The Evolution of Massive Stars. III. Hydrogen Exhaustion Through the Onset of Carbon-Burning

The evolution of a population I star of 15.6 solar masses and age-zero composition, X = 0.90, V = 0.08, and Z = 0.02, has been computed for four advanced evolutionary phases: (1) hydrogen exhaustion in the convective core, (2) the subsequent gravitational contraction of the core, (3) helium-burning, (4a) the onset of carbon-burning, and (4b) the onset of neon-burning in the absence of a preceding carbon- burning phase. We have assumed that there is no mass loss from the stellar surface, that no mixing occurs except in the convective core, and that the opacity is due entirely to electron scattering. Radiation pressure has been taken fully into account. The present research builds upon the stellar model whose principal hydrogen-burning phase was treated by Sakashita, Ono, and Hayashi (1959). The hydrogen-exhaustion phase is taken to begin when X, = 002. The effective temperature increases slightly for 1.4 X 101 years, while X, , decreases to 0.0001. Hydrogen-burning in the core gradually ceases to be effective. When the energy sources due to gravitational contraction and hydrogen-burning in a thin shell at the core boundary become important (simultaneously), the envelope begins to expand rapidly. An excursion in the evolutionary track of A(B - V) = +0.38 mag. and AM,, = -3.1 mag. takes place in 7 X 10 years, at which point the star begins to burn helium as an A3 supergiant. The hydrogenburning shell source continues to be important. The star then evolves to the left in the C-M diagram for 8 X 1O years until V,,,,, = 0.35 and the spectral class is B3. The direction of the track again reverses. In an additional 3 X 1O years the star again becomes an A3 supergiant, then rapidly crosses the Hertzsprung gap, reaching the M-type super- giant region in another 2 X 10 years, with the helium in the core nearly exhausted. The mass of the convective core in the helium-burning phase increases monotonically, at least until V,,,, becomes a small as 0016. This circumstance is favorable, in that no new inhomogeneous radiative zone, whose composition is dependent on the evolutionary history, is created. The total time spent in helium-burning, 1.2 X 106 years, is about one-fourteenth of the period spent in hydrogen-burning Helium-burning accounts for the early-type supergiant branch of luminous galactic clusters such as h and x Persei. Furthermore, the suggestion of a gap which appears in the C-M diagram of h and x Persei between the upper main-sequence stars and the early-supergiant branch is to be expected according to our results. The clusters NGC 330 and NGC 458 in the SMC show the gap more clearly. For the sake of comparison, some computations have been performed for a star of 10.1 solar masses and a more "normal" age-zero population I composition, X = 0.61, V = 037, and Z = 002. Preliminary results have been obtained for the onsets of the subsequent carbon- and neon-burning phases. The very large stellar radii obtained will be reduced considerably when we have taken the surface convection zone into account, while the quantities which characterize the inner structure are expected to remain essentially unchanged. Carbon-burning and more advanced evolutionary phases, which have a total lifetime of the order of 106 years, will probably account for the M-type super-giant branch of h and x Persei and similar clusters.