Modeling Radial Velocity Data of Resonant Planets to Infer Migration Histories
Sam Hadden, Matthew J. Payne
Abstract
Abstract A number of giant-planet pairs with period ratios ≲2 discovered by the radial velocity (RV) method may reside in mean motion resonances. Convergent orbital migration and resonant capture at the time of formation would naturally explain the present-day resonant orbital configurations of these systems. Planets that experience smooth migration and eccentricity-damping forces due to a protoplanetary disk should not only be captured into mean motion resonances but also end up in a specific dynamical configuration within the resonance, sometimes referred to as apsidal corotation resonance (ACR). Here we develop a method for testing the hypothesis that a planet pair resides in an ACR by directly fitting RV data. The ACR hypothesis strongly restricts the number of free parameters describing the RV signal, and we compare fits using this highly restricted model to fits using a more conventional two-planet RV model by using nested sampling simulations. We apply our method to HD 45364 and HD 33844, two systems hosting giant-planet pairs in 3:2 and 5:3 resonances, respectively. The observations of both systems are consistent with ACR configurations, which are formally preferred based on the Bayes factors computed from nested sampling simulations. We use the results of our ACR model fits to constrain the possible migration histories of these systems.