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A number of giant planet pairs discovered by the radial velocity method withperiod ratios $\lesssim 2$ may reside in mean motion resonances. Convergentorbital migration and resonant capture at the time of formation would naturallyexplain the present-day resonant orbital configurations of these systems.Planets that experience smooth migration and eccentricity damping forces due toa proto-planetary disk should not only capture into mean motion resonances butalso end up in a specific dynamical configuration within the resonance,sometimes referred to as apsidal corotation resonance (ACR). Here we develop amethod for testing the hypothesis that a planet pair resides in an ACR bydirectly fitting radial velocity data. The ACR hypothesis strongly restrictsthe number of free parameters describing the radial velocity signal and wecompare fits using this highly restricted model to fits using a moreconventional two-planet RV model by using nested sampling simulations. We applyour method to HD 45364 and HD 33844, two systems hosting giant planet pairs in3:2 and 5:3 resonances, respectively. We demonstrate that the observations ofboth systems support an ACR configuration and we use the results of our ACRmodel fits to constrain possible migration histories of these systems.

Modeling Radial Velocity Data of Resonant Planets to Infer Migration Histories