Migration and dynamical relaxation in crowded systems of giant planets

This paper explores the intermediate-time dynamics of newly formed solar systems with a focus on possible mechanisms for planetary migration. We consider two limiting corners of the available parameter space—crowded systems containing N = 10 giant planets in the outer solar system and solar systems with N = 2 planets that are tidally interacting with a circumstellar disk. Crowded planetary systems can be formed in accumulation scenarios—if the disk is metal rich and has large mass—and through gravitational instabilities. The planetary system adjusts itself toward stability by spreading out, ejecting planets, and sending bodies into the central star. For a given set of initial conditions, dynamical relaxation leads to a well-defined distribution of possible solar systems. For each class of initial conditions, we perform large numbers (hundreds to thousands) of N-body simulations to obtain a statistical description of the possible outcomes. For N = 10 planet systems, we consider several different planetary mass distributions; we also perform secondary sets of simulations to explore chaotic behavior and longer term dynamical evolution. For systems with 10 planets initially populating the radial range 5 AU ≤ a ≤ 30 AU, these scattering processes naturally produce planetary orbits with a ∼ 1 AU and the full range of possible eccentricity (0 ≤ ε ≤ 1). Shorter period orbits (smaller a) are difficult to achieve. To account for the observed eccentric giant planets, we also explore a mechanism that combines dynamical scattering and tidal interactions with a circumstellar disk. This combined model naturally produces the observed range of semimajor axis a and eccentricity ε. We discuss the relative merits of the different migration mechanisms for producing the observed eccentric giant planets.