigma _{\delta _k\nu }$ ) of the signature of the BCZ in different variables: $\Delta \nu$ (dashed line), ${\delta _2\nu }$ (solid line), $\delta _4\nu$ (dotted line) and $\delta _6\nu$ (dots and dashes), normalized by the SNR ( $A_\nu /\sigma _\nu$ ) directly observed in the mode frequencies. This relative SNR is plotted as a function of the BCZ acoustic radius ( $t_{\rm BCZ}$ ) normalized to the stellar acoustic radius (T).
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{0898f02.eps} \end{figure}$ Figure 2: The second difference ${\delta _2\nu }$ observed in the Sun with GOLF after 6-year observations. Symbols: +: $\ell =0$ , $\Diamond$ : $\ell =1$ and $\Box$ : $\ell =2$ . The solid curve is a least-squares fit of the data with Eq. (5). Both oscillating components are plotted: the dotted line shows the effect of the He II ionization and the dashed one the oscillation due to the BCZ.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{0898f03.eps} \end{figure}$ Figure 3: The second difference ${\delta _2\nu }$ observed in the Sun with GOLF after 6-year observations. Symbols: +: $\ell =0$ , $\Diamond$ : $\ell =1$ and $\Box$ : $\ell =2$ . The solid line is the smooth curve which is removed before doing the spectral analysis.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{0898f04.eps} \end{figure}$ Figure 4: Spectral analysis of ${\delta _2\nu }$ in the Sun (Fig. 3) using modes $\ell =0,1,2$ (solid line) or only $\ell =0,1$ (dashed line). Both curves are very similar. The highest peak around 2300 s is due to the BCZ.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0898f05.eps} \end{figure}$ Figure 5: ${\delta _2\nu }$ and $\beta ^*$ observed in $\alpha$ Cen A (from Bouchy & Carrier 2002). Although these observations are remarkable, the accuracy obtained on the frequencies do not allow us to derive the BCZ. The resulting noise on ${\delta _2\nu }$ or $\beta ^*$ is too large to retrieve the oscillation due to the BCZ.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{0898f06.eps} \end{figure}$ Figure 6: On this HR diagram are placed the positions of models used for this study. $\times$ : the Sun ( SEISMIC₁, Turck-Chièze et al. 2001) and $\alpha$ Cen A (Ballot et al. 2003). The dashed lines are the evolutionary tracks of the models M1.30 and M0.90 (see the text for details) and + indicates some specific ages.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0898f07.eps} \end{figure}$ Figure 7: Effect of the observational length ( $T_{\rm obs}$ ) on the determination of the BCZ in the solar case (cf. simulations described in Sect. 3.4). Each line corresponds to the use of a different variable. For each one, the rate of good determination of the BCZ acoustic radius (within 5%) is plotted as a function of $T_{\rm obs}$ . The best results are obtained with ${\delta _2\nu }$ : with a 150-day observation the success rate is around 90%.
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In the text

$\begin{figure} \par\includegraphics[width=17.6cm,clip]{0898f08.eps} \end{figure}$ Figure 8: Effect of the observational length ( $T_{\rm obs}$ ) on the determination of the BCZ in the solar case (cf. simulations described in Sect. 3.4). Each picture shows the spectral analyses of ${\delta _2\nu }$ in 500 realizations for the different simulated observational lengths. In each picture, each line corresponds to a spectrum similar to the one plotted in Fig. 4.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{0898f09.eps} \end{figure}$ Figure 9: Distributions of results of $\tilde{t}_{\rm BCZ}$ extraction with ${\delta _2\nu }$ in the solar case for 3 observational lengths ( $T_{\rm obs} =90,~150$ and $300~\mbox{days}$ ). The hatched areas indicate the detections considered as bad (i.e. with an error larger than $5\%$ , see the text and Fig. 7). For each simulation, the success rate (SR), i.e. the rate of good detections, is given. The dashed line is a normal distribution with a standard deviation $\sigma^{{\rm obs}}_{\tilde{t}}$ fitting the result distribution. The Y axis represents a "density of results'': for each bin $[t,t+{\rm d}t]$ , the number of realizations where $\tilde{t} \in [t,t+{\rm d}t]$ is divided by the total number of realizations and normalized by the bin size ( ${\rm d}t$ ). Thus the integral of this quantity is always equal to one.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0898f10.eps} \end{figure}$ Figure 10: ${\delta _2\nu }$ for M1.30 at 20 Myr. See Fig. 2 for the description. For this not very stratified young star, the amplitude of the BCZ signature is around 0.1-0.3 $\mu$ Hz.
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In the text

