Binary stars provide a valuable test of stellar structure and evolution, because the masses of the individual stellar components can be derived with high accuracy and in a model-independent way. In this work, we study Spica, an eccentric double-lined spectroscopic binary system with a beta Cep type variable primary component. We use state-of-the-art modelling tools to determine accurate orbital elements of the binary system and atmospheric parameters of both stellar components. We interpret the short-period variability intrinsic to the primary component, detected on top of the orbital motion both in the photometric and spectroscopic data. The non-LTE based spectrum analysis reveals two stars of similar atmospheric chemical composition consistent with the present day cosmic abundance standard defined by Nieva&Przybilla (2012). The masses and radii of the stars are found to be 11.43+/-1.15 M_sun and 7.21+/-0.75 M_sun, and 7.47+/-0.54 R_sun and 3.74+/-0.53 R_sun for the primary and secondary, respectively. We find the primary component to pulsate in three independent modes, of which one is identified as a radial mode, while the two others are found to be non-radial, low degree l modes. The frequency of one of these modes is an exact multiple of the orbital frequency, and the l=m=2 mode identification suggests a tidal nature for this particular mode. We find a very good agreement between the derived dynamical and evolutionary masses for the Spica system to within the observational errors of the measured masses. The age of the system is estimated to be 12.5+/-1 Myr.
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