Context. Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular 7Li, 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 7Li 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 7Li 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 7Li 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 7Li 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 νadd 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 7Li depletion to be reproduced. The main sequence depletion of 7Li 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 7Li 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.

Context. Open clusters provide unambiguous clues to understand the evolution of 7Li at the surface of low-mass stars and its possible correlation with stellar rotation, which is a challenge for both stellar hydrodynamics and Galactic chemical evolution. Aims. We aim to quantify the efficiency of the transport processes for both angular momentum and chemicals that are required to explain simultaneously the observed behaviour of surface 7Li (and 9Be) and rotation as well as the internal rotation profiles inferred from helio- and asteroseismology in F- and G-type main sequence stars. Methods. We apply the model for the transport of angular momentum and chemicals that we tailored in a previous work for solar-type stars to an extended range of initial masses and metallicities corresponding to F- an G-type stars in a sample of 20 Galactic open clusters. We evaluate its ability to explain the 7Li, 9Be, and rotation periods observations. This model includes atomic diffusion, rotation-induced processes (for which we tested different prescriptions for shear turbulence), penetrative convection with a rotational dependence, parametric viscosity and turbulence, and magnetic braking. Results. Over the entire range of masses, metallicities, and ages explored, we reproduce the evolution of the surface rotation rates and predict, for the first time, the observed anti-correlation between the surface rotation rate and 7Li depletion as a consequence of the penetrative convection prescription. The 7Li behaviour and its evolution with time is well reproduced for G-type stars. However, the ability of the model to reproduce the so-called 7Li dip centred around ∼6600 K strongly depends on the adopted prescriptions for shear turbulence. It also requires a stellar mass dependence for the parametric viscosity adopted for the transport of angular momentum, similar to the behaviour predicted for the generation and luminosity of internal gravity waves generated by stellar convective envelopes. Finally, the model predicts internal rotation profiles in good agreement with asteroseismic constraints in main sequence stars. Conclusions. We provide an efficient way to model G-type stars of different ages and metallicities successfully. However, the 7Li and 9Be dip constraints urgently call for further hydrodynamical studies to better model turbulence in stars, and for the exploration of physical processes such as tachocline mixing for the transport of chemicals and internal gravity waves for the transport of angular momentum. Finally, additional data for the internal rotation and for 9Be in main sequence low-mass stars are definitively needed.