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

We seek signatures of the current experimental ¹²C ${\left(\alpha ,\gamma \right)}^{16}{\rm{O}}$ 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 ¹²C ${\left(\alpha ,\gamma \right)}^{16}{\rm{O}}$ 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 ${\left(\alpha ,\gamma \right)}^{16}{\rm{O}}$ 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 ¹²C ${\left(\alpha ,\gamma \right)}^{16}{\rm{O}}$ reaction rate could, in principle, be extractable from the period spectrum of observed variable WDs.