Period Ratio Sculpting Near Second-Order Mean-Motion Resonances

Second-order mean-motion resonances lead to an interesting phenomenon in the sculpting of the period ratio distribution due to their shape and width in period-ratio/eccentricity space. As the osculating periods librate in resonance, the time-averaged period ratio approaches the exact resonance location. The width of second order resonances increases with increasing eccentricity, and thus more eccentric systems have a stronger peak at the resonance location when averaged over sufficient time. The libration period is short enough that this time-averaging behavior is expected to appear on the timescale of the Kepler mission. In this talk, I will present results obtained from N-body integrations of simulated planet pairs near the 5:3 and 3:1 mean-motion resonances. I will demonstrate how these results constrain the eccentricity distributions of real Kepler planets near second-order resonance, placing an upper limit on the Rayleigh scale parameter, σ, at σ = 0.245 (3:1) and σ = 0.095 (5:3) at 95% confidence.