The calculation of the thermal stratification in the superadiabatic layers of stellar models with convective envelopes is a long standing problem of stellar astrophysics , and has a major impact on predicted observational properties like radius and effective temperature .
The Mixing Length Theory , almost universally used to model the superadiabatic convective layers , contains effectively one free parameter to be calibrated – \alpha _ { ml } – whose value controls the resulting effective temperature .
Here we present the first self-consistent stellar evolution models calculated by employing the atmospheric temperature stratification , Rosseland opacities , and calibrated variable { \alpha _ { ml } } ( dependent on effective temperature and surface gravity ) from a large suite of three-dimensional radiation hydrodynamics simulations of stellar convective envelopes and atmospheres for solar stellar composition ( Trampedach et al .
2013 ) .
From our calculations ( with the same composition of the radiation hydrodynamics simulations ) , we find that the effective temperatures of models with the hydro-calibrated variable \alpha _ { ml } ( that ranges between \sim 1.6 and \sim 2.0 in the parameter space covered by the simulations ) display only minor differences , by at most \sim 30-50 K , compared to models calculated at constant solar \alpha _ { ml } ( equal to 1.76 , as obtained from the same simulations ) .
The depth of the convective regions is essentially the same in both cases .
We have also analyzed the role played by the hydro-calibrated T ( \tau ) relationships in determining the evolution of the model effective temperatures , when compared to alternative T ( \tau ) relationships often used in stellar model computations .
The choice of the T ( \tau ) can have a larger impact than the use of a variable \alpha _ { ml } compared to a constant solar value .
We found that the solar semi-empirical T ( \tau ) by Vernazza et al .
( 1981 ) provides stellar model effective temperatures that agree quite well with the results with the hydro-calibrated relationships .