A methodology for studying physical and dynamical properties of multiple stars. Application to the system of red dwarfs Gl 22

Aims. The main aim of this study is the elaboration of a methodology for studying physical and dynamical properties of multiple stars and its application to the hierarchical triple system Gl 22. A careful evaluation of the components' masses and a study of the system's overall stability and long-term dynamical evolution were also pursued. Methods. New NIR speckle interferometric observations with the 6 m telescope of the Special Astrophysical Observatory (Russia) in the Kphotometric band have been carried out. We have made use of the method for orbit calculation reported by Docobo (1985). Results. An original methodology was elaborated and applied to evaluate the most probable elements of the outer orbit. Due to the almost definitive orbit of the inner pair, which just covered a full revolution, the motion of B relative to MCA has been carefully calculated. The position of MCA was estimated on the basis of differential photometry and empirical mass-luminosity relationships. A weak sinusoidal pattern in the apparent motion of the component B was noticed. Conclusions. Our methodology was successfully applied to the triple system Gl 22. The newly calculated outer orbit exhibits a moderate eccentricity (e = 0.29), which differs from the previously known circular solutions. Both orbits are coplanar and co- revolving. This already known suggestion is now based on a much larger set of observational data, including a significant number of speckle measurements. Gl 22 is most likely a dynamically stable system, at least on the time scale of 10 Myr. The sinusoidal pattern in the motion of the B component could be caused by a fourth, unseen, very low-mass object with a mass of 0.015 M� (16 MJ )o n a circular orbit around B with a period of ∼15 yr and semimajor axis 0. 35.