  Recent results from interferometry and asteroseismology require models of
rapidly rotating stars that are more and more precise. We describe the basic
structure and the hydrodynamics of a fully radiative star as a preliminary step
towards more realistic models of rotating stars. We consider a solar mass of
perfect gas enclosed in a spherical container. The gas is self-gravitating and
rotating, and 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. We computed 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 the ratio of the polar to the equatorial energy flux by almost a
factor 2. We also determine the Brunt-Vaisala 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), as
long as viscosity and Prandlt number remain small.
