Z Draconis with two companions in a 2：1 mean-motion resonance

All available mid-eclipse times of the eclipsing binary Z Draconis are analyzed, and three sets of cyclic variations with periods of 20.1, 29.96 and 59.88 yr are found. The low-amplitude variations with a period of 20.1 yr may be attributed to the unavoidable slight imperfection in the double-Keplerian model, which gives periods of 29.96 and 59.88 yr. Interestingly, the Z Draconis system is close to a 2:1 mean-motion resonance, or a 6:3:2 mean-motion resonance if the 20.1 yr period really exists. We also find that the best solutions tend to give the minimum eccentricities. Based on Kepler’s third law, the outermost companion has a minimum mass of ~ 0.77 M ⊙ , whereas the middle companion is an M dwarf star with a mass of ~ 0.40 M ⊙ , suggesting that Z Draconis is a general N-body system.