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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.
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Relativistic Corrections in White Dwarf Asteroseismology
With the precision now afforded by modern space-based photometric observations from the retired K2 and current TESS missions, the effects of general relativity (GR) may be detectable in the light curves of pulsating white dwarfs (WDs). Almost all WD models are calculated using a Newtonian description of gravity and hydrodynamics. To determine if the inclusion of GR leads to observable effects, we used idealized models of compact stars and made side-by-side comparisons of mode periods computed using a: (i) Newtonian and (ii) GR description of the equilibrium structure and nonradial pulsations. For application to WDs, it is only necessary to include the first post- Newtonian (1PN) approximation to GR. The mathematical nature of the linear nonradial pulsation problem is then qualitatively unchanged and the GR corrections can be written as extensions of the classic Dziembowski equations. As such, GR effects might easily be included in existing asteroseismology codes. The idealized stellar models are (i) 1PN relativistic polytropes and (ii) stars with a cold degenerate electron equation of state featuring a near-surface chemical transition from μe = 2 to μe = 1, simulating a surface hydrogen layer. A comparison of Newtonian and 1PN normal mode periods reveals fractional differences in the order of the surface gravitational redshift z. For a typical WD, this fractional difference is ∼10−4 and is greater than the period uncertainty σΠ/Π of many WD pulsation modes observed by TESS. Consistent theoretical modeling of periods observed in these stars should, in principle, include GR effects to 1PN order.
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- Award ID(s):
- 2110335
- PAR ID:
- 10544982
- Publisher / Repository:
- The Astrophysical Journal
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 952
- Issue:
- 1
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 87
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3847/1538-4357/acd446
