ES-01-0005

When, where, and how many planets end up in first-order resonances?

Shuo Huang

The theory of Type~I migration has been widely used in many studies. Transiting multi-planet systems offer us the opportunity to examine the consistency between observation and theory, especially for those systems harboring planets in Mean Motion Resonance. The displacement these resonant pairs show from exact commensurability provides us with information on their migration and eccentricity-damping histories. Here, we adopt a probabilistic approach, characterized by two distributions -- appropriate for either the resonant or non-resonant planets -- to fit the observed planet period ratio distribution. With the Markov chain Monte Carlo method, we find that ?15% of exoplanets are in first-order MMRs, the ratio of eccentricity-to-semi-major axis damping is too high to allow overstable librations and the results are by-and-large consistent with Type-I migration theory. In addition, our modeling finds that a small fraction of resonant pairs is captured into resonance during migration, implying late planet formation (gas-poor). Most resonant pairs park themselves at the migration barrier, indicating early planet formation (gas-rich). Furthermore, after improving the criterion on two-body resonant trapping, we obtain an upper limit of the disc surface density when the planets are locked in resonance.