The Impact of White Dwarf Luminosity Profiles on Oscillation Frequencies

KIC 08626021 is a pulsating DB white dwarf (WD) of considerable recent interest, and the 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 WD models choose a luminosity profile where the luminosity is proportional to the enclosed mass, ${L}_{r}\,\propto \,{M}_{r}$, independent of the effective temperature Teff. Evolutionary models of young WDs with Teff ≳ 25,000 K suggest that neutrino emission gives rise to luminosity profiles with Lr ${/}\!\!\!\!\!\!{\propto }$ Mr. We explore this contrast by comparing the oscillation frequencies between two nearly identical WD 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 that the low-order g-mode frequencies differ by up to ≃70 μHz 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 μHz. A mean frequency difference of 30 μHz, based on linearly extrapolating published results, suggests a template model uncertainty in the fit precision of ≃12% in WD mass, ≃9% in the radius, and ≃3% in the central oxygen mass fraction.