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 \leq T _ { eff } ( K ) \leq 15 , 000 and the surface gravity range 7.0 \leq \log g \leq 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 T _ { eff } \sim 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 .