A calibration of the mixinglength for solartype stars based on hydrodynamical simulations. I. Methodical aspects and results for solar metallicity
Abstract
Based on detailed 2D numerical radiation hydrodynamics (RHD) calculations of timedependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of solartype stars. The RHD models provide information about the convective efficiency in the superadiabatic region at the top of convective envelopes and predict the asymptotic value of the entropy of the deep, adiabatically stratified layers (Fig. \ref{f:sstarhd}). This information is translated into an effective mixinglength parameter \alpha_{MLT} suitable to construct standard stellar structure models. We validate the approach by a detailed comparison to helioseismic data. The grid of RHD models for solar metallicity comprises 58 simulation runs with a helium abundance of Y=0.28 in the range of effective temperatures 4300pun {K}<=T_{eff}<= 7100pun {K} and gravities 2.54<={log g}<= 4.74. We find a moderate, nevertheless significant variation of \alpha_{MLT} between about 1.3 for Fdwarfs and 1.75 for Ksubgiants with a dominant dependence on T_{eff} (Fig. \ref{f:mlp}). In the close neighbourhood of the Sun we find a plateau where \alpha_{MLT} remains almost constant. The internal accuracy of the calibration of \alpha_{MLT} is estimated to be +/ 0.05 with a possible systematic bias towards lower values. An analogous calibration of the convection theory of Canuto &\ Mazzitelli (1991, 1992; CMT) gives a different temperature dependence but a similar variation of the free parameter (Fig. \ref{f:mlpcm}). For the first time, values for the gravitydarkening exponent beta are derived independently of mixinglength theory: beta = 0.07... 0.10. We show that our findings are consistent with constraints from stellar stability considerations and provide compact fitting formulae for the calibrations.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 1999
 arXiv:
 arXiv:astroph/9811179
 Bibcode:
 1999A&A...346..111L
 Keywords:

 CONVECTION;
 HYDRODYNAMICS;
 STARS: LATETYPE;
 STARS: EVOLUTION;
 Astrophysics
 EPrint:
 14 pages, 6 figures, 4 tables