On Trapped Modes in Variable White Dwarfs as Probes of the 12C(α, γ)16O Reaction Rate

Abstract

We seek signatures of the current experimental 12C 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 12C reaction rate probability distribution function. We find an average spread in relative period shifts of ΔP/P ≃ ±2% for the identified trapped g-modes over the ±3σ uncertainty in the 12C 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 12C reaction rate could, in principle, be extractable from the period spectrum of observed variable WDs.