$\begin{figure} \par\includegraphics[width=7.65cm,clip]{0898f11.eps} \end{figure}$ Figure 11: ${\delta _2\nu }$ for M1.30 at 3.15 Gyr. See Fig. 2 for the description. For this relatively old star, the amplitude of the BCZ signature is around 0.7-1 $\mu$ Hz.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0898f12.eps} \end{figure}$ Figure 12: Effect of the observational length ( $T_{\rm obs}$ ) on the determination of the BCZ for different modelled stars (cf. Table 1 and the simulations described in Sect. 3.5). The different symbols correspond to the different stars, and for the same star, different lines indicate different ages. For each one, the rate of good determination of the BCZ acoustic radius (within $5\%$ ) derived from ${\delta _2\nu }$ - except for M0.90@15Gyr: $\beta ^*$ - is plotted as a function of $T_{\rm obs}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.6cm,clip]{0898f13.eps} \end{figure}$ Figure 13: Spectral analysis of ${\delta _2\nu }$ for three VIRGO series, using $\ell =0,1$ and 2 modes (solid curve) and only $\ell =0$ and 1 (dashed curve). The dot-dashed line indicates the expected BCZ position.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0898f14.eps} \end{figure}$ Figure 14: Detected acoustic radius of the BCZ compared to its expected value for the 12 continuous series. The symbols with solid error bars indicate the results of detection. $\Box$ : $\ell =0,1,2$ modes are used; $\Diamond$ : $\ell =0,1$ only. The dashed lines indicate the zone where $\vert\tilde{t}_{\rm BCZ(obs.)}-{t}_{\rm BCZ(exp.)}\vert < 5\%~T$ . For the bad detections the position of the peak which have the second larger amplitude is also plotted with a dotted error bar.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0898f15.eps} \end{figure}$ Figure 15: Similar to Fig. 14 for the discontinuous series.
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In the text

$\begin{figure} \par\includegraphics[height=17.2cm,width=7.8cm,clip]{0898fb1a.eps... ...mm} \includegraphics[height=17.2cm,width=8.05cm,clip]{0898fb1b.eps} \end{figure}$ Figure B.1: An example of one realization coming from the Monte Carlo simulation for a 150-day simulated observation (cf. Sect. 3.4). a)- e) The variables $\Delta \nu$ , ${\delta _2\nu }$ , $\delta _4\nu$ , $\delta _6\nu$ and $\beta ^*$ . Symbols with error bars: +: $\ell =0$ , $\Diamond$ : $\ell =1$ and $\Box$ : $\ell =2$ . The crosses ( $\times$ ) indicate the theoretic values (without noise). a')- e') The spectral analyses of these variables. The dotted line shows the expected position for the BCZ peak, the dashed line gives the extracted position.

In the text

$\begin{figure} \par\includegraphics[height=17.2cm,width=7.7cm,clip]{0898fb2a.eps... ...*{4mm} \includegraphics[height=17.2cm,width=8cm,clip]{0898fb2b.eps} \end{figure}$ Figure B.2: An example of one realization coming from the Monte Carlo simulation for a 150-day simulated observation (cf. Sect. 3.4). a)- e) The variables $\Delta \nu$ , ${\delta _2\nu }$ , $\delta _4\nu$ , $\delta _6\nu$ and $\beta ^*$ . Symbols with error bars: +: $\ell =0$ , $\Diamond$ : $\ell =1$ and $\Box$ : $\ell =2$ . The crosses ( $\times$ ) indicate the theoretic values (without noise). a')- e') The spectral analyses of these variables. The dotted line shows the expected position for the BCZ peak, the dashed line gives the extracted position.

