New evolutionary calculations for the born again scenario

We present evolutionary calculations to describe the born-again scenario for post-AGB remnant stars of 0.5842 and 0.5885 $M_{\odot}$. Results are based on a detailed treatment of the physical processes responsible for the chemical abundance changes. We considered two theories of convection: the standard mixing length theory (MLT) and the double-diffusive GNA convection. The latter accounts for the effect of the chemical gradient ($\nabla\mu$) in the mixing processes and in the transport of energy. We also explore the dependence of born-again evolution on some physical hypotheses, such as the effect of the existence of non-zero chemical gradients, the prescription for the velocity of the convective elements and the size of the overshooting zones. Attention is paid to the behavior of the born-again times and to the chemical evolution during the ingestion of protons. We find that in our calculations born again times are dependent on time resolution. In particular when the minimum allowed time step is below 5 $\times$ 10 -5 yr we obtain, with the standard mixing length theory, born again times of 5–10 yr. This is true without altering the prescription for the efficiency of convective mixing during the proton ingestion. On the other hand we find that the inclusion of chemical gradients in the calculation of the mixing velocity tends to increase the born again times by about a factor of two. In addition we find that proton ingestion can be altered if the occurrence of overshooting is modified by the $\nabla\mu$-barrier at the H-He interface, significantly changing born again times.