Ing-Guey Jiang

Warps and cosmic infall

N-body simulations show that when infall reorientates the outer parts of a galactic halo by several degrees per Gyr, a self-gravitating disc that is embedded in the halo develops an integral-sign warp that is comparable in amplitude to observed warps. Studies of angular-momentum acquisition suggest that the required rate of halo reorientation is realistic for galaxies like the Milky Way.

The Persistence of Warps in Spiral Galaxies with Massive Haloes

ABSTRA C T We study the persistence of warps in galactic discs in the presence of massive haloes. A disc is approximated by a set of massive rings, while a halo is represented by a conventional n-body simulation. We confirm the conclusion of Nelson & Tremaine that a halo responds strongly to an embedded precessing disc. This response invalidates the approximations made in the derivation of classical ‘modified tilt’ modes. We show that the response of the halo causes the line of nodes of a disc that starts from a modified tilt mode to wind up within a few dynamical times. We explain this finding in terms of the probable spectrum of true normal modes of a combined disc‐halo system. The key physical point is that in each radial range the halo rapidly aligns with the disc, so calculations based on the assumption that, in the presence of a warped disc, the halo retains a regular spheroidal structure are based on a fatally flawed assumption.

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.

On the Chermnykh-Like Problems: II. The Equilibrium Points

Motivated by Papadakis (2005a, b), 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.

On the Chermnykh-Like Problems: I. the Mass Parameter μ = 0.5

Following Papadakis (2005)s numerical exploration of the Chermnykhs 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.

On the fate of close-in extrasolar planets

It has been shown from the current observational data that there is a possible mass-period correlation for extrasolar planets, and this correlation is, in fact, related to the absence of massive close-in planets, which are strongly influenced by tidal interaction with the central star. We confirm that the model in Patzold & Rauer 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 timescale 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 drag-induced resonant capture for Kuiper Belt objects

It has been an interesting question as to why one-third of Kuiper Belt objects (KBOs) are trapped into the 3 : 2 resonance but, in contrast, only a few KBOs are claimed to be associated with the 2 : 1 resonance. In a model proposed by Zhou et al., 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 protostellar discs on the resonance capture. Our results show that the gaseous drag of a protostellar 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.

DYNAMICAL EFFECTS FROM ASTEROID BELTS FOR PLANETARY SYSTEMS

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.

Data analysis on the extrasolar planets using robust clustering

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.

Data Analysis on the Extra-solar Planets Using Robust Clustering

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.