High-precision elements of double-lined spectroscopic binaries from combined interferometry and spectroscopy

Application to the β Cephei star β Centauri

¹ Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
² Department of Astrophysics, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
³ Chatterton Astronomy Department, School of Physics, University of Sydney, NSW 2006, Australia
⁴ Astronomical Institute of the Charles University, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
⁵ Astronomical Institute, Academy of Sciences, 251 65 Ondřejov, Czech Republic

Received: 9 January 2006
Accepted: 10 April 2006

Abstract

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 β Cephei star β Centauri. We also present a detailed analysis of β 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 β Centauri with a precision of 6% and 4%, respectively. Modelling allowed us to refine the mass estimates to 1% precision resulting in and , and to derive the age of the system as being  years. We deduce two oscillation frequencies for the broad-lined primary of β Centauri: c d^-1 and  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.