On the chaotic orbits of disk-star-planet systems

Following Tancredi et al.'s criteria of chaos, two ways of setting initial velocities are used in numerical surveys to explore possible chaotic and regular orbits for disk-star-planet systems. We find that the chaotic boundary does not depend much on the disk mass for type I initial conditions, but can change a lot for different disk masses for type II initial conditions. A few sample orbits are further studied. Both the Poincare surface of section and the Lyapunov exponent indicator are calculated, and they are consistent with each other. We also find that the influence from the disk can change the locations of equilibrium points and the orbital behaviors for both types of initial conditions. Because chaotic orbits are less likely to become stable resonant orbits, we conclude that the protostellar disk plays important roles for the capture and depletion histories of resonant orbits of both the asteroid and Kuiper belts during the formation of the solar system.