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Astron. Astrophys. 349, L5-L8 (1999)

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4. Evolution through the very late thermal pulse

Two cases of the born-again scenario should be distinguished. Depending on the time when the post-AGB thermal pulse occurs, shell hydrogen burning may still be active or may already have ceased.

In the first case, the He-flash driven convection zone cannot extend into the hydrogen-rich envelope due to the entropy barrier generated by the burning shell (Iben, 1976). In the second case, which is realized in our model sequence, hydrogen shell burning is extinct and the star has entered the white dwarf cooling domain (Fig. 1). We designate a TP in this situation as a very late TP.

[FIGURE] Fig. 1. Track in the HR diagram of our post-AGB model during the evolution through a very late TP. At the first mark along the track, the He-flash has already caused a prominent convectively unstable region. At the second mark, the outwards growing convection zone has reached the envelope and protons start to enter the convective zone (compare Fig. 2 and Fig. 3). At the third mark the hydrogen luminosity has reached its peak (see Fig. 2 and Fig. 4). The surface composition is hydrogen-free beyond the last mark.

As the helium luminosity increases in the course of the He-flash in our model sequence (first mark in Fig. 1), the corresponding region of convective instability enlarges (Fig. 2). When the upper convective boundary reaches the mass coordinate where the hydrogen abundance increases, convective mixing transports protons downwards into the hot interior (Fig. 3). The protons are at some point captured by [FORMULA] via the reaction [FORMULA]. The peak of the resulting luminosity due to hydrogen burning (see also Fig. 2) is located at the mass coordinate where the nuclear time scale equals the mixing time scale ([FORMULA]).

[FIGURE] Fig. 2. Evolution of the top boundary of the convection zone (dash-dotted line with filled circle for every second stellar model, left scale) as it extends into the hydrogen-rich envelope, and the nuclear luminosity due to hydrogen burning (solid line, right scale). The four grey dots along the solid line correspond to the marks in Fig. 1. The dashed line shows the mass coordinate of the hydrogen-free core which is for [FORMULA] identical with the total stellar mass.

[FIGURE] Fig. 3. Internal structure and composition at the onset of hydrogen ingestion into the He-flash convection zone during the very late TP (second mark in Fig. 1). Top panel: The nuclear energy generation is dominated by processing of helium at the bottom of the He-flash convection zone. Energy due to proton capture is released in the upper part of the He-flash convection zone (left scale). The hydrogen profile reflects the simultaneous nuclear burning and convective mixing (right scale). The surface composition at this stage is still hydrogen-rich. Bottom panel: The diffusion coefficient (left scale) visualizes the convectively unstable region corresponding to the He-flash, which has just reached the lower part of the hydrogen-rich envelope.

The profile of hydrogen in Fig. 3 and 4 demonstrates that a correct treatment of simultaneous burning and convective mixing is essential for this evolutionary phase. A treatment of convective mixing which does not include the simultaneous computation of the isotopic abundances according to the equations of the nuclear network would fail to predict a correct hydrogen profile. In particular, such a treatment would possibly let the protons travel too deep into the convective region, without considering that they would have been captured already on the way. Then, the energy generation rate due to proton captures may be overestimated and not correctly located.

The energy from proton captures is released in the upper part of the He-flash driven convection zone, which leads to a split (at [FORMULA]) of the convective region (Fig. 4). The two convective regions are then connected by the overlapping overshoot extensions, but Fig. 2 shows that the second convective zone is only short lived since the amount of hydrogen available in the envelope is quickly consumed.

[FIGURE] Fig. 4. Internal structure and composition at the time of maximum energy generation due to proton captures (third mark in Fig. 1). Top panel: Nuclear energy generation due to hydrogen burning and helium burning (left scale) and hydrogen profile (right scale). Bottom panel: The diffusion coefficient (left scale) shows that the convectively unstable region of the thermal pulse is split into two ([FORMULA]).

Fig. 4 shows that the hydrogen burning convection zone extends over [FORMULA] and reaches from [FORMULA] up to the surface of the stellar model. The surface hydrogen abundance declines rapidly due to mixing and proton captures in the deeper layers. The period of the largest hydrogen burning luminosity (shown in Fig. 4) of [FORMULA] lasts for less than a week, and the whole episode of convective hydrogen burning is a matter of about a month. Overall, [FORMULA] of hydrogen are burnt. At peak hydrogen luminosity the hydrogen mass fraction at the surface is [FORMULA] and the total amount of hydrogen still present in the star is [FORMULA]. Thus, in this sequence the star is already hydrogen-deficient before it returns to the AGB domain in the HRD.

Fig. 5 shows abundance profiles before and after the mixing and burning event due to the very late TP. While the star still shows the typical hydrogen-rich AGB abundance pattern before the convective region has reached into the envelope (top panel, Fig. 5), the mixing during the convective hydrogen burning leads to a hydrogen-free surface with [He/C/O]=[0.38/0.36/0.22] and a mass fraction of [FORMULA] of neon. The step in the abundances of [FORMULA], [FORMULA] and [FORMULA] at [FORMULA] (lower panel) corresponds to the split of the convective region due to hydrogen burning. While the hydrogen burning leads not to a significant abundance changes for the major isotopes (only [FORMULA] of hydrogen are processed), helium burning continues to process helium at the bottom of the He-flash convective zone. The final surface abundances are very similar to the intershell abundances during the thermal pulse.

[FIGURE] Fig. 5. Chemical profiles (mass fraction vs. mass coordinate) of the upper mass region also covered by Fig. 4. Top panel: Profile before the convective region of the He-flash has reached the envelope corresponding to position of first mark in Fig. 1 Bottom panel: Profile corresponding to position of last mark in Fig. 1 after all hydrogen has been processed (only trace amounts of [FORMULA] are left in the whole star), the abundance at the surface differs only slightly from the intershell abundance.

After most of the hydrogen is burnt, the corresponding upper convection zone disappears when the local luminosity drops. It takes about one year until the He-flash convection zone has recovered to its original extent (Fig. 2). The star then follows the evolution as known from the born-again scenario (for a recent account on this scenario see Blöcker and Schönberner, 1997). Energetically, the return into the AGB domain is almost exclusively driven by the energy release due to helium burning, which exceeds the additional supply of energy from hydrogen burning by orders of magnitude.

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© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999