Sakurai's Object, V605 Aquilae, and FG Sagittae: An Evolutionary Sequence Revealed

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_solar 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 born-again 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^-4, 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.