Diagnoses to unravel secular hydrodynamical processes in          rotating main sequence stars

International audienceContext. With the progress of observational constraints on stellar          rotation and on the angular velocity profile in stars, it is necessary to understand how          angular momentum is transported in stellar interiors during their whole evolution. In this          context, more highly refined dynamical stellar evolution models have been built that take          into account transport mechanisms.Aims. Internal gravity waves (IGWs) excited by convective regions          constitute an efficient transport mechanism over long distances in stellar radiation          zones. They are one of the mechanisms that are suspected of being responsible for the          quasi-flat rotation profile of the solar radiative region up to            0.2 R⊙. Therefore, we include them in our detailed analysis          started in Paper I of the main physical processes responsible for the transport of angular          momentum and chemical species in stellar radiation zones. Here, we focus on the complete          interaction between differential rotation, meridional circulation, shear-induced          turbulence, and IGWs during the main sequence.Methods. We improved the diagnosis tools designed in Paper I to unravel          angular momentum transport and chemical mixing in rotating stars by taking into account          IGWs. The star’s secular hydrodynamics is treated using projection on axisymmetric          spherical harmonics and appropriate horizontal averages that allow the problem to be          reduced to one dimension while preserving the non-diffusive character of angular momentum          transport by the meridional circulation and IGWs. Wave excitation by convective zones is          computed at each time-step of the evolution track. We choose here to analyse the evolution          of a 1.1 M⊙, Z⊙ star in which IGWs          are known to be efficient.Results. We quantify the relative importance of the physical mechanisms          that sustain meridional currents and that drive the transport of angular momentum, heat,          and chemicals when IGWs are taken into account. First, angular momentum extraction,          Reynolds stresses caused by IGWs, and viscous stresses sustain a large-scale          multi-cellular meridional circulation. This circulation in turn advects entropy, which          generates temperature fluctuations and a new rotation profile because of thermal wind.Conclusions. We have refined our diagnosis of secular transport          processes in stellar interiors. We confirm that meridional circulation is sustained by          applied torques, internal stresses, and structural readjustments, rather than by thermal          imbalance, and we detail the impact of IGWs. These large-scale flows then modify the          thermal structure of stars, their internal rotation profile, and their chemical          stratification. The tools we developed in Paper I and generalised for the present analysis          will be used in the near future to study secular hydrodynamics of rotating stars taking          into account IGWs in the whole Hertzsprung-Russell diagram