The Staggergrid: A grid of 3D stellar atmosphere models. III. The relation to mixing length convection theory
Abstract
Aims: We investigate the relation between 1D atmosphere models that rely on the mixing length theory and models based on full 3D radiative hydrodynamic (RHD) calculations to describe convection in the envelopes of latetype stars.
Methods: The adiabatic entropy value of the deep convection zone, s_{bot}, and the entropy jump, ∆s, determined from the 3D RHD models, were matched with the mixing length parameter, α_{MLT}, from 1D hydrostatic atmosphere models with identical microphysics (opacities and equationofstate). We also derived the mass mixing length parameter, α_{m}, and the vertical correlation length of the vertical velocity, C[v_{z},v_{z}], directly from the 3D hydrodynamical simulations of stellar subsurface convection.
Results: The calibrated mixing length parameter for the Sun is α^{๏}_{MLT} (S_{bot}) = 1.98. . For different stellar parameters, α_{MLT} varies systematically in the range of 1.7  2.4. In particular, α_{MLT} decreases towards higher effective temperature, lower surface gravity and higher metallicity. We find equivalent results for α^{๏}_{MLT} (∆S). In addition, we find a tight correlation between the mixing length parameter and the inverse entropy jump. We derive an analytical expression from the hydrodynamic meanfield equations that motivates the relation to the mass mixing length parameter, α_{m}, and find that it qualitatively shows a similar variation with stellar parameter (between 1.6 and 2.4) with the solar value of α^{๏}_{m} = 1.83.. The vertical correlation length scaled with the pressure scale height yields 1.71 for the Sun, but only displays a small systematic variation with stellar parameters, the correlation length slightly increases with T_{eff}.
Conclusions: We derive mixing length parameters for various stellar parameters that can be used to replace a constant value. Within any convective envelope, α_{m} and related quantities vary strongly. Our results will help to replace a constant α_{MLT}. Appendices are available in electronic form at http://www.aanda.orgFull Table A.1 is only available at the CDS via anonymous ftp to http://cdsarc.ustrasbg.fr (ftp://130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/573/A89 as well as at http://www.staggerstars.net
 Publication:

Astronomy and Astrophysics
 Pub Date:
 January 2015
 DOI:
 10.1051/00046361/201423760
 arXiv:
 arXiv:1403.1062
 Bibcode:
 2015A&A...573A..89M
 Keywords:

 convection;
 hydrodynamics;
 stars: atmospheres;
 stars: evolution;
 stars: latetype;
 stars: solartype;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 Accepted for publication in A&