Seismic Signatures of the 12C(α, γ)16O Reaction Rate in White Dwarf Models with Overshooting

We consider the combined effects that overshooting and the ¹²C(α, γ)¹⁶O 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 ¹²C(α, γ)¹⁶O reaction rate probability distribution function when overshooting is included in the evolution. These signatures hold because the resonating mantle region, encompassing ≃0.2 M _⊙ in a typical ≃0.6 M _⊙ 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 ¹²C(α, γ)¹⁶O reaction rate probability distribution function. Both g-mode signatures induce average relative period shifts of ΔP/P = 0.44% and ΔP/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 ¹²C(α, γ)¹⁶O reaction rate. The g ₆ period signature generally separates the slower and faster reaction rates, and has a maximum relative period shift of ΔP/P = 3.45%. We conclude that low-order g-mode periods from CO WDs may still serve as viable probes for the ¹²C(α, γ)¹⁶O reaction rate probability distribution function when overshooting is included in the evolution.