On the Chaotic Orbits of Disc-Star-Planet Systems

TL;DR

This study investigates how proto-stellar discs influence the chaotic and regular orbits in disc-star-planet systems, revealing that disc mass impacts chaos boundaries and orbital stability, which affects planetary formation processes.

Contribution

It introduces two initial velocity conditions to explore chaos in disc-star-planet systems and analyzes how disc mass alters chaotic boundaries and orbital behaviors.

Findings

Chaotic boundary is insensitive to disc mass for Type I initial conditions.

Disc influence shifts equilibrium points and orbital dynamics.

Chaotic orbits are less likely to become stable resonant orbits.

Abstract

Following Tancredi, Sanchez and Roig (2001)'s criteria of chaos, two ways of setting initial velocities are used in the numerical surveys to explore the possible chaotic and regular orbits for the disc-star-planet systems. We find that the chaotic boundary does not depend much on the disc mass for Type I initial condition, but can change a lot for different disc masses for Type II initial condition. A few sample orbits are further studied. Both Poincare surface of section and the Lyapounov Exponent Indicator are calculated and they are consistent with each other. We also find that the influence from the disc can change the locations of equilibrium points and the orbital behaviors for both types of initial conditions. Because the chaotic orbits are less likely to become the stable resonant orbits, we conclude that the proto-stellar disc shall play important roles for the capture and depletion histories of resonant orbits of both Asteroid Belt and Kuiper Belt during the formation of Solar System.