In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{0898f02.eps} \end{figure}$	Figure 2: The second difference ${\delta _2\nu }$ observed in the Sun with GOLF after 6-year observations. Symbols: +: $\ell =0$ , $\Diamond$ : $\ell =1$ and $\Box$ : $\ell =2$ . The solid curve is a least-squares fit of the data with Eq. (5). Both oscillating components are plotted: the dotted line shows the effect of the He II ionization and the dashed one the oscillation due to the BCZ.
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{0898f03.eps} \end{figure}$	Figure 3: The second difference ${\delta _2\nu }$ observed in the Sun with GOLF after 6-year observations. Symbols: +: $\ell =0$ , $\Diamond$ : $\ell =1$ and $\Box$ : $\ell =2$ . The solid line is the smooth curve which is removed before doing the spectral analysis.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{0898f04.eps} \end{figure}$	Figure 4: Spectral analysis of ${\delta _2\nu }$ in the Sun (Fig. 3) using modes $\ell =0,1,2$ (solid line) or only $\ell =0,1$ (dashed line). Both curves are very similar. The highest peak around 2300 s is due to the BCZ.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0898f05.eps} \end{figure}$	Figure 5: ${\delta _2\nu }$ and $\beta ^$ observed in $\alpha$ Cen A (from Bouchy & Carrier 2002). Although these observations are remarkable, the accuracy obtained on the frequencies do not allow us to derive the BCZ. The resulting noise on ${\delta _2\nu }$ or $\beta ^$ is too large to retrieve the oscillation due to the BCZ.
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$\begin{figure} \par\includegraphics[width=7.7cm,clip]{0898f06.eps} \end{figure}$	Figure 6: On this HR diagram are placed the positions of models used for this study. $\times$ : the Sun ( SEISMIC₁, Turck-Chièze et al. 2001) and $\alpha$ Cen A (Ballot et al. 2003). The dashed lines are the evolutionary tracks of the models M1.30 and M0.90 (see the text for details) and + indicates some specific ages.
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$\begin{figure} \par\includegraphics[width=17.6cm,clip]{0898f08.eps} \end{figure}$	Figure 8: Effect of the observational length ( $T_{\rm obs}$ ) on the determination of the BCZ in the solar case (cf. simulations described in Sect. 3.4). Each picture shows the spectral analyses of ${\delta _2\nu }$ in 500 realizations for the different simulated observational lengths. In each picture, each line corresponds to a spectrum similar to the one plotted in Fig. 4.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0898f10.eps} \end{figure}$	Figure 10: ${\delta _2\nu }$ for M1.30 at 20 Myr. See Fig. 2 for the description. For this not very stratified young star, the amplitude of the BCZ signature is around 0.1-0.3 $\mu$ Hz.
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$\begin{figure} \par\includegraphics[width=7.65cm,clip]{0898f11.eps} \end{figure}$	Figure 11: ${\delta _2\nu }$ for M1.30 at 3.15 Gyr. See Fig. 2 for the description. For this relatively old star, the amplitude of the BCZ signature is around 0.7-1 $\mu$ Hz.
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$\begin{figure} \par\includegraphics[width=8.6cm,clip]{0898f13.eps} \end{figure}$	Figure 13: Spectral analysis of ${\delta _2\nu }$ for three VIRGO series, using $\ell =0,1$ and 2 modes (solid curve) and only $\ell =0$ and 1 (dashed curve). The dot-dashed line indicates the expected BCZ position.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{0898f15.eps} \end{figure}$	Figure 15: Similar to Fig. 14 for the discontinuous series.
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