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Contact: F.X.Timmes
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On The Impact Of 22Ne On The Pulsation Periods Of Carbon-Oxygen White Dwarfs With Helium Dominated Atmospheres (2021)

In this article, we explore changes in the low-order g-mode pulsation periods of 0.526, 0.560, and 0.729 M$_{\odot}$ carbon-oxygen white dwarf models with helium-dominated envelopes due to the presence, absence, and enhancement of 22Ne in the interior. The observed g-mode pulsation periods of such white dwarfs are typically given to 6-7 significant figures of precision. Usually white dwarf models without 22Ne are fit to the observed periods and other properties. The root-mean-square residuals to the ≈ 150-400 s low-order g-mode periods are typically in the range of $\sigma_{\rm rms}$ $\lesssim$ 0.3 s, for a fit precision of $\sigma_{\rm rms}/ P$ $\lesssim$ 0.3 %. We find average relative period shifts of $\Delta P/P$ ≈ $\pm$ 0.5 % for the low-order dipole and quadrupole g-mode pulsations within the observed effective temperature window, with the range of $\Delta P/P$ depending on the specific g-mode, abundance of 22Ne, effective temperature, and mass of the white dwarf model. This finding suggests a systematic offset may be present in the fitting process of specific white dwarfs when 22Ne is absent. As part of the fitting processes involves adjusting the composition profiles of a white dwarf model, our study on the impact of 22Ne can provide new inferences on the derived interior mass fraction profiles. We encourage routinely including 22Ne mass fraction profiles, informed by stellar evolution models, to future generations of white dwarf model fitting processes.

DB WD from a 2.1 M$_{\odot}$, Z=0.02, ZAMS model
element diffusion in the 0.560 M$_{\odot}$ WD
propagation diagram
approximation to Brunt-Väisälä frequency
mass-radius with markers of key transitions
period evolution
period changes in the 0.560 M$_{\odot}$ WD with zero or supersolar 22Ne
what causes the period changes
period changes in the 0.526 and 0.729 M$_{\odot}$ WD with zero and supersolar 22Ne

The Impact of White Dwarf Luminosity Profiles on Oscillation Frequencies (2018)

KIC 08626021 is a pulsating DB white dwarf of considerable recent interest, and first of its class to be extensively monitored by Kepler for its pulsation properties. Fitting the observed oscillation frequencies of KIC 08626021 to a model can yield insights into its otherwise-hidden internal structure. Template-based white dwarf models choose a luminosity profile where the luminosity is proportional to the enclosed mass, $L_r \propto M_r$, independent of the effective temperature $T_{\rm eff}$. Evolutionary models of young white dwarfs with $T_{\rm eff} \gtrsim$ 25,000 K suggest neutrino emission gives rise to luminosity profiles with $L_r$ $\not\propto$ $M_r$.

In this article we explore this contrast by comparing the oscillation frequencies between two nearly identical white dwarf models: one with an enforced $L_r \propto M_r$ luminosity profile and the other with a luminosity profile determined by the star's previous evolution history. We find the low order g-mode frequencies differ by up to $\simeq$ 70 $\mu$Hz over the range of Kepler observations for KIC 08626021.

This suggests that by neglecting the proper thermal structure of the star (e.g., accounting for the effect of plasmon neutrino losses), the model frequencies calculated by using an $L_r \propto M_r$ profile may have uncorrected, effectively-random errors at the level of tens of $\mu$Hz. A mean frequency difference of 30 $\mu$Hz, based on linearly extrapolating published results, suggests a template model uncertainty in the fit precision of $\simeq$ 12% in white dwarf mass, $\simeq$ 9% in the radius, and $\simeq$ 3% in the central oxygen mass fraction.


white dwarf structure
propagation diagram
mode frequency differences
weight function shifts
white dwarf cooling