Gross model characteristics during the interpulse phase and the characteristics of the convective shell that occurs during thermal pulses near limiting amplitude are investigated for stellar models of 7 solar masses and Population I composition which contain a carbon-oxygen core of 0.96, 1.16, and 1.36 solar masses. For each 0.2-solar-mass increase in core mass, it is found that: (1) both the maximum mass contained in and the duration of the convective shell appearing during a pulse decrease by roughly one order of magnitude; (2) the maximum temperature achieved at the base of the shell increases by about 50 million K; and (3) the magnitude of the entropy barrier which prevents merging of the shell and envelope convective regions approximately doubles. The relationship between core mass and luminosity during the interpulse phase is shown to be a strong function of total stellar mass and the assumed value of the mixing length relative to the pressure scale height. The results also indicate that while the relationship between core mass and luminosity is insensitive to the assumed envelope opacity, the model radius decreases by 25% for every factor-of-10 decrease in the assumed heavy-element content in the envelope.
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Jr. Iben I. (1977) studied this question.