Abstract
Evolution from the main sequence to the red-giant phase is discussed for Population I stars of mass M/Mo = 1,1.25, and 1 5. Prior to the giant phase in all three stars, energy generation by the p-p chain reactions dominates over energy generation by the CN cycle reactions. During the main hydrogen- burning phase, a convective core is not present in the 1 Mo star but does occur in both the 1.25 Mo and 1.5 Mo stars. Over a major portion of the main-sequence phase, the convective core grows in both the 1.25 Mo and 1.5 Mo stars as the CN cycle reactions become increasingly important. As each star rises along the red-giant branch, the CN cycle reactions eventually become the major source of energy in the hydrogen-burning shell. The time spent by a star burning hydrogen in a thick shell relative to the time spent in the core hydrogen-burning phase is found to be a strongly decreasing function of stellar mass. Partially responsible for this mass dependence are three factors: (1) for more massive stars, the mass fraction in the convective core, and hence the mass over which hydrogen is exhausted at the end of the core hydrogen-burning phase, is closer to the effective -Chandrasekhar limit; (2) with decreasing stellar mass, the variation of hydrogen through the shell becomes more gradual, and (3) with decreasing mass, electron degeneracy becomes more important in the hydrogen-exhausted core during the thick shell-burning phase. The latter two factors have the effect of increasing the -Chandrasekhar limit. In contrast with the case of more massive stars discussed in earlier papers of this series, electron degeneracy is responsible for a major fraction of the pressure and electron conduction is the major mode of energy flow in the hydrogen-exhausted core of all three stars during the giant phase The result is that all three stars possess a nearly isothermal core along the giant branch. During and following the shell-narrowing phase in all three stars, the surface lithium abundance decreases regularly with decreasing surface temperature as envelope convection extends deeper and deeper into the star. Such is the case also for the surface ratio of C12 to N14. Comparatively large amounts of He3 are made in all three stars, and it is suggested that a large fraction of the He3 in the galactic disk was perhaps formed in ordinary stars. Comparison of individual tracks with cluster diagrams for NGC 1.88 and M67 provides evidence for the qualitative correctness of several characteristic features of the theoretical tracks. The pronounced and rapid change in luminosity and in surface temperature during the phase of over-all contraction is related to a "gap" in M67; the decrease with decreasing mass in the magnitude of the luminosity drop during the shell-narrowing phase is related to the change with cluster age in the slope of the subgiant branch; for a given luminosity, the decrease with decreasing mass in surface temperature along the giant branch is related to the decrease with increasing cluster age in surface temperature along the cluster giant branch. The ages of NGC 188 and M67 are estimated to be (11 + 2) x 1O yr and (5.5 + 1) X 1O yr, respectively.