High-precision elements of double-lined spectroscopic binaries from combined interferometry and spectroscopy -: Application to the β Cephei star β Centauri

Aims. We present methodology to derive high-precision estimates of the fundamental parameters of double-lined spectroscopic binaries. We apply the methods to the case study of the double-lined beta Cephei star beta Centauri. We also present a detailed analysis of beta Centauri's line-profile variations caused by its oscillations. Methods. High-resolution spectral time series and visual or interferometric data with a good phase distribution along the orbital period are required. We point out that a systematic error in the orbital amplitudes, and any quantities derived from them, occurs if the radial velocities of blended component lines are computed without spectral disentangling. This technique is an essential ingredient in the derivation of the physical parameters if the goal is to obtain a precision of only a few percent. We have devised iteration schemes to obtain the orbital elements for systems whose lines are blended throughout the orbital cycle. Results. We derive the component masses and dynamical parallax of beta Centauri with a precision of 6% and 4%, respectively. Modelling allowed us to refine the mass estimates to 1% precision resulting in M-1 = 10.7 +/- 0.1 M-circle dot and M-2 = 10.3 +/- 0.1 M-circle dot, and to derive the age of the system as being (14.1 +/- 0.6) x 10(6) years. We deduce two oscillation frequencies for the broad-lined primary of beta Centauri: f(1) = 7.415 c d(-1) and f(2) = 4.542 c d(-1) or one of their aliases. The degrees of these oscillation modes are higher than 2 for both frequencies, irrespective of the alias problem. No evidence of oscillations in the narrow-lined secondary was found. Conclusions. We propose that our iteration schemes be used in any future derivations of the spectroscopic orbital parameters of double-lined binaries with blended component lines to which disentangling can be successfully applied. The combination of parameters resulting from the iteration schemes with high-precision estimates of the orbital inclination and the angular semi-major axis from interferometric or visual measurements allows a complete solution of the system.