The first two-dimensional stellar structure and evolution models of rotating stars

Contact. Rotation is a key ingredient in the theory of stellar structure and evolution. Until now, stellar evolution codes operate in a one-dimensional framework for which the validity domain in regards to the rotation rate is not well understood. Aims. In this Letter, we present the first results of self-consistent stellar models in two spatial dimensions, which compute the time evolution of a star and its rotation rate along the main sequence (MS). We also present a comparison to observations. Methods. We make use of an extended version of the ESTER code, which solves the stellar structure of a rotating star in two dimensions with time evolution, including chemical evolution, and an implementation of rotational mixing. We computed evolution tracks for a 12 M ⊙ model, once for an initial rotation rate equal to 15% of the critical frequency, and once for 50%. Results. We first show that our model initially rotating at 15% of the critical frequency is able to reproduce all the observations of the β Cephei star HD 192575, which was recently studied with asteroseismology. Beyond the classical surface parameters, such as effective temperature or luminosity, our model also reproduces the core mass along with the rotation rate of the core and envelope at the estimated age of the star. This particular model also shows that the meridional circulation has a negligible influence on the transport of chemical elements such as nitrogen, for which the abundance may be increased at the stellar surface. Furthermore, it shows that in the late MS, nuclear evolution is faster than the relaxation time needed to reach a steady state of stellar angular momentum distribution. Conclusions. We demonstrate that we have successfully taken a new step towards two-dimensional evolutionary modelling of rotating stars. This opens new perspectives on the understanding of the dynamics of fast rotating stars and on the way rotation impacts stellar evolution.