Evolution of a Star with Intermediate Mass after Hydrogen Burning. I

Abstract

The evolution of a population I star of 4 M/sub sub solar /, after the formation of a dehydrogenized core and a hydrogen burning shell, is calculated up to the stage when helium has almost burnt out in the central region. This course of the evolution is divided into three phases. In the first phase, the star has a hydrogen-burning shell and an isothermal core, and 2.1 x 10/sup 6 years, until the mass fraction of the core grows to 0.120 beyond which there exists no solution with an isothermal core. In the second phase, the core of the star contracts rapidly releasing gravitational energy while the envelope expands. The central temperature increases and the star comes to the red giant region in 1.1 x 10/sup 6/ years before helium begins to burn. In this course electrons do not become degenerate and 4 M/sub sub solar / is found to be near a critical stellar mass devoid of the formation of a degenerate isothermal core. Finally, in the phase of helium burning, the core expands and the envelope shrinks slowly until the helium content in the central region decreases to 0.3. Afterwards the envelope expands again. The lifetime of themore » helium burning phase is 2.1 x 10/sup 7/ years and the star spends half of this time as an A-type giant near the turning point. Effects of uncertainties in nuclear energy generation rates, opacities, and chemical compositions on the structure of this A-type giant are examined. Even if these uncertainties are taken into account, a separate group of A-type giants in the HerzsprungRussell diagram of NGC 458 can be identified with the helium-burning phase. The observed number of these stars is consistent with the calculated lifetime. (auth)« less