Abstract
Context. Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular 7 Li, and the evolution of their rotation rates. For the Sun, inversions of helioseismic data indicate that the radial profile of angular velocity in its radiative zone is nearly uniform, which implies the existence of angular momentum transport mechanisms that are efficient over evolutionary timescales. While there are many independent transport models for angular momentum and chemical species, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the present-day observations of solar lithium abundances and radial rotation profiles. Aims. We explore how additional transport processes can improve the agreement between evolutionary models of rotating stars and observations for 7 Li depletion, the rotation evolution of solar-type stars, and the solar rotation profile. Methods. Models of solar-type stars are computed including atomic diffusion and rotation-induced mixing with the code STAREVOL. We explore different additional transport processes for chemicals and for angular momentum such as penetrative convection, tachocline mixing, and additional turbulence. We constrain the resulting models by simultaneously using the evolution of the surface rotation rate and 7 Li abundance in the solar-type stars of open clusters with different ages, and the solar surface and internal rotation profile as inverted from helioseismology when our models reach the age of the Sun. Results. We show the relevance of penetrative convection for the depletion of 7 Li in pre-main sequence and early main sequence stars. The rotational dependence of the depth of penetrative convection yields an anti-correlation between the initial rotation rate and 7 Li depletion in our models of solar-type stars that is in agreement with the observed trend. Simultaneously, the addition of an ad hoc vertical viscosity ν add leads to efficient transport of angular momentum between the core and the envelope during the main sequence evolution and to solar-type models that match the observed profile of the Sun. We also self-consistently compute for the first time the thickness of the tachocline and find that it is compatible with helioseismic estimations at the age of the Sun, but we highlight that the associated turbulence does not allow the observed 7 Li depletion to be reproduced. The main sequence depletion of 7 Li in solar-type stars is only reproduced when adding a parametric turbulent mixing below the convective envelope. Conclusions. The need for additional transport processes in stellar evolution models for both chemicals and angular momentum in addition to atomic diffusion, meridional circulation, and turbulent shear is confirmed. We identify the rotational dependence of the penetrative convection as a key process. Two additional and distinct parametric turbulent mixing processes (one for angular momentum and one for chemicals) are required to simultaneously explain the observed surface 7 Li depletion and the solar internal rotation profile. We highlight the need of additional constraints for the internal rotation of young solar-type stars and also for the beryllium abundances of open clusters in order to test our predictions.