Seismic Signatures of the C-12(& alpha;, & gamma;)O-16 Reaction Rate in White Dwarf Models with Overshooting

We consider the combined effects that overshooting and the C-12(& alpha;, & gamma;)O-16 reaction rate have on variable white dwarf (WD) stellar models. We find that carbon-oxygen (CO) WD models continue to yield pulsation signatures of the current experimental C-12(& alpha;, & gamma;)O-16 reaction rate probability distribution function when overshooting is included in the evolution. These signatures hold because the resonating mantle region, encompassing & SIME;0.2 M (& ODOT;) in a typical & SIME;0.6 M (& ODOT;) WD model, still undergoes radiative helium burning during the evolution to a WD. Our specific models show two potential low-order adiabatic g-modes, g (2) and g (6), that signalize the C-12(& alpha;, & gamma;)O-16 reaction rate probability distribution function. Both g-mode signatures induce average relative period shifts of & UDelta;P/P = 0.44% and & UDelta;P/P = 1.33% for g (2) and g (6), respectively. We find that g (6) is a trapped mode, and the g (2) period signature is inversely proportional to the C-12(& alpha;, & gamma;)O-16 reaction rate. The g (6) period signature generally separates the slower and faster reaction rates, and has a maximum relative period shift of & UDelta;P/P = 3.45%. We conclude that low-order g-mode periods from CO WDs may still serve as viable probes for the C-12(& alpha;, & gamma;)O-16 reaction rate probability distribution function when overshooting is included in the evolution.