Atomic diffusion and turbulent mixing in solar-like stars: Impact on the fundamental properties of FG-type stars

Context. Chemical composition is an important factor that affects stellar evolution. The element abundance on the stellar surface evolves along the lifetime of the star because of transport processes, including atomic diffusion. However, models of stars with masses higher than about 1.2 M⊙ predict unrealistic variations at the stellar surface. This indicates the need for competing transport processes that are mostly computationally expensive for large grids of stellar models. Aims. The purpose of this study is to implement turbulent mixing in stellar models and assess the possibility of reproducing the effect of radiative accelerations with turbulent mixing for elements like iron in order to make the computation of large grids possible. Methods. We computed stellar models with the Module for Experiments in Stellar Astrophysics code and assessed the effects of atomic diffusion (with radiative acceleration) in the presence of turbulent mixing. Starting from a turbulent mixing prescription already calibrated on helium surface abundances of F-type stars as a reference, we parametrised the effect of radiative accelerations on iron with a turbulent diffusion coefficient. Finally, we tested this parametrisation by modelling two F-type stars of the Kepler Legacy sample. Results. We found that, for iron, a parametrisation of turbulent mixing that simulates the effect of radiative acceleration is possible. This leads to an increase in the efficiency of the turbulent mixing to counteract the effect of gravitational settling. This approximation does not affect significantly the surface abundances of the other elements we studied, except for oxygen and calcium. We demonstrate that this parametrisation has a negligible impact on the accuracy of the seismic properties inferred with these models. Moreover, turbulent mixing makes the computation of realistic F-type star models including the effect atomic diffusion possible. This leads to differences of about 10% in the inferred ages compared to results obtained with models that neglect these processes. Conclusions. The inclusion of turbulent mixing and atomic diffusion with radiative accelerations allows a more realistic characterisation of F-type stars. The parametrisation of the effect of radiative acceleration on iron opens the possibility to compute larger grids of stellar models in a reasonable amount of time, which is currently difficult when the different chemical transport mechanisms, especially radiative accelerations, are considered, although this parametrisation cannot simulate the evolution of abundances of all elements (e.g. calcium)