Effects of anisotropic winds on massive star evolution

Context. Whenever stars rotate very rapidly, such that Omega/Omega(crit) > 0.7 where Omega(crit) is the Keplerian angular velocity of the star accounting for its deformation, radiative stellar winds are enhanced in polar regions. This theoretical prediction has now been confirmed by interferometric observations of rapidly rotating stars. Aims. Polar winds remove less angular momentum than spherical winds, thus allow the star to retain more angular momentum. We quantitatively assess the importance of this effect. Methods. We first use a semi-analytical approach to estimate the variation in the angular momentum loss when the rotation parameter increases. We then compute complete 9 M-circle dot stellar models at very high angular velocities (starting on the ZAMS with Omega/Omega(crit) = 0.8 and reaching the critical velocity during the main sequence) with and without radiative wind anisotropies. Results. When wind anisotropies are accounted for, the angular-momentum loss rate is reduced by less than 4% for Omega/Omega(crit) < 0.9 relative to the case for spherical winds. The reduction amounts to at most 30% when the star is rotating near the critical velocity. These values result from two counteracting effects: on the one hand, polar winds reduce the loss of angular momentum, and on the other hand, surface deformations imply that the mass that is lost at high co-latitude is lost at a larger distance from the rotational axis and thus removes more angular momentum. Conclusions. In contrast to previous studies that neglected surface deformations, we show that the radiative wind anisotropies have a relatively modest effect on the evolution of the angular momentum content of rapidly rotating stars.