On Trapped Modes in Variable White Dwarfs as Probes of the <sup>12</sup>C(α, γ)<sup>16</sup>O Reaction Rate
Morgan T. Chidester, Ebraheem Farag, F. X. Timmes
Abstract
Abstract We seek signatures of the current experimental 12 C <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">O</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">O</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">O</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">O</mml:mi> </mml:math> reaction rate could, in principle, be extractable from the period spectrum of observed variable WDs.