The dynamics of a fully radiative rapidly rotating star

Context. Recent results of interferometry and asteroseismology require more and more precise models of rapidly rotating stars. Aims. We describe the basic structure and the hydrodynamics of a fully radiative star as a preliminary step towards more realistic models of rotating stars. Methods. We consider a solar mass of perfect gas enclosed in a spherical container. The gas is self-gravitating and rotating; it is the seat of nuclear heating and heat diffusion is due to radiative diffusion with Kramers type opacities. Equations are solved numerically with spectral methods in two dimensions with a radial Gauss-Lobatto grid and spherical harmonics. Results. We compute the centrifugally flattened structure of such a star; the von Zeipel model, which says that the energy flux is proportional to the local effective gravity is tested: we show that it overestimates by almost a factor 2 the ratio of the polar to the equatorial energy flux. We determine also the Brunt-Väisälä frequency distribution and show that outer equatorial regions in a radiative zone are convectively unstable when the rotation is fast enough. We compute the differential rotation and meridional circulation stemming from the baroclinicity of the star and show that, in such radiative zones, equatorial regions rotate faster than polar ones. The surface differential rotation is also shown to reach a universal profile when rotation is slow enough (less than 36% of the breakup one), viscosity and Prandlt number being small.