Advanced Evolution of Massive Stars. I. Helium Burning

This is the first in a series of papers which will describe a survey of the later stages of evolution of massive stars, beginning at helium burning and proceeding through the final hydrodynamic stages. In this paper, (1) the motivation and astrophysical background for the survey are developed and discussed, (2) the methods and approximations to be used are described, (3) the initial models for the survey are developed, (4) the techniques to be used are compared with other investigations of helium stars, (5) the "single-star" approximation is examined by explicit comparison with published evolutionary sequences of core helium burning, (6) the relation between helium core mass Ala and total mass Al is calibrated, and (7) helium-burning nucleosynthesis is reexplored using a revised rate for 3a - 11C and various values for the rate of 11C(a, ) 160. The latter results are fitted by a simple function of Ala and of Oal for the 7.12-MeV level in 160.