On Trapped Modes In Variable White Dwarfs As Probes Of The $^{12}$C($\alpha, \gamma$)$^{16}$O Reaction Rate

TL;DR

This study investigates how the pulsation periods of variable white dwarfs can reveal information about the $^{12}$C$( extalpha, extgamma)^{16}$O nuclear reaction rate, potentially providing astrophysical constraints on this fundamental nuclear process.

Contribution

It demonstrates that trapped g-modes in white dwarfs are sensitive to the $^{12}$C$( extalpha, extgamma)^{16}$O reaction rate, establishing a quantitative link between pulsation periods and nuclear reaction uncertainties.

Findings

Trapped g-modes show ~2% period shifts over reaction rate uncertainties.

White dwarf pulsation periods are precise enough to constrain nuclear reaction rates.

Sensitivity persists across different white dwarf models and temperature ranges.

Abstract

We seek signatures of the current experimental $^{12}$C$(\alpha,\gamma)^{16}$O reaction rate probability distribution function in the pulsation periods of carbon-oxygen white dwarf 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$(\alpha,\gamma)^{16}$O reaction rate probability distribution function. We find an average spread in relative period shifts of $\Delta P/P \simeq \pm$ 2\% for the identified trapped g-modes over the $\pm$ 3$\sigma$ uncertainty in the $^{12}$C$(\alpha,\gamma)^{16}$O reaction rate probability distribution function -- across the effective temperature range of observed DAV and DBV white dwarfs and for different white dwarf masses, helium shell masses, and hydrogen shell masses. The g-mode pulsation periods of observed white dwarfs are typically given to 6-7 significant figures of precision. This suggests that an astrophysical constraint on the $^{12}$C$(\alpha,\gamma)^{16}$O reaction rate could, in principle, be extractable from the period spectrum of observed variable white dwarfs.