We have completed a grid of stellar evolution calculations to study the behavior of the born-again phenomenon. All our evolutionary sequences begin with a uniform composition 1 M star on the pre-main-sequence Hayashi phase and end on the white dwarf cooling track. The effects of combined helium and hydrogen burning and time-dependent convective mixing are included. We artificially vary the mass-loss rate beginning at the peak of the last thermal pulse on the asymptotic giant branch in order to create a range of He-layer masses for the post-asymptotic giant branch (AGB) evolution. We find that a very late thermal pulse occurs in 10%-15% of cases. Our models supply an answer to the question of why the born-again stars V4334 Sgr (Sakurai's object) and V605 Aql have a significantly shorter evolutionary timescale than the otherwise similar bornagain star FG Sge. FG Sge has been observed to undergo born-again behavior for more than 120 yr, while the other two objects have evolved in a similar way but in less then 10 yr. Models with low convective mixing efficiency, $10 À4 , first evolve quickly to the AGB, return to the blue, and then evolve more slowly back to the AGB for a second time before finally returning to the white dwarf cooling track. The difference in evolution timescales can then be explained by proposing that Sakurai's object is evolving to the AGB for the first time but that FG Sge has been observed during its second return to the AGB. Our models allow us to make some testable predictions: (1) Sakurai's object will increase in effective temperature in the next 20-50 yr and will then resemble V605 Aql's present high effective temperature state; (2) V605 Aql will cool back toward the AGB some time in the next 50-70 yr, at which point it will evolve in the same way as has been observed for FG Sge over the last 120 yr; and (3) FG Sge will show signs of increasing its effective temperature by about 1500-2000 K in as soon as 10-20 yr, depending on the metallicity of its progenitor main-sequence star.

We use two sets of ‘cradle‐to‐grave’ evolutionary calculations to investigate how the mass of the helium buffer layer between the CO core and the hydrogen‐burning shell in thermally pulsing asymptotic giant branch (AGB) stars depends on the initial stellar mass and heavy element abundance. Cool star mass loss is included by augmenting the Reimers' formula with fits to mass‐loss rates observed for Galactic Mira variables, obscured Large Magellanic Cloud (LMC) AGB variables and Galactic OH/IR sources. Resulting white dwarf masses are in good agreement with the semi‐empirical final mass–initial mass relation. We derive lower and upper limits on the mass of helium in white dwarfs as functions of their mass and initial heavy element abundance. We find that stars that experience a very late thermal pulse (VLTP) have final helium masses that are about 25 per cent below the lower limit for stars that do not experience a VLTP. We have derived a modified form of Iben's criterion for a star to experience a post‐AGB helium shell flash, and subcriteria for discriminating between the occurrence of late and VLTPs. We find that a post‐AGB flash does not necessarily result in formation of a non‐DA white dwarf. Furthermore, we find that the relative amount of time spent burning helium or hydrogen depends on how the mass‐loss rate varies with stellar surface parameters. These two considerations complicate the relationship between the probability that a star experiences a post‐AGB flash and the relative formation rates of DA and non‐DA white dwarfs. However, our calculations do lead to a non‐DA/DA ratio that is consistent with the observed ratio. We find that our predicted abundances for PG1159 stars agree within the error bars with the observed abundances, without the need of convective overshoot. We also find that nitrogen is produced during VLTPs but not in the other evolutionary paths to hydrogen‐deficient objects. Hence, we propose this as the reason why nitrogen is observed in some PG1159 stars but not all. Our VLTP models also produce surface abundances close to those of the low‐gravity hybrid PG1159 stars. An inconsistency between asteroseismological and our evolutionary model determinations of helium layer mass remains.

We present new stellar evolution models that show that the born‐again phenomenon, also known as a very late thermal pulse, is a viable explanation for the behaviour of V838 Monocerotis if a period of accretion is included. Based on this model, we assert that V838 Mon is a variation of a born‐again giant in close orbit with a main‐sequence binary companion of mass greater than 0.7 M⊙.