Distribution Of Orbital Eccentricities Research Articles

The California Legacy Survey. IV. Lonely, Poor, and Eccentric: A Comparison between Solitary and Neighborly Gas Giants

We compare systems with single giant planets to systems with multiple giant planets using a catalog of planets from a high-precision radial velocity survey of FGKM stars. Our comparison focuses on orbital properties, planet masses, and host-star properties. We use hierarchical methods to model the orbital eccentricity distributions of giant singles and giant multiples, and find that the distributions are distinct. The multiple giant planets typically have moderate eccentricities and their eccentricity distribution extends to e = 0.47 (90th percentile), while the single giant planets have a pileup of nearly circular orbits and a long tail that extends to e = 0.77. We determine that the stellar hosts of multiple giants are distinctly more metal rich than the hosts of solitary giants, with respective mean metallicities of 0.228 ± 0.027 versus 0.129 ± 0.019 dex. We measure the distinct occurrence distributions of single and multiple giants with respect to orbital separation, and find that single gas giants have a ∼2.3σ significant hot Jupiter (a < 0.06) pileup not seen among multigiant systems. We find that the median mass () of giants in multiples is nearly double that of single giants (1.71 M J versus 0.92 M J). We find that giant planets in the same system have correlated masses, analogous to the “peas in a pod” effect seen among less-massive planets.

Orbital eccentricity and inclination distribution of main-belt asteroids—The Statistical model revisited

The distribution and evolution of the Main-belt Asteroid (MBA) orbital eccentricity and inclination provide clues for a deeper understanding of the dynamic evolution of our solar system. This paper presents an analysis of the orbital eccentricity and inclination of 460,000 known MBAs and fits MBA eccentricities and inclinations to a distribution model and further onto a dynamic model. We find that outer-belt MBAs fully fit a Rayleigh distribution; the orbital inclination grouped by the absolute magnitude generally not fully conformed to a Rayleigh distribution. Three evolutionary models of the MBAs were built; Model 1 follows the assumptions of a Rayleigh distribution and Model 2 follows the assumptions of a 2D Cauchy distribution; for the only orbital inclination, a Gaussian distribution was assumed as Model 3. For eccentricity, the distribution mode parameter fits by about 0.074∼0.086 in Model 1 and about 0.03 in Model 2 for the cases grouped by the absolute magnitude, the excitation parameter decreases as the magnitude increases. For the cases grouped by the heliocentric distance, the Model 1 fits the samples better than Model 2; the outer belt also fits Model 1 well, and its fit goodness is about 0.21. For inclination, when the samples were grouped by the absolute magnitude, the distribution mode and excitation parameters were consistent as well. Model 3 overall fits the data better than Models 1 and 2. In summary, the MBA excitation mechanism appears basically consistent with all models when the MBAs were classified by absolute magnitude for both eccentricity and inclination. The cases grouped by absolute magnitude can be fit well in Model 1 for eccentricities and Model 3 for inclinations. When the samples classified by heliocentric distance, the eccentricity and inclination distribution mode was correlated with heliocentric distance, and the influence of excitation was highly related to that distance as well.

The orbital eccentricity distribution of planets orbiting M dwarfs

We investigate the underlying distribution of orbital eccentricities for planets around early-to-mid M dwarf host stars. We employ a sample of 163 planets around early- to mid-M dwarfs across 101 systems detected by NASA's Kepler Mission. We constrain the orbital eccentricity for each planet by leveraging the Kepler lightcurve together with a stellar density prior, constructed using metallicity from spectroscopy, Ks magnitude from 2MASS, and stellar parallax from Gaia. Within a Bayesian hierarchical framework, we extract the underlying eccentricity distribution, assuming alternately Rayleigh, half-Gaussian, and Beta functions for both single- and multi-transit systems. We described the eccentricity distribution for apparently single-transiting planetary systems with a Rayleigh distribution with [Formula: see text], and for multitransit systems with [Formula: see text]. The data suggest the possibility of distinct dynamically warmer and cooler subpopulations within the single-transit distribution: The single-transit data prefer a mixture model composed of two distinct Rayleigh distributions with [Formula: see text] and [Formula: see text] over a single Rayleigh distribution, with 7:1 odds. We contextualize our findings within a planet formation framework, by comparing them to analogous results in the literature for planets orbiting FGK stars. By combining our derived eccentricity distribution with other M dwarf demographic constraints, we estimate the underlying eccentricity distribution for the population of early- to mid-M dwarf planets in the local neighborhood.

