Ab initio modelling of steady rotating stars

Modelling isolated rotating stars at any rotation rate is a challenge for the next generation of stellar models. These models will couple dynamical aspects of rotating stars, like angular momentum and chemicals transport, with classical chemical evolution, gravitational contraction or mass-loss. Such modelling needs to be achieved in two dimensions, combining the calculation of the structure of the star, its mean flows and the time-evolution of the whole. We present here a first step in this challenging programme. It leads to the first self-consistent two-dimensional models of rotating stars in a steady state generated by the ESTER code. In these models the structure (pressure, density and temperature) and the flow fields are computed in a self-consistent way allowing the prediction of the differential rotation and the associated meridian circulation of the stars. After a presentation of the physical properties of such models and the numerical methods at work, we give the first grid of such models describing massive and intermediate-mass stars for a selection of rotation rates up to 90 % of the breakup angular velocity.