Inferred Properties of Planets in Mean-Motion Resonances are Biased by Measurement Noise

Abstract

Planetary systems with mean-motion resonances (MMRs) hold special value in terms of their dynamical complexity and their capacity to constrain planet formation and migration histories. The key towards making these connections, however, is to have a reliable characterization of the resonant dynamics, especially the so-called "libration amplitude", which qualitatively measures how deep the system is into the resonance. In this work, we identify an important complication with the interpretation of libration amplitude estimates from observational data of resonant systems. Specifically, we show that measurement noise causes inferences of the libration amplitude to be systematically biased to larger values, with noisier data yielding a larger bias. We demonstrated this through multiple approaches, including using dynamical fits of synthetic radial velocity data to explore how the the libration amplitude distribution inferred from the posterior parameter distribution varies with the degree of measurement noise. We find that even modest levels of noise still result in a slight bias. The origin of the bias stems from the topology of the resonant phase space and the fact that the available phase space volume increases non-uniformly with increasing libration amplitude. We highlight strategies for mitigating the bias through the usage of particular priors. Our results imply that many known resonant systems are likely deeper in resonance than previously appreciated.