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.

中文翻译：

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模拟共振行星的径向速度数据以推断迁移历史

通过径向速度法发现的许多周期比为 $\lesssim 2$ 的巨行星对可能存在于平均运动共振中。形成时的收敛轨道迁移和共振捕获自然可以解释这些系统目前的共振轨道配置。由于原行星盘而经历平滑迁移和偏心阻尼力的行星不仅应该捕获平均运动共振，而且还应该在共振内形成特定的动态配置，有时称为顶点共转共振 (ACR)。在这里，我们开发了一种通过直接拟合径向速度数据来测试行星对位于 ACR 中的假设的方法。ACR 假设强烈限制了描述径向速度信号的自由参数的数量，我们将使用这种高度受限模型的拟合与使用嵌套采样模拟使用更传统的两行星 RV 模型的拟合进行比较。我们将我们的方法应用于 HD 45364 和 HD 33844，这两个系统分别以 3:2 和 5:3 共振承载巨行星对。我们证明了两个系统的观察结果都支持 ACR 配置，并且我们使用我们的 ACR 模型拟合的结果来限制这些系统的可能迁移历史。