Asteroseismic modelling of Kepler 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 a detailed modelling of a subsample of these stars for which the surface lithium abundance has also been observed by the LAMOST survey and a photometric surface rotation as been measured. Aims. We aim at studying 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 use detailed asteroseismic modelling techniques combining global and local minimization techniques. We start by using standard models and then aim at improving this solution by 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 ($\sim 1M_\odot$) have no problem in reproducing the observed lithium depletion using only turbulence in the radiative zone, similarly to solar models. F-type stars, having a shallower convective envelope, are unaffected by additional turbulence at the BCZ, 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 ($\sim 1.5M_\odot$), 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.