...

Member of the Carrera del Investigador Científico y Tecnológico, CONICET, Argentina.

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... 0.228)

In particular, the surface abundance of oxygen depends on the free parameter f of overshooting (which is a measure of the extent of the overshoot region) and the number of thermal pulses considered during the AGB phase (see Herwig 2000).

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... mass

We change the stellar mass in the following way. In our evolutionary code, the independent variable is $\xi= \ln(1 - m_r/M_*)$, where M_* is the stellar mass and m_r the mass contained in a sphere of radius r. When the stellar mass is changed (say to M'_*), the $\xi$ values at each grid point are the same as before; so, the new mass at a given $\xi$ is $m'_r= M'_* (1 - \exp (\xi))$. The chemical composition at each $\xi$ is the same as before, but the mass contained at $\xi$ is different. For instance, if M'_* < M_*, then m'_r < m_r at a given $\xi$. Note that this procedure is different from, for instance, simply extracting mass from the outer layers.

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...$\log T_{\rm eff}-\log g$plane

This procedure has been employed, for instance, by O'Brien (2000) on a 0.573-$M_{\odot }$ post-AGB evolutionary model.

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...1974)

Specifically, a mode is classified as g if the number of nodes in the G-region exceeds the number of nodes in the P-region ( $n_{\rm G} > n_{\rm P}$), and is classified as p if $n_{\rm G} < n_{\rm P}$. We then assign the radial order according to $k= n_{\rm G} - n_{\rm P}$ for g-modes, or $k= n_{\rm P} - n_{\rm G}$ for p-modes.

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