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

Abstract

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.