3D atmospheric models of helium-dominated atmosphere white dwarfs

All stars below around 10M will eventually become white dwarfs, making them the most common type of stellar remnant. Due to the large densities of white dwarfs, their atmospheres are dominated by the lightest element present, with around 80% of white dwarfs in magnitude-limited samples possessing hydrogen-dominated atmospheres. A significant portion of the remaining white dwarfs posses helium-dominated atmospheres, which are the result of born-again or late thermal pulse scenarios, where hydrogen is either completely burned or is diluted during or after the AGB phase. These white dwarfs are the subject of this thesis. A major uncertainty in the current 1D atmospheric models of white dwarfs lies in the treatment of convective energy transport, usually modelled under the mixing length approximation, which depends on a free parameter called the mixing length parameter, ML2/α. 3D simulations improve upon this by treating convection from first principles and by not relying on any free parameters, resulting in more physical models. In this thesis, I present the first 3D atmospheric models of white dwarfs that posses cool pure-helium atmospheres (DB) and helium-dominated atmospheres with traces of hydrogen (DBA). These models were calculated with the CO5BOLD radiation-hydrodynamics code and cover the hydrogen-to-helium number ratios of −10.0 ≤ log H/He ≤ −2.0, surface gravities of 7.5 ≤ log g ≤ 9.0 and effective temperatures of 12 000 K . Teff . 34 000 K. To determine the 3D effects on spectroscopic parameters, I compare the synthetic spectra computed from 3D and 1D models. In 1D models, the mixing length parameter is set to a commonly used value of 1.25. The 3D corrections on spectroscopically-derived values of hydrogen abundance and effective temperature are similar in magnitude to typical observational errors. However, the 1D models overestimate the surface gravity for Teff 22 000 K. By increasing hydrogen abundance in the atmosphere, the surface gravity corrections shift to a lower effective temperature range. To test the 3D spectroscopic corrections, the Sloan Digital Sky Survey (SDSS) spectroscopic sample of DB and DBA white dwarfs is used, alongside the astrometric and photometric data from Gaia data release 2. Both 1D and 3D spectroscopic parameters are found to agree with Gaia within 1-3σ for individual white dwarfs, yet neither type of model produces a perfect agreement. The uncertainty in line broadening caused by the effect of the neutral helium atom on its own species is also investigated to better understand additional systematic issues in current 1D and 3D model spectra. By comparing several samples of DA and DB/DBA white dwarfs, I show that the precision and accuracy of both types of 3D models are similar. To extend the usefulness of 3D atmospheric models, I perform the calibration of the mixing length parameter for the bottom of the convection zone in order to determine more accurate bulk properties of the convection zone, such as its mass. Thus, the calibration is applicable for studies of planetary debris around white dwarfs, carbon dredge-up from the core, envelope and astero-seimological models. Overall, the calibrated value of the mixing length parameter is found to be around 0.8 and is much lower than the commonly used value of ML2/α = 1.25 in DB and DBA 1D modelling, meaning that convective efficiency was previously overestimated by a significant factor. This is the first step in investigating convective overshoot in helium-dominated atmosphere white dwarfs

Pure-helium 3D model atmospheres of white dwarfs

We present the first grid of 3D simulations for the pure-helium atmospheres of DB white dwarfs. The simulations were computed with the CO5BOLD radiation-hydrodynamics code and cover effective temperatures and surface gravities between 12 000 K ≲ Teff ≲ 34 000 K and 7.5 ≤ log g (cgs units) ≤ 9.0, respectively. In this introductory work, synthetic spectra calculated from the 3D simulations are compared to appropriate 1D model spectra under a differential approach. This results in the derivation of 3D corrections for the spectroscopically derived atmospheric parameters of DB stars with respect to the 1D ML2/α = 1.25 mixing-length parametrization. No significant Teff corrections are found for the V777 Her instability strip region, and therefore no 3D revision is expected for the empirical blue and red edges of the strip. However, large log g corrections are found in the range 12 000 K < Teff < 23 000 K for all log g values covered by the 3D grid. These corrections indicate that 1D model atmospheres overpredict log g, reminiscent of the results found from 3D simulations of pure-hydrogen white dwarfs. The next step will be to compute 3D simulations with mixed helium and hydrogen atmospheres to comprehend the full implications for the stellar parameters of DB and DBA white dwarfs

Fundamental parameter accuracy of DA and DB white dwarfs in Gaia Data Release 2

We report on a comparison of spectroscopic analyses for hydrogen (DA) and helium atmosphere (DB) white dwarfs with Gaia Data Release 2 (DR2) parallaxes and photometry. We assume a reddening law and a mass–radius relation to connect the effective temperatures (Teff) and surface gravities (log g) to masses and radii. This allows the comparison of two largely independent sets of fundamental parameters for 7039 DA and 521 DB stars with high-quality observations. This subset of the Gaia white dwarf sample is large enough to detect systematic trends in the derived parameters. We find that spectroscopic and photometric parameters generally agree within uncertainties when the expectation of a single star is verified. Gaia allows the identification of a small systematic offset in the temperature scale between the two techniques, as well as confirming a small residual high-mass bump in the DA mass distribution around 11 000–13 000 K. This assessment of the accuracy of white dwarf fundamental parameters derived from Gaia is a first step in understanding systematic effects in related astrophysical applications such as the derivation of the local stellar formation history, initial-to-final mass relation, and statistics of evolved planetary systems

Calibration of the mixing-length theory for structures of helium-dominated atmosphere white dwarfs

