2010ApJ...711..772R

We develop an idealized dynamical model to predict the typical properties of outer extrasolar planetary systems, at radii comparable to the Jupiter-to-Neptune region of the solar system. The model is based upon the hypothesis that dynamical evolution in outer planetary systems is controlled by a combination of planet-planet scattering and planetary interactions with an exterior disk of small bodies ("planetesimals"). Our results are based on 5000 long duration N-body simulations that follow the evolution of three planets from a few to 10 AU, together with a planetesimal disk containing 50 M_⊕ from 10 to 20 AU. For large planet masses (M ≳ M_Sat), the model recovers the observed eccentricity distribution of extrasolar planets. For lower-mass planets, the range of outcomes in models with disks is far greater than that which is seen in isolated planet-planet scattering. Common outcomes include strong scattering among massive planets, sudden jumps in eccentricity due to resonance crossings driven by divergent migration, and re-circularization of scattered low-mass planets in the outer disk. We present the distributions of the eccentricity and inclination that result, and discuss how they vary with planet mass and initial system architecture. In agreement with other studies, we find that the currently observed eccentricity distribution (derived primarily from planets at a ≲ 3 AU) is consistent with isolated planet-planet scattering. We explain the observed mass dependence–which is in the opposite sense from that predicted by the simplest scattering models–as a consequence of strong correlations between planet masses in the same system. At somewhat larger radii, initial planetary mass correlations and disk effects can yield similar modest changes to the eccentricity distribution. Nonetheless, strong damping of eccentricity for low-mass planets at large radii appears to be a secure signature of the dynamical influence of disks. Radial velocity measurements capable of detecting planets with K {&x2248;} 5 m/s and periods in excess of 10 years will provide constraints on this regime. Finally, we present an analysis of the predicted separation of planets in two-planet systems, and of the population of planets in mean-motion resonances (MMRs). We show that, if there are systems with ∼ Jupiter-mass planets that avoid close encounters, the planetesimal disk acts as a damping mechanism and populates MMRs at a very high rate (50%-80%). In many cases, resonant chains (in particular the 4:2:1 Laplace resonance) are set up among all three planets. We expect such resonant chains to be common among massive planets in outer planetary systems.