  A number of giant planet pairs discovered by the radial velocity method with
period ratios $\lesssim 2$ 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 proto-planetary disk should not only capture 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 radial velocity data. The ACR hypothesis strongly restricts
the number of free parameters describing the radial velocity 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. We demonstrate that the observations of
both systems support an ACR configuration and we use the results of our ACR
model fits to constrain possible migration histories of these systems.
