Z Draconis with two companions in a 2∶1 mean-motion resonance
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摘要:
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 meanmotion 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.