Germanium Production in Asymptotic Giant Branch Stars: Implications for Observations of Planetary Nebulae

Observations of planetary nebulae (PNe) by Sterling, Dinerstein and Bowershave revealed abundances in the neutron-capture element Germanium (Ge) fromsolar to factors of 3 -- 10 above solar. The enhanced Ge is an indication thatthe slow-neutron capture process (s process) operated in the parent star duringthe thermally-pulsing asymptotic giant branch (TP-AGB) phase. We compute thedetailed nucleosynthesis of a series of AGB models to estimate the surfaceenrichment of Ge near the end of the AGB. A partial mixing zone of constantmass is included at the deepest extent of each dredge-up episode, resulting inthe formation of a 13C pocket in the top ~1/10th of the He-rich intershell. Allof the models show surface increases of [Ge/Fe] less than about 0.5, except the2.5Msun, Z=0.004 case which produced a factor of 6 enhancement of Ge. Near thetip of the TP-AGB, a couple of extra TPs could occur to account for thecomposition of the most Ge-enriched PNe. Uncertainties in the theoreticalmodeling of AGB stellar evolution might account for larger Ge enhancements thanwe predict here. Alternatively, a possible solution could be provided by theoccurrence of a late TP during the post-AGB phase. Difficulties related tospectroscopic abundance estimates also need to be taken into consideration.Further study is required to better assess how the model uncertainties affectthe predictions and, consequently, if a late TP should be invoked.Comment: accepted for publication in the Astrophysical Journal Letter