Period Ratio Sculpting near Second-order Mean-motion Resonances

Abstract Second-order mean-motion resonances lead to an interesting phenomenon in the sculpting of period-ratio distribution, due their shape and width period-ratio/eccentricity space. As osculating periods librate resonance, time-averaged period ratio approaches exact commensurability. The second-order increases with increasing eccentricity, thus more eccentric systems have a stronger peak at commensurability when averaged over sufficient time. libration is short enough that this time-averaging behavior expected appear on timescale Kepler mission. Using N -body integrations simulated planet pairs near 5:3 3:1 resonances, we investigate eccentricity distribution consistent observed by Kepler. This analysis, approach independent from previous studies, shows no statistically significant resonance small placing upper limit Rayleigh scale parameter, σ , planets = 0.245 (3:1) 0.095 (5:3) 95% confidence, results other methods.