Formation and Resonance Architecture of the nu Oph and HD 202206 Brown Dwarf Systems

Abstract

The K giant ν Oph has two brown dwarf companions locked in a strong 6:1 mean-motion resonance (MMR), while the main-sequence star HD 202206 has an eccentric inner brown dwarf companion and an outer Jovian mass planet forming a 5:1 MMR pair. These are the highest order MMRs discovered to date, and they are important for probing planetary formation and evolution scenarios. In particular, they hint that brown dwarfs can form like planets in a circumstellar disk around the star and be captured into MMR by disk induced migration. To determine the probabilities of capture at their current 5:1 and 6:1 MMR, we have performed a series of three-body simulations using SyMBA modified to include a forced migration rate ((da/dt)/a) in Jacobi orbital elements. Starting with different migration rates (da/dt)/a and initial orbital geometries beyond the MMR ratio, we find that the resonances of ν Oph and HD 202206 can be accurately reproduced, if the initial orbits are eccentric and the migration rate is rather slow. Our analysis showed that for (da/dt)/a = 10^-6 to 10^-7 the probability of capture into the 6:1 and 5:1 MMR are approximately 15% and 20%, respectively.