Structure coefficients for different initial metallicities for use in stellar analysis

Abstract

Internal structure coefficients for zero age Main Sequence (ZAMS) model stars with different initial metallicities are presented. A series of (Eggleton) stellar models with masses between $1\mbox{--}40\,M_{\odot}$ and metallicities $Z=0.0001$, $Z=0.001$, $Z=0.004$, $Z=0.01$, $Z=0.02$, and $Z=0.03$ were used. We have also calculated the same coefficients for a recommended solar metallicity value $Z=0.0134$ (Asplund et al. in Annu. Rev. Astron. Astrophys. 47:481, 2009). For each model, values of the internal structure constants $k_{2}$, $k_{3}$, $k_{4}$ and related coefficients have been derived by numerically integrating Radau’s equation with the (FORTRAN) program RADAU. The (Eggleton) stellar models used come from the ‘EZ-Web’ compilation of the Dept. of Astronomy, University of Wisconsin, Madison. The calculations follow the procedure given by Inlek and Budding (Astrophys. Space Sci. 342:365, 2012). These new results were compared with others in the literature.

We deduce that the current state of theoretical evaluation of structure coefficients is generally in sufficient agreement with data obtained from apsidal advance rates of selected well-observed eccentric eclipsing binary stars at the present time, given the probable errors of the latter. However, new results coming from more precise and extensive data sets in the wake of the Kepler Mission, or similar future surveys, may call for further theoretical specification or refinement. The derivation of structure coefficients from observations of apsidal motion in close eccentric binary systems requires specification of relevant parameters from light curve analysis. A self-consistent treatment then implies inclusion of the structure coefficients within the fitting function of such analysis.