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

Abstract

All available mid-eclipse times of the eclipsing binary Z Draconis are analysed, and three sets of cyclic variations with periods of 20.1, 29.96 and 59.88 yr are found. The low-amplitude variations with the period of 20.1 yr may be attributed to the unavoidable and slight imperfection in the double-Keplerian model, which gives the periods of 29.96 and 59.88 yr. Interestingly, the Z Draconis system is close to a 2:1 mean-motion resonance, or 6:3:2 mean-motion resonance if the period of 20.1 yr is true. We also find that the best solutions tend to give the minimum eccentricities. Based on Kepler's third law, the outermost companion has the minimum mass of $\sim0.77M_{\bigodot}$, whereas the middle companion is an M dwarf star with a mass of $\sim0.40M_{\bigodot}$, suggesting that Z Draconis is a general N-body system.