Calculation of the Masses of the Binary Star HD 93205 by Application of the Theory of the 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 the radii and the internal structure constants of them can be obtained from theoretical models. For this reason the use of this equation makes the method presented here model dependent. We apply this method to calculate the mass of the components of the non-eclipsing massive binary system HD 93205 (O3V+O8V), which is suspected to be a very young system. To this end, we computed a grid of evolutionary models covering the mass range of interest, and taking the mass of the primary (M_1) as the only independent variable, we solve the equation of apsidal motion for M_1 as a function of the age of the system. The mass of the primary we find ranges from M_1= 60+-19 msun for ZAMS models, which sets an upper limit for M_1, down to M_1= 40+-9 msun for an age of 2 Myr. Accordingly, the upper limit derived for the mass of the secondary (M_2= Q M_1) is M_2= 25 msun is in very good agreement with the masses derived for other O8V stars occurring in eclipsing binaries.