Seminar

Three-body resonance is the mean-motion resonance between 3 planets. A remarkable example is the TRAPPIST-1 system, where the planets have orbital period ratios near 8:5, 5:3, 3:2, 3:2, 4:3, 3:2 from the innermost to the outermost pair, and all 7 planets are interlocked in a chain of 3-body resonances. Other systems are also detected in 3-body resonance or chain of 3-body resonances, such as Kepler-60, Kepler-80 and Kepler-223. We investigate and explain several research gaps about resonance dynamics. We derive the critical migration rate and linear regime of several 2-body resonances. We find that pure 3-body resonance can be explained by large free eccentricities and that the multiple libration centers of 3-body resonances can be explained by orbital phase counting. Finally, for migration in an adiabatic protoplanetary disk, we show that the minimum mass solar nebula, the viscously heated disk, or the radiatively heated disk cannot maintain the planets in 3-body resonance. Instead, a migration halting mechanism such as magnetospheric truncation of disk is required to explain the origin of these resonant chain systems.

Additional information: Mr. WONG Ka Ho, rrrwongkaho@yahoo.com.hk