We explore the possibility that the observed eccentricity distribution of extrasolar planets arose through planet-planet interactions , after the initial stage of planet formation was complete .
Our results are based on \sim 3250 numerical integrations of ensembles of randomly constructed planetary systems , each lasting 100 Myr .
We find that for a remarkably wide range of initial conditions the eccentricity distributions of dynamically active planetary systems relax towards a common final equilibrium distribution , well described by the fitting formula dn \propto e \exp [ - { 1 \over 2 } ( e / 0.3 ) ^ { 2 } ] de .
This distribution agrees well with the observed eccentricity distribution for e \gtrsim 0.2 , but predicts too few planets at lower eccentricities , even when we exclude planets subject to tidal circularization .
These findings suggest that a period of large-scale dynamical instability has occurred in a significant fraction of newly formed planetary systems , lasting 1–2 orders of magnitude longer than the \sim 1 Myr interval in which gas-giant planets are assembled .
This mechanism predicts no ( or weak ) correlations between semimajor axis , eccentricity , inclination , and mass in dynamically relaxed planetary systems .
An additional observational consequence of dynamical relaxation is a significant population of planets ( \gtrsim 10 % ) that are highly inclined ( \gtrsim 25 ^ { \circ } ) with respect to the initial symmetry plane of the protoplanetary disk ; this population may be detectable in transiting planets through the Rossiter-McLaughlin effect .