Early Post Asymptotic Giant Branch Instability: Does it Affect White Dwarf Hydrogen Envelope Mass?

Although most white dwarf stars have hydrogen-dominated atmospheres, a significant fraction have atmospheres in which hydrogen is spectroscopically absent, with the fraction of hydrogen-free atmo- spheres varying with effective temperature. Estimates of the total mass of hydrogen, M_H , in the stellar envelope from either asteroseismology or spectral evolution are at odds with predicted values from theoretical stellar evolution modeling. Recent work has found that models in the early post Asymptotic Giant Branch (AGB) phase of evolution can exhibit thermally and dynamical unstable behavior. Here we investigate whether this Early Post AGB Instability (EPAGBI) can help resolve the conflict in MH values determined from white dwarf spectral evolution, analysis of DAV pulsations and canonical stellar evolution modeling, by evolving solar composition models of mass 1 and 2 M_⊙ through the AGB phases and to the white dwarf cooling track. We present results for when the EPAGBI phase of evolution is followed in detail, and for comparison purposes, when it is suppressed by forcing the time step to be large compared to the growth time of the instability. The M_H values at the end of the calculations are in the range consistent with asteroseismological determinations. However, we caution that, because hydrodynamic behavior is not included in our modeling, it is possible that all hydrogen would be removed. Thus, it is unclear whether the occurrence of the EPAGBI resolves the discrepancy between predictions of stellar evolution modeling and the asteroseismological hydrogen envelope mass determinations. The major impact of EPAGBIs is that they cause loops in the HRD, which are absent when the EPAGBI is suppressed. For models of AGB-departure mass 0.567 and 0.642 M_⊙, it takes approximately 100 and 10 yr for a single HRD loop, respectively. Such loops might be detectable in a long-term monitoring program, or perhaps by their imprint on planetary nebula morphology imparted by the cyclically varying mass loss rate. Since the characteristic timescale of the looping in the HRD depends on the stellar mass, if measurable, it could provide a way to determine the stellar mass just after AGB departure, particularly if it is ≳ 0.72 M_⊙ for which we stimate a 1 yr loop timescale. Another signature of the EPAGBI is the production of lithium by the Cameron-Fowler process. During the EPAGBI phase the photospheric temperature is always much higher than the temperatures of stars of appropriate log g for which the Li I resonance line can be detected, and Li detection is unlikely to be a way to identify the EPAGBI phase. However, the Li precursor, ⁷Be, is convected to the photosphere in significant amounts (up to ∼ 400 times the solar photospheric mass fraction) at various times in the EPAGBI phase, which may be detectable by observing the Be II resonance doublet.