2 Test procedure

We therefore selected the largest set of VB-SB2 objects for which there are enough observations to undertake such an orbit determination. The resulting set contains the following 38 systems (the numbers refer to the Hipparcos catalogue Hipparcos): 677, 2941, 4463, 7580, 8903, 10064, 10644, 10952, 12390, 12623, 14328, 24608, 28360, 38382, 45170, 46404, 57565, 65378, 71683/1, 73182, 75312, 85667, 87895, 88601, 89937, 91636, 95995, 96683, 98416, 99376, 99473, 103655, 104858, 104987, 108917, 111170, 111528 and 114576. We refer to Poubaix (1998a) for the complete description of the different data sets used in this analysis.

 

Figure 1:  Evolution of the efficiency when SB2 data are added to a set of VB observations

For all systems (except HIP 111170, for which there are only two visual observations available so that a VB solution cannot be computed), there are enough observations to estimate system parameters independently, i.e., determine orbits independently from the visual and spectroscopic observations. The methods used to derive the orbital parameters were described elsewhere Pourbaix (1994, 1998a). The ten parameters used to model the VB-SB2 data supersede those of the VB observations. One can thus directly analyze the evolution of the efficiency from one data set to the other.

As shown in Fig. 1, the efficiency does grow for all binaries but one. Note particularly that even if the efficiency is almost 0 for a VB solution, the efficiency of a VB-SB2 solution for the same object can go up to an impressive 0.6. This confirms that adding radial velocities does indeed nearly always reduce the correlation between the orbital parameters. There is, however, one exception: HIP 91636. Is this just a numerical accident? Is such behavior predictable?

If we assume (for the sake of illustration) that there is strictly no correlation between the seven parameters of the visual orbit, the efficiency would be equal to 1. Radial velocities could therefore not introduce any correlations among the VB-parameters. If, however, the radial velocities cover only a small part of the curves, one could have a high correlation between V₀, the radial velocity of the system's center of gravity and $\kappa$, the fractional mass. It is then likely for the efficiency computed on the whole data set to decrease. It is indeed impossible that the visual observations exhibit such a correlation since it holds only between parameters not occurring in the visual model. This is exactly the situation with HIP 91636.

Thus we confirm that the efficiency of combined solutions is larger than that of individual ones except in freak cases, and that VB-SB2 solutions allow one the estimation of system parameters (in particular, parallaxes and masses of the individual components) which could never be obtained from adjusting only visual observations without some extraneous material.