Asteroseismic modelling of <i>Kepler</i> Legacy stars including lithium depletion

Context. The Kepler Legacy sample is, to this day, the sample of solar-like oscillators with the most exquisite asteroseismic data. In this work, we carry out detailed modelling of a sub-sample of these stars for which the surface lithium abundance has also been observed by the LAMOST survey and a photometric surface rotation has been measured. Aims. We aim to study the impact of additional mixing processes on the asteroseismic modelling of Kepler Legacy G and F-type stars. We also investigate whether a single process can be invoked to reproduce the lithium depletion and asteroseismic constraints at the same time Methods. We used detailed asteroseismic modelling techniques combining global and local minimisation techniques. We started by using standard models and then aimed to improve this solution with the addition of extra mixing at the border of convective regions using either convective penetration or turbulence in radiative layers. Results. We find that lower-mass models (≈ 1 M ⊙ ) have no problem in reproducing the observed lithium depletion using only turbulence in the radiative zone, similarly to solar models. F-type stars, which have a shallower convective envelope, are unaffected by additional turbulence at the base of the convective zone, but require significant convective penetration values to actually reproduce the observed lithium depletion. The extent of this penetration is, however, incompatible with the frequency separation ratios. Conclusions. We conclude that the impact of extra mixing is moderate for solar-type stars of the Kepler Legacy sample and well within the requirements of the PLATO mission. For more massive stars (≈ 1.5 M ⊙ ), we conclude that the behaviour of the frequency separation ratios must be further investigated, as even models with large convective penetration at the base of their convective envelope are unable to reproduce them.