The discovery of over 400 extrasolar planets allows us to statistically test our understanding of the formation and dynamics of planetary systems via numerical simulations. Traditional N-body simulations of multiple-planet systems without gas disks have successfully reproduced the eccentricity (e) distribution of the observed systems by assuming that the planetary systems are relatively closely packed when the gas disk dissipates, so that they become dynamically unstable within the stellar lifetime. However, such studies cannot explain the small semimajor axes a of extrasolar planetary systems, if planets are formed, as the standard planet formation theory suggests, beyond the ice line. In this paper, we numerically study the evolution of three-planet systems in dissipating gas disks, and constrain the initial conditions that reproduce the observed a and e distributions simultaneously. We adopt initial conditions that are motivated by the standard planet formation theory, and self-consistently simulate the disk evolution and planet migration, by using a hybrid N-body and one-dimensional gas disk code. We also take into account eccentricity damping, and investigate the effect of saturation of corotation resonances on the evolution of planetary systems. We find that the a distribution is largely determined in a gas disk, while the e distribution is determined after the disk dissipation. We also find that there may be an optimum disk mass which leads to the observed a-e distribution. Our simulations generate a larger fraction of planetary systems trapped in mean-motion resonances (MMRs) than the observations, indicating that the disk's perturbation to the planetary orbits may be important to explain the observed rate of MMRs. We also find a much lower occurrence of planets on retrograde orbits than the current observations of close-in planets suggest.
- methods: numerical
- planets and satellites: dynamical evolution and stability
- planet-disk interactions
- protoplanetary disks