1 Introduction

More than 20 years ago, Morbey (1975) wrote a paper about the simultaneous adjustment of visual and spectroscopic observations. Obviously, the last two decades have not brought as many such systems as Morbey expected in 1975. Favorable conditions to apply a simultaneous solution are still rare even if, nowadays, it is becoming important due to new instruments and observation techniques. Unfortunately, adjustments are still frequently realized separately Docobo et al. (1992); Hummel et al. (1994).

More recently, Barlow et al. (1993) got the orbital parameters of Capella using a simultaneous solution. Unfortunately, the paper does not clearly mention how the authors build the initial solution. The final solution is effectively simultaneous but that is not necessary the case in the first part of the process. In other words, if the function that is minimized in the final step take all aspects of the orbit into account, nothing indicates that the components of the initial solution (used as the minimization starting point) do not come from disjoint solutions.

The aim of this paper is to present a different computational way to combine visual and spectroscopic data to get only one estimate of the parameters of the orbit: the orbit which simultaneously minimizes a certain function of the residuals of the different data sets. We present the sub-parts of such a procedure: the set of parameters, the function to minimize, the procedure to get the global minimum and the local improvement.

To reach this goal, different steps are required. The first one is to select the most suitable set of orbital parameters among the different equivalent ones (e.g., Thiele-Innes constants or semi-major axis and Eulerian angles). The set fixes the working space. The definition of what we call the objective function (that is the function to be minimized by an appropriate choice of the parameters) is also very important. To find the global minimum of that function, the procedure is divided into two parts: the identification of a neighborhood of the global minimum and then the improvement of this solution with a local search.

We illustrate our analysis with HR 466 (WDS 01376-0924) using speckle observations Hartkopf et al. (1996) and radial velocities Tokovinin (1993). This example is intended to shows that, starting from scratch, the proposed method provides results consistent with the three sets of measurements.