2D dynamics of radiative zone of low-mass stars
Delphine Hypolite (CEA ), Stéphane Mathis (CEA), Michel Rieutord (IRAP)

The internal rotation of low-mass stars all along their evolution is of primary interest when studying their rotational dynamics, internal mixing and magnetic fields generation. In this context, helio- and asterosismology probe angular velocity gradients deep within Solar-type stars. Still the rotation of the close center of such stars on the main-sequence is hardly detectable and the dynamical interactions of the radiative core with the surface convective envelope is not well understood. Among them, the influence of the differential rotation profile sustained by convection and applied as a boundary condition to the radiation zone may be very important leading to the formation of tachoclines. Indeed, in the Solar convective region, the equator is rotating faster than the pole while anti-solar rotation can also be expected in other low-mass stars envelopes since numerical simulations predict a bistable state. In this work, we therefore build for the first time 2D hydrodynamical models of solar-type stars radiation zone providing a full 2D description of their dynamics and studying the influence of a general shear boundary condition accounting for a solar or anti-solar differential rotation in the convective envelope. We compute coherently differential rotation and the associated meridional circulation using the anelastic approximation which is compared to the simplest Boussinesq one. Analytically, we demonstrate that the imposed shear implies a cylindrical differential rotation. Moreover, flux of angular momentum both in the radial and latitudinal directions are proportional to the shear and the radial flux is concentrated near the surface to counterbalance its action. The core to the surface rotation ratio decreases as the shear increases. These results will be discussed in the framework of seismic observables while perspectives to improve our modeling by including magnetic field or transport by waves will be presented.