![]() This rate may depend on some general parameters of the star (luminosity, effective temperature, etc.). Often, the spherical symmetry of the models is coupled to a very simplified modelling of mass and angular momentum loss where the star is pealed off at a given rate (e.g. Until now, stellar evolution codes cope with this question using more or less sophisticated recipes. ![]() Moreover, the shape of a fast rotating star strongly deviates from the spherical symmetry and its spheroidal shape emphasises the anisotropy of the wind. It is clear that a strong mass loss at the equator of the star is more efficient at extracting angular momentum than a strong mass loss at the pole. Angular momentum losses depend on various phenomena but in particular on the mass loss distribution at the surface of the star. The most important ones may be those that transport and/or extract angular momentum within the stellar interior and at the surface of the star, and in the first place the losses due to radiation-driven winds, possibly modified by the presence of a magnetic field. The rotation rate of a star indeed depends on several un-mastered magneto-hydrodynamic mechanisms. The evolution of the rotation rate of stars is one of the open challenges of current stellar physics. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Moreover, the very existence of the bi-stability jump in mass-loss rate remains to be substantiated by observations. ![]() However, predicting the rotational fate of a massive star is difficult, mainly because of the non-linearity of the phenomena involved and their strong dependence on uncertain prescriptions. In the two-wind regime, mass loss and angular momentum loss are strongly increased at low latitudes inducing a faster slow-down of the rotation. This discontinuity now shows up in the latitude variations of the mass-flux surface density, endowing rotating massive stars with either a single-wind regime (no discontinuity) or a two-wind regime (a discontinuity). Our model includes the so-called bi-stability jump of the Ṁ − T eff relation of 1D-models. We find that this angular momentum extraction from the outer layers can prevent massive stars from reaching critical rotation and greatly reduce the degree of criticality at the end of the MS. More massive stars are subject to radiation-driven winds and to an associated loss of mass and angular momentum. We show that stars with Z = 0.02 and masses between 5 and 7 M ⊙ reach criticality during the main sequence provided their initial angular velocity is larger than 50% of the Keplerian one. We have used the 2D ESTER code to compute and evolve isolated rapidly rotating early-type stellar models along the MS, with and without anisotropic mass loss. In this paper, we aim to clarify the rotational evolution of rapidly rotating early-type stars along the main sequence (MS). The understanding of the rotational evolution of early-type stars is deeply related to that of anisotropic mass and angular momentum loss. ![]() IRAP, Université de Toulouse, CNRS, UPS, CNES, 14, Avenue Édouard Belin, 31400 Toulouse, FranceĮ-mail: of Astronomy, University of Geneva, Chemin des MailletVersoix, SwitzerlandĮ-mail: Research Group, University of Alcalá, 28871 Alcalá de Henares, Spain
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