The evolution of rotating stars

First, we 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 is enhancing the mass loss by stellar winds and reciprocally high mass loss is removing a lot of angular momentum. The problem of the ``break-up'' or $\Omega$-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 W-R stars, 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, as well as 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 $\Omega$ as well.Comment: 78 pages, 7 figures, review for Annual Review of Astronomy and Astrophysics, vol. 38 (2000

Accurate masses and radii of normal stars: modern results and applications

This paper presents and discusses a critical compilation of accurate, fundamental determinations of stellar masses and radii. We have identified 95 detached binary systems containing 190 stars (94 eclipsing systems, and alpha Centauri) that satisfy our criterion that the mass and radius of both stars be known to 3% or better. To these we add interstellar reddening, effective temperature, metal abundance, rotational velocity and apsidal motion determinations when available, and we compute a number of other physical parameters, notably luminosity and distance. We discuss the use of this information for testing models of stellar evolution. The amount and quality of the data also allow us to analyse the tidal evolution of the systems in considerable depth, testing prescriptions of rotational synchronisation and orbital circularisation in greater detail than possible before. The new data also enable us to derive empirical calibrations of M and R for single (post-) main-sequence stars above 0.6 M(Sun). Simple, polynomial functions of T(eff), log g and [Fe/H] yield M and R with errors of 6% and 3%, respectively. Excellent agreement is found with independent determinations for host stars of transiting extrasolar planets, and good agreement with determinations of M and R from stellar models as constrained by trigonometric parallaxes and spectroscopic values of T(eff) and [Fe/H]. Finally, we list a set of 23 interferometric binaries with masses known to better than 3%, but without fundamental radius determinations (except alpha Aur). We discuss the prospects for improving these and other stellar parameters in the near future.Comment: 56 pages including figures and tables. To appear in The Astronomy and Astrophysics Review. Ascii versions of the tables will appear in the online version of the articl