... scenario

Appendix A is only available in electronic form at http://www.edpsciences.org

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...

Fellow of CONICET, and IALP CONICET/FCAG-UNLP, Argentina.

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...

Member of the Carrera del Investigador Científico y Tecnológico and IALP, CONICET/FCAG-UNLP, Argentina.

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...

Fellow of CONICET, and IALP CONICET/FCAG-UNLP, Argentina.

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... account

For example Stancliffe et al. (2004) find much stronger He burning luminosities during the thermal pulses at the AGB if structural and composition equations are solved simultaneously.

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... model

Also it is expected that the H-driven expansion may depend on the mass of the model. Explicitly, the authors have found that in a 0.664 $M_{\odot }$ model the H-driven expansion stops at log  $T_{\rm eff}=4.8$.

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... sequence

Comparing the predictions of the two sequences we have to keep in mind that the stellar masses of the remnants are not strictly the same.

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... choice

We note that for our best model the energy liberated by proton burning is in the range of expected values from the following rough estimation: If the whole H-mass (6.3 $\times$ 10^-5 $M_{\odot }$) were burned only through the chain ${^{12}{\rm C}} + {\rm p} \rightarrow {^{13}{\rm N}} + \gamma \rightarrow {^{13}{\rm C}} + {\rm e}^+ + \nu_{\rm e}$ (in which each burned proton liberates 3.4573 Mev, as it happens initially) then  $\int{L{\rm _H dt}}$ = 4.15 $\times$ 10⁴⁷ erg. While if the complete H-mass were burned through the two important reactions (the previous one and also ${^{13}{\rm C}} + {\rm p} \rightarrow {^{14}{\rm N}} + \gamma$) working at the same rate (in this case 5.504 Mev are liberated per burned proton) then $\int{L{\rm _H dt}}$ = 6.6 $\times$ 10⁴⁷ erg.

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...v

In the previous work by Althaus et al. (2005) the relation used was D= l $\times$ v and that is (mainly) why they find greater born again times than in the present work.

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...1985)

We have also performed some simulations using the expresion for D derived from Cox & Giuli (1968) $\left(D=\alpha^{4/3} H_{\rm P} \left[\frac{c}{\kappa \rho} (1-\beta) \nabla_{\rm ad} (\nabla_{\rm rad}-\nabla)\right]^{1/3}\right)$. We find that no significant difference arises from this change.

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... larger

Because of the very short time during which this process takes place, the H distribution is not homogeneous.

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... discussion

Changing the efficiency of overshooting during the thermally pulsing phase is expected to modify the amount of ¹⁶O in the intershell region below the helium buffer (Herwig 2000).

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