We perform a calibration of the mixing-length parameter at the bottom boundary of the convection zone for helium-dominated atmospheres of white dwarfs. This calibration is based on a grid of 3D DB (pure-helium) and DBA (helium-dominated with traces of hydrogen) model atmospheres computed with the co5bold radiation-hydrodynamics code, and a grid of 1D DB and DBA envelope structures. The 3D models span a parameter space of hydrogen-to-helium abundances in the range −10.0 ≤ log (H/He) ≤−2.0, surface gravities in the range 7.5 ≤ log g ≤ 9.0, and effective temperatures in the range 12 000 K ≲ Teff ≲ 34 000 K. The 1D envelopes cover a similar atmospheric parameter range, but are also calculated with different values of the mixing-length parameter, namely 0.4 ≤ ML2/α ≤ 1.4. The calibration is performed based on two definitions of the bottom boundary of the convection zone: the Schwarzschild and the zero convective flux boundaries. Thus, our calibration is relevant for applications involving the bulk properties of the convection zone including its total mass, which excludes the spectroscopic technique. Overall, the calibrated ML2/α is smaller than what is commonly used in evolutionary models and theoretical determinations of the blue edge of the instability strip for pulsating DB and DBA stars. With calibrated ML2/α we are able to deduce more accurate convection zone sizes needed for studies of planetary debris mixing and dredge-up of carbon from the core. We highlight this by calculating examples of metal-rich 3D DBAZ models and finding their convection zone masses. Mixing-length calibration represents the first step of in-depth investigations of convective overshoot in white dwarfs with helium-dominated atmospheres

Core crystallization and pile-up in the cooling sequence of evolving white dwarfs

White dwarfs are stellar embers depleted of nuclear energy sources that cool over billions of years. These stars, which are supported by electron degeneracy pressure, reach densities of 10^7 grams per cubic centimetre in their cores. It has been predicted that a first-order phase transition occurs during white-dwarf cooling, leading to the crystallization of the non-degenerate carbon and oxygen ions in the core, which releases a considerable amount of latent heat and delays the cooling process by about one billion years. However, no direct observational evidence of this effect has been reported so far. Here we report the presence of a pile-up in the cooling sequence of evolving white dwarfs within 100 parsecs of the Sun, determined using photometry and parallax data from the Gaia satellite. Using modelling, we infer that this pile-up arises from the release of latent heat as the cores of the white dwarfs crystallize. In addition to the release of latent heat, we find strong evidence that cooling is further slowed by the liberation of gravitational energy from element sedimentation in the crystallizing cores. Our results describe the energy released by crystallization in strongly coupled Coulomb plasmas, and the measured cooling delays could help to improve the accuracy of methods used to determine the age of stellar populations from white dwarfs

Horizontal spreading of planetary debris accreted by white dwarfs

White dwarfs with metal-polluted atmospheres have been studied widely in the context of the accretion of rocky debris from evolved planetary systems. One open question is the geometry of accretion and how material arrives and mixes in the white dwarf surface layers. Using the three-dimensional (3D) radiation hydrodynamics code co5bold, we present the first transport coefficients in degenerate star atmospheres that describe the advection–diffusion of a passive scalar across the surface plane. We couple newly derived horizontal diffusion coefficients with previously published vertical diffusion coefficients to provide theoretical constraints on surface spreading of metals in white dwarfs. Our grid of 3D simulations probes the vast majority of the parameter space of convective white dwarfs, with pure-hydrogen atmospheres in the effective temperature range of 6000–18 000 K and pure-helium atmospheres in the range of 12 000–34 000 K. Our results suggest that warm hydrogen-rich atmospheres (DA; ${\gtrsim} 13\, 000$ K) and helium-rich atmospheres (DB and DBA; ${\gtrsim} 30\, 000$ K) are unable to efficiently spread the accreted metals across their surface, regardless of the time dependence of accretion. This result may be at odds with the current non-detection of surface abundance variations in white dwarfs with debris discs. For cooler hydrogen- and helium-rich atmospheres, we predict a largely homogeneous distribution of metals across the surface within a vertical diffusion time-scale. This is typically less than 0.1 per cent of disc lifetime estimates, a quantity that is revisited in this paper using the overshoot results. These results have relevance for studies of the bulk composition of evolved planetary systems and models of accretion disc physics

Orbital Decay in a 20 Minute Orbital Period Detached Binary with a Hydrogen-poor Low-mass White Dwarf

We report the discovery of a detached double white dwarf binary with an orbital period of ≈20.6 minutes, PTF J053332.05+020911.6. The visible object in this binary, PTF J0533+0209B, is a ≈0.17 M⊙ mass white dwarf with a helium-dominated atmosphere containing traces of hydrogen. This object exhibits ellipsoidal variations due to tidal deformation, and is the visible component in a single-lined spectroscopic binary with a velocity semi-amplitude of K_B = 618.7 ± 6.9 km s⁻¹. We have detected significant orbital decay due to the emission of gravitational radiation, and we expect that the Laser Interferometer Space Antenna (LISA) will detect this system with a signal to noise of 8.4^(+4.2)_(-3.0) after four years of operation. Because this system already has a well-determined orbital period, radial velocity semi-amplitude, temperature, atmospheric composition, surface gravity, and orbital decay rate, a LISA signal will help fully constrain the properties of this system by providing a direct measurement of its inclination. Thus, this binary demonstrates the synergy between electromagnetic and gravitational radiation for constraining the physical properties of an astrophysical object