ON WHY INTERMEDIATE-MASS STARS BECOME GIANTS AFTER THE EXHAUSTION OF HYDROGEN IN THEIR CORES

Several numerical experiments are performed in an attempt to isolate those factors which do, or do not, play a primary role in the expansion to giant dimensions of intermediate-mass stars after they have exhausted hydrogen in their cores. Experiment characteristics are (A) opacity kappa = 0.2 (1 + X) cm2 g-1; (B) kappa = 0.2 (1 + 0.71) cm2 g-1; (C) kappa = 2 cm2 g-1, molecular weight constant at mu = 0.61; (D) kappa = 2 cm2 g-1, mu realistically variable; (E) kappa = 2 cm2 g-1, mu realistic, convection forced when temperature T < 1.1 x 10(6) K; (F) kappa and mu realistic, normal criterion for convection. The stability of (D), (E), and (F) models is investigated. It is concluded that (1) a gravothermal instability in the hydrogen-exhausted core, which sets in when core mass is larger than a critical value, or, equivalently, when central density exceeds the density at the center of the hydrogen-burning shell by a factor of about 32, acts as the ''clock'' which sets the time scale for envelope expansion; (2) the physics of energy transfer in a region of modest mass within and above the hydrogen-burning shell creates a zone of rapidly decreasing density which separates the envelope from the core; (3) absorption of energy in the expanding envelope of a Population I model star in quasi-static equilibrium is not responsible for the expansion of the envelope, but the increasing opacity in the envelope is responsible for absorption; (4) if convection becomes important near the surface, an instability in the envelope occurs when the mass in the convective portion of the envelope relative to the mass in the radiative part becomes larger than a critical value and this instability ceases when most of the envelope has become convective; and (5) the transition from main sequence to giant branch involves a complicated interplay between a core, an envelope, and a nuclear-burning shell, and a ''simple explanation'' as to how this interplay causes stars to become giants can be an inappropriate and misleading description of a complex situation.