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

Abstract

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 harbouring planets in Mean Motion Resonance (MMR). 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 (MCMC) method, we find that $\approx 15\%$ of exoplanets are in first order ($j+1:j$) MMRs, the ratio of eccentricity-to-semi-major axis damping is too high to allow overstable librations and that 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 of the 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 at the time the planets are locked in resonance.

arXiv comment19 pages, 18 figures. Figures' clarity and discussions are improved. Accepted for publication in MNRAS

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