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Overstable Librations can account for the Paucity of Mean Motion Resonances among Exoplanet Pairs

We assess the multi-planet systems discovered by the Kepler satellite in terms of current ideas about orbital migration and eccentricity damping due to planet-disk interactions. Our primary focus is on mean motion resonances. Only a few percent of planet pairs are in close proximity to a resonance. However, predicted migration rates (parameterized by $τ_n=n/{|\dot n|}$) imply that during convergent migration most planets would have been captured into first order resonances. Eccentricity damping (parameterized by $τ_e=e/{|\dot e|}$) offers a plausible resolution. Estimates suggest $τ_e/τ_n\sim (h/a)^2\sim 10^{-2}$, where $h/a$ is the ratio of disk thickness to radius. Together, eccentricity damping and orbital migration give rise to an equilibrium eccentricity, $e_{eq}\sim(τ_e/τ_n)^{1/2}$. Capture is permanent provided $e_{eq}\lesssim μ^{1/3}$, where $μ$ denotes the planet to star mass ratio. But for $e_{eq}\gtrsim μ^{1/3}$, capture is only temporary because librations around equilibrium are overstable and lead to passage through resonance on timescale $τ_e$. Most Kepler planet pairs have $e_{eq}>μ^{1/3}$. Since $τ_n>> τ_e$ is the timescale for migration between neighboring resonances, only a modest percentage of pairs end up trapped in resonances after the disk disappears. Planet pairs close to a mean motion resonance typically exhibit period ratios 1-2% larger than those for exact resonance. The direction of this shift undoubtedly reflects the same asymmetry that requires convergent migration for resonance capture. Permanent resonance capture at these separations from exact resonance would demand $μ(τ_n/τ_e)^{1/2}\gtrsim 0.01$, a value that estimates of $μ$ from transit data and $(τ_e/τ_n)^{1/2}$ from theory are insufficient to match. Plausible alternatives involve eccentricity damping during or after disk dispersal. (Abridged)