Presupernova evolution of rotating massive stars. I. Numerical method and evolution of the internal stellar structure

The evolution of rotating stars with zero-age main-sequence (ZAMS) masses in the range 8-25 M_⊙ is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ∼70% of breakup. The stars rotate rigidly on the ZAMS as a consequence of angular momentum redistribution during the pre-main-sequence evolution. Redistribution of angular momentum and chemical species are then followed as a consequence of Eddington-Sweet circulation, Solberg-Høiland instability, the Goldreich-Schubert-Fricke instability, and secular and dynamic shear instability. The effects of the centrifugal force on the stellar structure are included. Convectively unstable zones are assumed to tend toward rigid rotation, and uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (nonmagnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlying material of 10¹⁶-10¹⁷ cm² s^-1. These values are insensitive to the initial angular momentum and to uncertainties in the efficiencies of rotational mixing. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to breakup. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.