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Rotating massive stars through the ages, with applications to WR stars, Pop III stars and Gamma Ray Bursts

This article first reviews the basic physics of rotating stars and their evolution. We examine in particular the changes of the mechanical and thermal equilibrium of rotating stars. An important (predicted and observed) effect is that rotating stars are hotter at the poles and cooler at the equator. We briefly discuss the mass loss by stellar winds, which are influenced by the anisotropic temperature distribution. These anisotropies in the interior are also driving circulation currents, which transports the chemical elements and the angular momentum in stars. Internal differential rotation, if present, creates instabilities and mixing, in particular the shear mixing, the horizontal turbulence and their interactions. A major check of the model predictions concerns the changes of the surface abundances, which are modified by mass loss in the very massive stars and by rotational mixing in O- and B-type stars. We show that the observations confirm the existence of rotational mixing, with much larger effects at lower metallicities. We discuss the predictions of stellar models concerning the evolution of the surface velocities, the evolutionary tracks in the HR diagram and lifetimes, the populations of blue, red supergiants and Wolf-Rayet stars, and the progenitors of type Ibc supernovae. We show, that in many aspects, rotating models provide a much better fit than non-rotating ones. Using the same physical ingredients as those which fit the best the observations of stars at near solar metallicities, we explore the consequences of rotating models for the status of Be stars, the progenitors of Gamma Ray Bursts, the evolution of Pop III stars and of very metal poor stars, the early chemical evolution of galaxies, the origin of the C-enhanced Metal Poor stars (CEMP) and of the chemical anomalies in globular clusters.