On the dynamics of the AB Doradus system

We present an astrometric analysis of the binary systems AB Dor A /AB Dor C and AB Dor Ba /AB Dor Bb. These two systems of well-known late-type stars are gravitationally associated and they constitute the quadruple AB Doradus system. From the astrometric data available at different wavelengths, we report: (i) a determination of the orbit of AB Dor C, the very low mass companion to AB Dor A, which confirms the mass estimate of 0.090 $M_\odot$ reported in previous works; (ii) a measurement of the parallax of AB Dor Ba, which unambiguously confirms the long-suspected physical association between this star and AB Dor A; and (iii) evidence of orbital motion of AB Dor Ba around AB Dor A, which places an upper bound of 0.4 $M_\odot$ on the mass of the pair AB Dor Ba /AB Dor Bb (50% probability). Further astrometric monitoring of the system at all possible wavelengths would determine with extraordinary precision the dynamical mass of its four components.