On the Formation of Elliptical Rings in Disk Galaxies

N-body simulations of galactic collisions are employed to investigate the formation of elliptical rings in disk galaxies. The relative inclination between disk and dwarf galaxies is studied with a fine step of five degrees. It is confirmed that the eccentricity of elliptical ring is linearly proportional to the inclination angle. Deriving from the simulational results, an analytic formula which expresses the eccentricity as a function of time and inclination angle is obtained. This formula shall be useful for the interpretations of the observations of ring systems, and therefore reveals the merging histories of galaxies.

The Period-Ratio and Mass-Ratio Correlation in Extra-Solar Multiple Planetary Systems

Employing the data from orbital periods and masses of extra-solar planets in 166 multiple planetary systems, the period-ratio and mass-ratio of adjacent planet pairs are studied. The correlation between the period-ratio and mass-ratio is confirmed and found to have a correlation coefficient of 0.5303 with a 99% confidence interval (0.3807, 0.6528). A comparison with the distribution of synthetic samples from a Monte Carlo simulation reveals the imprint of planet-planet interactions on the formation of adjacent planet pairs in multiple planetary systems.

Galaxies with Supermassive Binary Black Holes: (I) A Possible Model for the Centers of Core Galaxies

The dynamics of galactic systems with central binary black holes is studied. The model is a modification from the restricted three body problem, in which a galactic potential is added as an external potential. Considering the case with an equal mass binary black holes, the conditions of existence of equilibrium points, including Lagrange Points and additional new equilibrium points, i.e. Jiang-Yeh Points, are investigated. A critical mass is discovered to be fundamentally important. That is, Jiang-Yeh Points exist if and only if the galactic mass is larger than the critical mass. The stability analysis is performed for all equilibrium points. The results that Jiang-Yeh Points are unstable could lead to the core formation in the centers of galaxies.

On the Fundamental Mass-Period Functions of Extrasolar Planets

Employing a catalog of 175 extrasolar planets (exoplanets) detected by the Doppler-shift method, we constructed the independent and coupled mass-period functions. It is the first time in this field that the selection effect is considered in the coupled mass-period functions. Our results are consistent with those in Tabachnik and Tremaine (2002) with the major differences that we obtain a flatter mass function but a steeper period function. Moreover, our coupled mass-period functions show that about 2.5 percent of stars would have a planet with mass between Earth Mass and Neptune Mass, and about 3 percent of stars would have a planet with mass between Neptune Mass and Jupiter Mass.

The Galactic Mergers and Gravitational Unbound Populations

Motivated by the observations on the intra-cluster light (ICL) and inter-galactic stellar populations, n-body simulations are used to model the galactic merging events as a goal to investigate the production and distribution of gravitational unbound populations (GUPs). Both the parabolic and hyperbolic mergers are considered and each category includes six models with different relative orientations between two galaxies. Our results show that there are more (about a factor of two) GUP after a hyperbolic merging event than after a parabolic one. In general, depending on the relative orientation and also the relative velocity of the two galaxies in a merging pair, a head-on collision of a galaxy pair would only make a tiny fraction (less than one percent) of the initial stellar mass become luminous GUP but a considerable fraction (eight to fourteen percent) of the dark matter become dark GUP.

On the Vega Debris Discs Dust Grains: Short-Lived or Long-Lived ?

Through Spitzer Space Telescopes observations, Su et al. (2005) show that the Vega debris disc is dominated by grains which are small enough to be blown out by radiation pressure. This implies the lifetime of Vega debris discs grains is relatively short, about 1000 years, and a continuous dust production is necessary to maintain the observed debris disc. However, Krivov et al. (2006)s theoretical calculations show that the Vega debris disc is dominated by 10 micro-meter grains, which would be in bound orbits and thus long-lived, provided that the disc is in a steady state. In order to solve the above contradiction, through dynamical simulations, we determine the grains orbital evolutions and density profiles and seek a model of size distribution which can reproduce the observed surface brightness. Our results show that a self-consistent dynamical model with a 1/R disc density profile can be constructed when the grains have a power-law size distribution. Moreover, both types of models, dominated by short-lived and long-lived grains, are consistent with the observational data.

