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Abstract We consider the combined effects that overshooting and the¹²C(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 experimental¹²C(α,γ)¹⁶O reaction rate probability distribution function when overshooting is included in the evolution. These signatures hold because the resonating mantle region, encompassing ≃0.2M_⊙in a typical ≃0.6M_⊙WD model, still undergoes radiative helium burning during the evolution to a WD. Our specific models show two potential low-order adiabatic g-modes,g₂andg₆, that signalize the¹²C(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% forg₂andg₆, respectively. We find thatg₆is a trapped mode, and theg₂period signature is inversely proportional to the¹²C(α,γ)¹⁶O reaction rate. Theg₆period 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 the¹²C(α,γ)¹⁶O reaction rate probability distribution function when overshooting is included in the evolution. 

Abstract We seek signatures of the current experimental 12 C α , γ 16 O reaction rate probability distribution function in the pulsation periods of carbon–oxygen white dwarf (WD) models. We find that adiabatic g-modes trapped by the interior carbon-rich layer offer potentially useful signatures of this reaction rate probability distribution function. Probing the carbon-rich region is relevant because it forms during the evolution of low-mass stars under radiative helium-burning conditions, mitigating the impact of convective mixing processes. We make direct quantitative connections between the pulsation periods of the identified trapped g-modes in variable WD models and the current experimental 12 C α , γ 16 O reaction rate probability distribution function. We find an average spread in relative period shifts of Δ P / P ≃ ±2% for the identified trapped g-modes over the ±3 σ uncertainty in the 12 C α , γ 16 O reaction rate probability distribution function—across the effective temperature range of observed DAV and DBV WDs and for different WD masses, helium shell masses, and hydrogen shell masses. The g-mode pulsation periods of observed WDs are typically given to six to seven significant figures of precision. This suggests that an astrophysical constraint on the 12 C α , γ 16 O reaction rate could, in principle, be extractable from the period spectrum of observed variable WDs.