Calculation of the masses of the binary star HD 93205 by application of the theory of apsidal motion

Abstract

We present a method to calculate masses for components of both eclipsing and non-eclipsing binary systems as long as their apsidal motion rates are available. The method is based on the fact that the equation that gives the rate of apsidal motion is a supplementary equation that allows the computation of the masses of the components, if their radii and the internal structure constants can be obtained from theoretical models. For this reason the use of this equation makes the method presented here <i>model dependent</i>. We apply this method to calculate the mass of the components of the <i>non-eclipsing</i> massive binary system HD 93205 (O3 V + O8 V), which is suspected to be a very young system. To this end, we have computed a grid of evolutionary models covering the mass range of interest, and taking the mass of the primary (M<SUB>1</SUB>) as the only independent variable, we solve the equation of apsidal motion for M1 as a function of the age of the system. The mass of the primary that we find ranges from M<SUB>1</SUB> = 60 ± 19 M⊙ for zero-age main-sequence models, which sets an upper limit for M<SUB>1</SUB>, down to M1 = 40 ± 9 M⊙ for an age of 2 Myr. Accordingly, the upper limit derived for the mass of the secondary (M<SUB>2</SUB> = QM<SUB>1</SUB>) M<SUB>2</SUB> = 25 M⊙ is in very good agreement with the masses derived for other O8 V stars occurring in eclipsing binaries.