The Evolution of Rotating Stars

Abstract

▪ Abstract In this article we first review the main physical effects to be considered in the building of evolutionary models of rotating stars on the Upper Main-Sequence (MS). The internal rotation law evolves as a result of contraction and expansion, meridional circulation, diffusion processes, and mass loss. In turn, differential rotation and mixing exert a feedback on circulation and diffusion, so that a consistent treatment is necessary. We review recent results on the evolution of internal rotation and the surface rotational velocities for stars on the Upper MS, for red giants, supergiants, and W-R stars. A fast rotation enhances the mass loss by stellar winds and, conversely, high mass loss removes a lot of angular momentum. The problem of the breakup or Ω-limit is critically examined in connection with the origin of Be and LBV stars. The effects of rotation on the tracks in the HR diagram, the lifetimes, the isochrones, the blue-to-red supergiant ratios, the formation of Wolf-Rayet stars, and the chemical abundances in massive stars as well as in red giants and AGB stars are reviewed in relation to recent observations for stars in the Galaxy and Magellanic Clouds. The effects of rotation on the final stages and on the chemical yields are examined, along with the constraints placed by the periods of pulsars. On the whole, this review points out that stellar evolution is not only a function of mass M and metallicity Z, but of angular velocity Ω as well.

Critical study of the distribution of rotational velocities of Be stars

“…Other formulations of this relation for conservative and nonconservative rotation laws, produce , von Zeipel 1924;Lucy 1967;Smith & Worley 1974;Kippenhahn 1977;Hadrava 1992;Maeder 1999Maeder , 2009Lovekin et al 2006;Gillich et al 2008;Dall & Sbordone 2011;Espinosa Lara & Rieutord 2011;Claret 2012). Moreover, because of the simple fact that β 1 is colatitude θ-dependent, an observed β 1 is necessarily a function of the aspect angle (Domiciano de Souza et al 2014;Rieutord 2016;Zorec et al 2016).…”

“…Although in these cases we are not able to detect such motions, we should not conclude that they are not present, regardless of their physical origin. This is particularly valid in Be stars, where atmospheres can undergo significant upheavals maintained by nonradial pulsations, a large spectrum of instabilities induced by the rapid rotation, and possible disordered magnetic fields generated by underphotospheric convection (Clement 1979;Maeder et al 2008;Cantiello et al 2009;Cantiello & Braithwaite 2011).…”

Evolution and Nucleosynthesis of Massive Stars

“…The model rapidly reaches the critical velocity (the so called ΩΓ-limit if one takes into account the radiation pressure effect [29]). The star model loses very little mass during the MS phase, but a lot in the red supergiant phase due to the chemical enrichment and keeping at the ΩΓ-limit.…”

Hydrostatic Equilibria for Rotating Stars: Toward Evolutions of Deformed Stars

“…Studies on stellar evolutions are matured topics [1]. The most of the studies on rotating stellar evolution are, however, based on the slow rotation approximation, which assumes spherical stars.…”