All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{fig01.eps} \end{figure}$ Figure 1: The run of the squared Brunt-Väisälä frequency in terms of the mass coordinate, corresponding to a 0.5895- $M_{\odot }$ PG 1159 model at $T_{\rm eff}= 139~000$ K and $\log~(L/L_{\odot})= 2.31$ . The mass of the helium content is of $0.0052~M_{\odot}$ . Dark regions denote the contributions of the Ledoux term B (shown in the inset) to the Brunt-Väisälä frequency. The chemical profile of the main nuclear species is displayed in the upper zone of the plot.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{fig02.eps} \end{figure}$ Figure 2: The forward period spacing $\Delta \Pi$ vs. period $\Pi$ for dipole ( $\ell = 1$ ) modes for the same PG 1159 model analyzed in Fig. 1. Panel a) corresponds to pulsational calculations in which the Ledoux term B is computed self-consistently, whereas panel b) corresponds to the situation in which the Ledoux term has been artificially suppressed in the region at $M_{\rm r}/M_* \approx 0.96$ , and panel c) correspond to the case in which B= 0 at $M_{\rm r}/M_* \approx 0.4{-}0.6$ . See text for details.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{fig03.eps} \end{figure}$ Figure 3: The forward period spacing $\Delta \Pi$ vs. period $\Pi$ for dipole ( $\ell = 1$ ) modes for the same model analyzed in Fig. 2. Upper panel corresponds to pulsational computations in which the Ledoux term B is computed self-consistently (core overshooting), whereas middle panel correspond to the case in which B= 0 at $M_{\rm r}/M_* \approx 0.4{-}0.6$ ("no core overshooting''). The observed period spacings for PG 1159-035 are plotted in lower panel. See text for details.
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In the text