arXiv subjects
Publications and source records attributed to Li-Chin Yeh.
Motivated by Papadakis (2005a, 2005b), we study a Chermnykh-like problem, in which an additional gravitational potential from the belt is included. In addition to the usual five equilibrium points (three collinear and two triangular points), there are some new equilibrium points for this system. We studied the conditions for the existence of these new equilibrium points both analytically and numerically.
Following Papadakis (2005)'s numerical exploration of the Chermnykh's problem, we here study a Chermnykh-like problem motivated by the astrophysical applications. We find that both the equilibrium points and solution curves become quite different from the ones of the classical planar restricted three-body problem. In addition to the usual Lagrangian points, there are new equilibrium points in our system. We also calculate the Lyapunov Exponents for some example orbits. We conclude that it seems there are more chaotic orbits for the system when there is a belt to interact with.
We use both the conventional and more recently developed methods of cluster analysis to study the data of extra-solar planets. Using the data set with planetary mass M, orbital period P, and orbital eccentricity e, we investigate the possible clustering in the ln M, ln P, ln P-ln M, e, and ln P-e spaces. There are two main implications: (1) mass distribution is continuous and (2) orbital population could be classified into three clusters, which correspond to the exoplanets in the regimes of tidal, on-going tidal and disc interaction, respectively.
We study the migration and resonant capture of planetesimals in a planetary system consisting of a gaseous disc analogous to the primordial solar nebula and a Neptune-like planet. Using a simple treatment of the drag force we find that planetesimals are mainly trapped in the 3:2 and 2:1 resonances and that the resonant populations are correlated with the gaseous drag strength in a sense that the 3:2 resonant population increases with the stronger gaseous drag, but the 2:1 resonant population does not. Since planetesimals can lead to the formation of larger bodies similar to asteroids and Kuiper Belt Objects, the gaseous drag can play an important role in the configuration of a planetary system.
It has been an interesting question that why there are one-third of Kuiper Belt Objects (KBOs) trapped into the 3:2 resonance but, in contrast, only several KBOs are claimed to be associated with the 2:1 resonance. In a model proposed by Zhou et al. (2002), the stochastic outward migration of the Neptune could reduce the number of particles in the 2:1 resonance and thus the objects in the 3:2 resonance become more distinct. As a complementary study, we investigate the effect of proto-stellar discs on the resonance capture. Our results show that the gaseous drag of a proto-stellar disc can trap KBOs into the 3:2 resonance rather easily. In addition, no objects are captured into the 2:1 resonance in our simulation.
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.
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.
It has been shown that there is a possible mass-period correlation for extrasolar planets from the current observational data and this correlation is, in fact, related to the absence of massive close-in planets, which are strongly influenced by the tidal interaction with the central star. We confirm that the model in Pätzold & Rauer (2002) is a good approximation for the explanation of the absence of massive close-in planets. We thus further determine the minimum possible semimajor axis for these planets to be detected during their lifetime and also study their migration time scale at different semimajor axes by the calculations of tidal interaction. We conclude that the mass-period correlation at the time when these planets were just formed was less tight than it is now observed if these orbital migrations are taken into account.
The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: the one on the inner edge of the belt is asymptotically stable and the one on the outer edge of the belt is unstable. This is consistent with the observational picture of Asteroid Belt between the Mars and Jupiter: the Mars is moving stablely close to the inner edge but the Jupiter is quite far from the outer edge.
A simple dynamical model is employed to study the possible orbital evolution of scattered planets and phase plane analysis is used to classify the parameter space and solutions. Our results reconfirm that there is always an increase in eccentricity when the planet was scattered to migrate outward when the initial eccentricity is zero. Applying our study on the Solar System and considering the existence of the Kuiper Belt, this conclusion implies that Neptune was dynamically coupled with the Kuiper Belt in the early phase of the Solar System, which is consistent with the simulational model in Thommes, Duncan & Levison (1999).