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Register a new userCalibration of the mixing length theory for structures of helium-dominated atmosphere white dwarfs
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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 code, and a grid of 1D DB and DBA envelope structures. The 3D models span a parameter space of hydrogen-to-helium abundances between -10.0 and -2.0, surface gravities between 7.5 and 9.0 and effective temperatures between 12000 K and 34000 K. The 1D envelopes cover a similar atmospheric parameter range, but are also calculated with different values of the mixing length parameter, namely ML2/alpha between 0.4 and 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/alpha 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/alpha 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.
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Recently, Dufour et al. (2007) reported the unexpected discovery that a few white dwarfs found in the Sloan Digital Sky Survey had an atmosphere dominated by carbon with little or no trace of hydrogen and helium. Here we present a progress report on these new objects based on new high signal-to-noise follow-up spectroscopic observations obtained at the 6.5m MMT telescope on Mount Hopkins, Arizona.
We explore changes in the adiabatic 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 $^{22}$Ne 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 $^{22}$Ne are fit to the observed periods and other properties. The root-mean-square residuals to the $simeq$ 150$-$400 s low-order g-mode periods are typically in the range of $sigma_{rms}$ $lesssim$ 0.3 s, for a fit precision of $sigma_{rms}/ P$ $lesssim$ 0.3 %. We find average relative period shifts of $Delta P/P$ $simeq$ $pm$ 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 $^{22}$Ne, 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 $^{22}$Ne is absent. As part of the fitting processes involves adjusting the composition profiles of a white dwarf model, our study on the impact of $^{22}$Ne can provide new inferences on the derived interior mass fraction profiles. We encourage routinely including $^{22}$Ne mass fraction profiles, informed by stellar evolution models, to future generations of white dwarf model fitting processes.
In this paper, we present corrections to the spectroscopic parameters of DB and DBA white dwarfs with -10.0 < log(H/He) < -2.0, 7.5 < log(g) < 9.0 and 12000 K < T_eff < 34000 K, based on 282 3D atmospheric models calculated with the CO5BOLD radiation-hydrodynamics code. These corrections arise due to a better physical treatment of convective energy transport in 3D models when compared to the previously available 1D model atmospheres. By applying the corrections to an existing SDSS sample of DB and DBA white dwarfs, we find significant corrections both for the effective temperature and surface gravity. The 3D log(g) corrections are most significant for T_eff < 18000 K, reaching up to -0.20 dex at log(g) = 8.0. However, in this low effective temperature range, the surface gravity determined from the spectroscopic technique can also be significantly affected by the treatment of the neutral van der Waals line broadening of helium and by non-ideal effects due to the perturbation of helium by neutral atoms. Thus, by removing uncertainties due to 1D convection, our work showcases the need for improved description of microphysics for DB and DBA model atmospheres. Overall, we find that our 3D spectroscopic parameters for the SDSS sample are generally in agreement with Gaia DR2 absolute fluxes within 1-3{sigma} for individual white dwarfs. By comparing our results to DA white dwarfs, we have determined that the precision and accuracy of DB/DBA atmospheric models are similar. For ease of user application of the correction functions, we provide an example Python code.
Stellar convection is customarily described by Mixing-Length Theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and at all evolutionary phases. The aim of this study is to present a new theory of stellar convection that does not require the mixing length parameter. We present a self-consistent analytical formulation of stellar convection that determines the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and of the surrounding medium. This new theory is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism the motion of stellar convective cells inside convectively-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism. We obtain an analytical, non-local, time-dependent sub-sonic solution for the convective energy transport that does not depend on any free parameter. The theory is suitable for the outer convective zones of solar type stars and stars of all mass on the main sequence band. The predictions of the new theory are compared with those from the standard mixing-length paradigm for the most accurate calibrator, the Sun, with very satisfactory results.
We exploit the recent discovery of pulsations in mixed-atmosphere (He/H), extremely low-mass white dwarf precursors (ELM proto-WDs) to test the proposition that rotational mixing is a fundamental process in the formation and evolution of low-mass helium core white dwarfs. Rotational mixing has been shown to be a mechanism able to compete efficiently against gravitational settling, thus accounting naturally for the presence of He, as well as traces of metals such as Mg and Ca, typically found in the atmospheres of ELM proto-WDs. Here we investigate whether rotational mixing can maintain a sufficient amount of He in the deeper driving region of the star, such that it can fuel, through HeII-HeIII ionization, the observed pulsations in this type of stars. Using state-of-the-art evolutionary models computed with MESA, we show that rotational mixing can indeed explain qualitatively the very existence and general properties of the known pulsating, mixed-atmosphere ELM proto-WDs. Moreover, such objects are very likely to pulsate again during their final WD cooling phase.
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