Self-consistent 2D models of fast rotating early-type star
  This work aims at presenting the first two-dimensional models of an isolated
rapidly rotating star that include the derivation of the differential rotation
and meridional circulation in a self-consistent way.We use spectral methods in
multidomains, together with a Newton algorithm to determine the steady state
solutions including differential rotation and meridional circulation for an
isolated non-magnetic, rapidly rotating early-type star. In particular we
devise an asymptotic method for small Ekman numbers (small viscosities) that
removes the Ekman boundary layer and lifts the degeneracy of the inviscid
baroclinic solutions.For the first time, realistic two-dimensional models of
fast-rotating stars are computed with the actual baroclinic flows that predict
the differential rotation and the meridional circulation for intermediate-mass
and massive stars. These models nicely compare with available data of some
nearby fast-rotating early-type stars like Ras Alhague ($\alpha$ Oph), Regulus
($\alpha$ Leo), and Vega ($\alpha$ Lyr). It is shown that baroclinicity drives
a differential rotation with a slow pole, a fast equator, a fast core, and a
slow envelope. The differential rotation is found to increase with mass, with
evolution (here measured by the hydrogen mass fraction in the core), and with
metallicity. The core-envelope interface is found to be a place of strong shear
where mixing will be efficient.Two-dimensional models offer a new view of
fast-rotating stars, especially of their differential rotation, which turns out
to be strong at the core-envelope interface. They also offer more accurate
models for interpreting the interferometric and spectroscopic data of
early-type stars.
