Evolutionary Considerations Involving the Internal Density Concentration Parameter of Binary Stars

Details Evolutionary Considerations Involving the Internal Density Concentration Parameter of Binary Stars Evolutionary Considerations Involving the Internal Density Concentration Parameter of Binary Stars

Mar 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973ap%26ss..21..189p&link_type=abstract

Analytical Procedures for Eclipsing Binary Light Curves, Proceedings of IAU Colloq. 16, held in Philadelphia, PA, September, 197

Astronomy and Astrophysics

Astrophysics

26

Scientific paper

The evolutionary changes that occur in the internal density concentration parameterk 2 (called the apsidal constant for brevity) for a star of given mass and initial composition are examined in detail. The purpose is to ascertain whether or not such an approach leads to a reduction in the differences now noted between the theoretically derived values ofk 2 and the observed values derived from the secular advance of the periastron in close eclipsing binary systems. A series of stellar models of mass 2.0, 5.0, 10.0 and 20.0M &sun; were employed, with an initial compositional mixture ofX=0.739,Y=0.24 andZ=0.021. These models cover an evolutionary range from a point in time where the star has just completed the Hayashi phase of its pre-Main Sequence contraction through its entire Main Sequence phase to the point where hydrogen depletion in the core is complete. For each model, a value ofk 2 is determined by numerically integrating Radau's equation and using the values ofQ{text{ }}(a)/bar Q{text{ }}, the ratio of the star's density at pointa to its mean density, as taken from the models. The result is the time history ofk 2 for each stellar mass over the evolutionary range of interest. The results are then summarized in the (logk 2, logT e) plane which, for the first time, quantitatively indicates the variation ink 2 as a function of the evolutionary state of the star. A comparison between these theoretically derived values ofk 2 and a selected set of observationally determined ones immediately indicates that the secular variation ink 2 plays an extremely important part in any comparison between theory and observation. For most of the cases studied, the difference between the theoretically and observationally determined values ofk 2 can be reconciled in terms of the evolutionary history of the binary system. While tentatively providing a satisfactory explanation for the previously noted differences in the determination ofk 2, there now exists the problem of accurately pinpointing the evolutionary state of the observed binary system.

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