The Impact of White Dwarf Luminosity Profiles on Oscillation Frequencies

F X Timmes,C E Fields,Evan B Bauer,William M Wolf,Richard H D Townsend,Anne Thoul

doi:10.3847/2041-8213/aae70f

Abstract

Abstract 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, , independent of the effective temperature T eff. Evolutionary models of young WDs with T eff ≳ 25,000 K suggest that neutrino emission gives rise to luminosity profiles with L r M r . We explore this contrast by comparing the oscillation frequencies between two nearly identical WD models: one with an enforced 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 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.

Highlights

White dwarfs (WDs) are the final evolutionary state of stars whose zero age main-sequence (ZAMS) mass is 8 M (Liebert 1980; Fontaine et al 2001; Hansen 2004), which for a Salpeter initial mass function is ;98% of stars in the Milky Way (e.g., Salpeter 1955; Scalo 1986; Maschberger 2013)
In this Letter we explore the difference that this causes in the low-order g-mode oscillation frequencies by comparing two nearly identical WD models: one model that has an enforced Lr ∝ Mr luminosity profile, and another with a luminosity profile determined by the star’s evolution history
We have generated a pair of WD models that are “spectroscopic twins,” having the same effective temperature, surface gravity, and abundances

Summary

Introduction

White dwarfs (WDs) are the final evolutionary state of stars whose zero age main-sequence (ZAMS) mass is 8 M (Liebert 1980; Fontaine et al 2001; Hansen 2004), which for a Salpeter initial mass function is ;98% of stars in the Milky Way (e.g., Salpeter 1955; Scalo 1986; Maschberger 2013). Order to identify the spherical harmonic l and m of several modes ( see Zong et al 2016) Fitting these modes to ab initio WD models (e.g., White Dwarf Evolution Code (WDEC); Bischoff-Kim & Montgomery 2018), they found an effective temperature Teff = 29,650 K, mass M = 0.55 M , and evidence for a thin He layer. Stellar evolution models of young WDs with Teff 25,000 K suggest that neutrino emission dominates the energy loss budget for average-mass carbon–oxygen (CO) WDs, which yields luminosity profiles with Lr μ Mr (e.g., Vila 1966; Kutter & Savedoff 1969; Winget et al 2004; Bischoff-Kim & Montgomery 2018).

An Evolution Model Aiming at KIC 08626021

Imposing a Luminosity Profile

Frequency Differences

Cooling of the Evolution Model

Conclusions