On the orbit calculation of visual binaries with a very short arc: application to the PMS binary system, FW Tau AB

In the vast majority of cases when available astrometric measurements of a visual binary cover a very short orbital arc, it is practically impossible to calculate a good quality orbit. It is especially important for systems with pre-main-sequence components where standard mass-spectrum calibrations cannot be applied nor can a dynamical parallax be calculated. We have shown that the analytical method of Docobo allows us to put certain constraints on the most likely orbital solutions, using an available realistic estimate of the global mass of the system. As an example, we studied the interesting PMS binary, FW Tau AB, located in the Taurus-Auriga as well as investigated a range of its possible orbital solutions combined with an assumed distance between 120 and 160 pc. To maintain the total mass of FW Tau AB in a realistic range between 0.2 and 0.6M⊙, minimal orbital periods should begin at 105, 150, 335, and 2300 yr for distances of 120, 130, 140, and 150 pc, respectively (no plausible orbits were found assuming a distance of 160 pc). An original criterion to establish the upper limit of the orbital period is applied. When the position angle in some astrometric measurements was flipped by 180°, orbits with periods close to 45 yr are also plausible. Three example orbits with periods of 44.6, 180, and 310 yr are presented.