Studies in stellar structure and evolution

Abstract

We investigate stellar models for main-sequence and horizontal-branch stars constructed using the Carson opacities and make comparisons with models based on the Cox-Stewart opacities. A Henyey code based on the prescription of Kippenhahn et al (1967) is used for most of the calculations of stellar structure and evolution. In the equation of state we treat ionisation equilibrium and non-relativistic degeneracy for separate temperature-density regimes. The opacity is obtained by 4-dimensional linear interpolation in the Carson opacity tables. Nuclear energy generation rates are taken from Fowler et al (1975) and neutrino losses from the approximation due to Beaudet et al (1967). Electron-screening factors are from Reeves (1965). The standard local mixing-length theory of Bohm-Vitense (1958) is used to treat non-adiabatic convection, although some models are calculated with modifications due to Deupree et al (1979, 1980). We neglect semi convection. The Carson opacities have only a small effect on the position of ZAHB models, but this may be metallicity dependent. The drop in the hydrogen- shell luminosity due to the helium-core expansion during HB evolution is greater than that obtained with the Cox-Stewart opacities. Allowing for the inclusion of semi convection and convective overshooting, we find that adoption of the Carson opacities leads to a reduction of approximately 25% in the HB lifetimes. For a given range of values for the masses and envelope helium abundances of stars on a synthetic HB, the width in effective temperature is increased, and in luminosity the width is decreased. The dependence of the core luminosity on the falling core helium abundance is increased by approximately 16%. Studies of main-sequence stars lead to agreement with Stothers' (1974a, 1974b, 1976) results for homogeneous models constructed with the Carson opacities. The evolution of main-sequence stars of intermediate mass is unaffected by the change in the opacity. Two evolutionary sequences (for 1 Mo stars) suggest that the main-sequence lifetimes of low mass stars may be reduced by as much as 30%. Combined with a shift in the ZAMS position this will move isochrones for low mass stars towards lower effective temperatures and densities. If studies of red-giant evolution indicate little change in the luminosity level of the horizontal branch, globular cluster ages determined from the position of the main-sequence turnoff point may be substantially reduced (possibly by as much as 50%). This could save a conflict between observed values for globular cluster ages and a value for the Hubble constant of 90. Studies of the apsidal motion constant, k₂, for evolved MS stars shows that the discrepancy between observed values of k₁ for eclipsing binary systems and theoretical values obtained from homogeneous stellar models may be resolved by considering the evolution of the binary components. CO Lac is an exception to this result, but analysis of the observations suggests that a redetermination of the orbital semi-amplitudes may resolve the conflict.