Calibration of the Mixing-Length Theory for Convective White Dwarf Envelopes

TL;DR

This paper calibrates the mixing-length parameter in 1D models of hydrogen-atmosphere white dwarfs by comparing them with 3D hydrodynamical simulations, providing improved tools for modeling their structure and evolution.

Contribution

It introduces a calibration of the mixing-length parameter for white dwarf envelopes based on 3D simulations, addressing limitations of traditional local MLT.

Findings

The calibration applies to white dwarfs with 6000 < Teff < 15000 K and 7.0 < log g < 9.0.

Standard MLT cannot simultaneously reproduce all properties of 3D simulations.

Convection has negligible impact on cooling rates until the convective core coupling below 5000 K.

Abstract

A calibration of the mixing-length parameter in the local mixing-length theory (MLT) is presented for the lower part of the convection zone in pure-hydrogen atmosphere white dwarfs. The parameterization is performed from a comparison of 3D CO5BOLD simulations with a grid of 1D envelopes with a varying mixing-length parameter. In many instances, the 3D simulations are restricted to the upper part of the convection zone. The hydrodynamical calculations suggest, in those cases, that the entropy of the upflows does not change significantly from the bottom of the convection zone to regions immediately below the photosphere. We rely on this asymptotic entropy value, characteristic of the deep and adiabatically stratified layers, to calibrate 1D envelopes. The calibration encompasses the convective hydrogen-line (DA) white dwarfs in the effective temperature range 6000 < Teff (K) < 15,000 and the surface gravity range 7.0 < log g < 9.0. It is established that the local MLT is unable to reproduce simultaneously the thermodynamical, flux, and dynamical properties of the 3D simulations. We therefore propose three different parameterizations for these quantities. The resulting calibration can be applied to structure and envelope calculations, in particular for pulsation, chemical diffusion, and convective mixing studies. On the other hand, convection has no effect on the white dwarf cooling rates until there is a convective coupling with the degenerate core below Teff ~ 5000 K. In this regime, the 1D structures are insensitive to the MLT parameterization and converge to the mean 3D results, hence remain fully appropriate for age determinations.