On Grain Dynamics in Debris Discs: Continuous Outward Flows and Embedded Planets

This study employed grain dynamic models to examine the density distribution of debris discs, and discussed the effects of the collisional time-intervals of asteroidal bodies, the maximum grain sizes, and the chemical compositions of the dust grains of the models, in order to find out whether a steady out-moving flow with an 1/R profile could be formed. The results showed that a model with new grains every 100 years, a smaller maximum grain size, and a composition C400 has the best fit to the 1/R profile because: (1) the grains have larger values of beta on average,therefore, they can be blown out easily; (2) the new grains are generated frequently enough to replace those have been blown out. With the above two conditions, some other models can have a steady out-moving flow with an approximate 1/R profile. However, those models in which new grains are generated every 1000 years have density distributions far from the profile of a continuous out-moving flow. Moreover, the analysis on the signatures of planets in debris discs showed that there are no indications when a planet is in a continuous out-moving flow, however, the signatures are obvious in a debris disc with long-lived grains.

Construction of Coupled Period-Mass Functions in Extrasolar Planets through the Nonparametric Approach

Using the period and mass data of two hundred and seventy-nine extrasolar planets, we have constructed a coupled period-mass function through the non-parametric approach. This analytic expression of the coupled period-mass function has been obtained for the first time in this field. Moreover, due to a moderate period-mass correlation, the shapes of mass/period functions vary as a function of period/mass. These results of mass and period functions give way to two important implications: (1) the deficit of massive close-in planets is confirmed, and (2) the more massive planets have larger ranges of possible semi-major axes. These interesting statistical results will provide important clues into the theories of planetary formation.

Self-consistent triaxial de Zeeuw-Carollo Models

We use the usual method of Schwarzschild to construct self-consistent solutions for the triaxial de Zeeuw & Carollo (1996) models with central density cusps. ZC96 models are triaxial generalisations of spherical $gamma$-models of Dehnen whose densities vary as $r^{-gamma}$ near the center and $r^{-4}$ at large radii and hence, possess a central density core for $gamma=0$ and cusps for $gamma > 0$. We consider four triaxial models from ZC96, two prolate triaxials: $(p, q) = (0.65, 0.60)$ with $gamma = 1.0$ and 1.5, and two oblate triaxials: $(p, q) = (0.95, 0.60)$ with $gamma = 1.0$ and 1.5. We compute 4500 orbits in each model for time periods of $10^{5} T_{D}$. We find that a large fraction of the orbits in each model are stochastic by means of their nonzero Liapunov exponents. The stochastic orbits in each model can sustain regular shapes for $sim 10^{3} T_{D}$ or longer, which suggests that they diffuse slowly through their allowed phase-space. Except for the oblate triaxial models with $gamma =1.0$, our attempts to construct self-consistent solutions employing only the regular orbits fail for the remaining three models. However, the self-consistent solutions are found to exist for all models when the stochastic and regular orbits are treated in the same way because the mixing-time, $sim10^{4} T_{D}$, is shorter than the integration time, $10^{5} T_{D}$. Moreover, the ``fully-mixed solutions can also be constructed for all models when the stochastic orbits are fully mixed at 15 lowest energy shells. Thus, we conclude that the self-consistent solutions exist for our selected prolate and oblate triaxial models with $gamma = 1.0$ and 1.5.

On the Mass-Period Distributions and Correlations of Extrasolar Planets

In addition to fitting the data of 233 extra-solar planets with power laws, we construct a correlated mass-period distribution function of extrasolar planets, as the first time in this field. The algorithm to generate a pair of positively correlated beta-distributed random variables is introduced and used for the construction of correlated distribution functions. We investigate the mass-period correlations of extrasolar planets both in the linear and logarithm spaces, determine the confidence intervals of the correlation coefficients, and confirm that there is a positive mass-period correlation for the extrasolar planets. In addition to the paucity of massive close-in planets, which makes the main contribution on this correlation, there are other fine structures for the data in the mass-period plane.