4. Concluding remarks
The expansion phase of our model stars is due to the formation of a non-degenerate isothermal zone between the degenerate central part of the core and the polytropic envelope. This intermediate zone is formed to bridge the mismatch between the specific gravitational energy right on top of the fully degenerate part of the core and the specific internal energy fixed by the temperature for hydrogen burning. Otherwise, an envelope of a substantial amount of mass would not be in hydrostatic equilibrium with the core. Due to this intermediate zone, w approaches u, the envelope becomes less strongly bound and - according to Eq. (6) - it expands. This model includes the suggestions mentioned in the introduction as different aspects: There is a strong gravitational field of the core, there is a layer with , and there is a shell source with limited luminosity - all of them fitting into simple hydrostatic requirements.
This argument depends on degenerate cores forming in low mass stars. What about high mass stars with continually contracting cores? Contraction yields values of the specific gravitational energy on top of the cores which are again in excess of the value of the specific internal energy as determined by the hydrogen burning temperature. As will be shown in a forthcoming paper, these cores - under the assumtion of homologous contraction - consist of a nearly polytropic central part (with ) surrounded by a zone with larger n. This situation is similar to the present one and again leads to expanded envelopes.
Finally, for higher burning temperatures, the discrepancy between w and u could be avoided from the outset and post main sequence contraction should be expected. Indeed, evolved helium stars with now higher by a factor 10 evolve towards the left of the main sequence position (Deinzer and Salpeter, 1964). This once more points to the low hydrogen burning temperatures as the cause for expansion.
© European Southern Observatory (ESO) 1999
Online publication: February 23, 1999