Keck & APF radial velocities for HD 200964

MMR can allow planets to remain stable in regions of phase space where strong planet-planet interactions would otherwise destabilize the system. These stable orbits can occupy small phase space volumes, allowing MMRs to strongly constrain system parameters, but making searches for stable orbital parameters challenging.

Furthermore, libration of the resonant angle and dynamical interaction between the planets introduces another long-period variation into the observed RV signal, complicating analysis of the periods of the planets in the system. We discuss this phenomenon using the example of HD 200964. By searching through parameter space and numerically integrating each proposed set of planetary parameters to test for long-term stability, we find stable solutions in the 7:5 and 3:2 MMRs in addition to the originally identified 4:3 MMR.