On the shape of rapidly rotating stars

Aims. The critical surface of a rapidly rotating star is determined, assuming that the rotation is either uniform or shellular (angular velocity constant on level surfaces, but increasing with depth). Methods. A step beyond the classical Roche model, where the entire mass is assumed to be gathered at the center of the star, here the quadrupolar moment of the mass distribution is taken into account through a linear perturbation method. Results. The flattening (defined here as the ratio between the equatorial and the polar radius) can somewhat exceed the 3/2 value of the Roche model, depending on the strength of the interior rotation. The result is applied to a star of 7 solar masses, which is the mass of Achernar, the star with the largest flattening detected so far through optical interferometry.