Determination of the axial rotation rate using apsidal motion for early-type eclipsing binaries

Because the modern theory of stellar structure and evolution has a sound observational basis, we can consider that the apsidal parameters k(2) computed in terms of this theory correctly reflect the radial density distribution in stars of different masses and spectral types. This allows us to address the problem of apsidal motion in close binary systems in a new way. Unlike the traditional approach, in this paper we use the observed apsidal periods U-obs to estimate the angular axial velocities of components, omega(r), at fixed model values of k(2). We use this approach to analyse the observational data for 28 eclipsing systems with known U-obs and early-type primaries (M >= 1.6 M-circle dot or T-e >= 6000 K). We measure the age of the system in units of the synchronization time, t/t(syn). Our analysis yielded the following results. (i) There is a clear correlation between omega r/omega(syn) and t/t(syn): the younger a star, the higher the angular velocity of its axial rotation in units of omega(syn), the angular velocity at pseudo-synchronization. This correlation is more significant and obvious if the synchronization time, t(syn), is computed in terms of the Zahn theory. (ii) This observational fact implies that the synchronization of early- type components in close binary systems continues on the main sequence. The synchronization times for the inner layers of the components (i.e. those that are responsible for apsidal motion) are about 1.6 and 3.1 dex longer than those predicted by the theories of Zahn and Tassoul, respectively. The average initial angular velocities (for the zero-age main sequence) are equal to omega(0)/omega(syn) approximate to 2.0. The dependence of the parameter E-2 on stellar mass probably needs to be refined in the Zahn theory. (iii) Some components of the eclipsing systems of the sample studied show radially differential axial rotation. This is consistent with the Zahn theory, which predicts that the synchronization starts at the surface, where radiative damping of dynamical tides occurs, and develops toward the interior. Therefore, one would expect the inner parts of young double early-type stars to rotate faster than the outer parts.