2014MNRAS.439..878Y

New mid-eclipse times of the short-period eclipsing binary SW Lacertae are reported, and two cyclical variations are found in the corresponding O - C diagram. The proposed light-travel time model is refined. The best fit suggests that two possible circumbinary companions are in a near 3:1 mean-motion resonance with periods of 27.01 and 82.61yr. Based on the best-fitting solution, we have studied the stabilities of the two companions moving on a series of mutually inclined orbits. The results show that no orbital configurations can survive for >1000yr. Then, non-Keplerian corrections to the initial conditions and the more distant K-dwarf companion discovered by Rucinski, Pribulla & van Kerkwijk, moving on assumed circular orbits with wide ranges of orbital inclinations, are considered in our numerical simulations. The outcome similarly reveals that the whole system is yet short-term unstable. Perhaps, one or both cyclical variations in the mid-eclipse times are attributed to irregular mass exchange and/or magnetic cycles in the magnetically active W UMa system. Despite this, the instability of the system may also arise from the large uncertainties in orbital parameters. So, secular observations of this target are needed to determine the eccentricity of the outmost companion and the orbital period of the middle companion with much higher precision. Our results suggest that, if the two inner companions do exist, they should be on mutually inclined orbits of >100°, with the minimum masses of 0.62 and 1.94M_☉ for the innermost and middle components, respectively. Our work demonstrates that it is important and necessary to perform dynamical analyses before a discovery of two or more circumbinary companions is announced.