The Impact of White Dwarf Luminosity Profiles on Oscillation Frequencies

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 $L_r$ $\not\propto$ $M_r$. 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.