Presupernova Evolution of Rotating Massive Stars II: -- Evolution of the   Surface Properties
  We investigate the evolution of the surface properties of models for rotating massive stars, i.e., their luminosities, effective temperatures, surface rotational velocities, and surface abundances of all isotopes, from the zero age main sequence to the supernova stage. Our results are based on the grid of stellar models by Heger, Langer, & Woosley, which covers solar metallicity stars in the initial mass range 8 - 25 solar masses. Results are parameterized by initial mass, initial rotational velocity and major uncertainties in the treatment of the rotational mixing inside massive stars.   Rotationally induced mixing processes widen the main sequence and increase the core hydrogen burning lifetime, similar to the effects of convective overshooting. It can also significantly increase the luminosity during and after core hydrogen burning, and strongly affects the evolution of the effective temperature. Our models predict surface rotational velocities for various evolutionary stages, in particular for blue supergiants, red supergiants, and for the immediate presupernova stage.   We discuss the changes of the surface abundances due to rotationally induced mixing for main sequence and post main sequence stars. We single out two characteristics by which the effect of rotational mixing can be distinguished from that of massive close binary mass transfer, the only alternative process leading to non-standard chemical surface abundances in massive stars. A comparison with observed abundance anomalies in various types of massive stars supports the concept of rotational mixing in massive stars and indicates that it is responsible for most of the observed abundance anomalies. 
A. Heger (UCSC), N. Langer (Utrecht Univ.)