The Masses of a Sample of Radial-velocity Exoplanets with Astrometric Measurements

Being one of the most fundamental physical parameter of astronomical objects, mass plays a vital role in the study of exoplanets, including their temperature structure, chemical composition, formation, and evolution. However, nearly a quarter of the known confirmed exoplanets lack measurements of their masses. This is particularly severe for those discovered via the radial velocity (RV) technique, which alone could only yield the minimum mass of planets. In this study, we use published RV data combined with astrometric data from a cross-calibrated Hipparcos-Gaia Catalog of Accelerations to jointly constrain the masses of 115 RV-detected substellar companions, by conducting full orbital fits using the public tool orvara. Among them, 9 exoplanets with are reclassified to the brown dwarf (BD) regime, and 16 BD candidates () turn out to be low-mass M dwarfs. We point out the presence of a transition in the BD regime as seen in the distributions of host star metallicity and orbital eccentricity with respect to planet masses. We confirm the previous findings that companions with masses below 42.5 M Jup might primarily form in the protoplanetary disk through core accretion or disk gravitational instability, while those with masses above 42.5 M Jup formed through the gravitational instability of a molecular cloud like stars. Selection effects and detection biases, which may affect our analysis to some extent, are discussed.

The thermodynamics of stellar multiplicity: an analytic model for the dynamical evolution of binary star populations in dense stellar environments due to single–binary interactions

ABSTRACT We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings. Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker–Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single–binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady-state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.

Comprehensive bayesian modeling of tidal circularization in open cluster binaries part I: M 35, NGC 6819, NGC 188

Abstract Tidal friction has long been recognized to circularize the orbits of binary stars over time. In this study, we use the observed distribution of orbital eccentricities in populations of binary stars to probe tidal dissipation. In contrast to previous studies, we incorporate a host of physical effects often neglected in other analyses, provide a much more general description of tides, model individual systems in detail (in lieu of population statistics), and account for all observational uncertainties. The goal is to provide a reliable measurement of the properties of tidal dissipation that is fully supported by the data, properly accounts for different dissipation affecting each tidal wave on each object separately, and evolves with the internal structure of the stars. We extract high precision measurements of tidal dissipation in short period binaries of Sun-like stars in three open clusters. We find that the tidal quality factor on the main sequence falls in the range $5.7 &amp;lt; \log _{10}Q_\star ^{\prime } &amp;lt; 6$ for tidal periods between 3 and 7.5 days. In contrast, the observed circularization in the 150 Myr old M 35 cluster requires that pre-main sequence stars are much more dissipative: $Q_\star ^{\prime } &amp;lt; 4\times 10^4$. We test for frequency dependence of the tidal dissipation, finding that for tidal periods between 3 and 7.5 days, if a dependence exists, it is sub-linear for main-sequence stars. Furthermore, by using a more complete physical model for the evolution, and by accounting for the particular properties of each system, we alleviate previously observed tensions in the circularization in the open clusters analyzed.

The Unmixed Debris of Gaia-Sausage/Enceladus in the Form of a Pair of Halo Stellar Overdensities

In the first billion years after its formation, the Galaxy underwent several mergers with dwarf satellites of various masses. The debris of Gaia-Sausage/Enceladus (GSE), the galaxy responsible for the last significant merger of the Milky Way, dominates the inner halo and has been suggested to be the progenitor of both the Hercules-Aquila Cloud (HAC) and Virgo Overdensity (VOD). We combine SEGUE, APOGEE, Gaia, and StarHorse distances to characterize the chemodynamical properties and verify the link between HAC, VOD, and GSE. We find that the orbital eccentricity distributions of the stellar overdensities and GSE are comparable. We also find that they have similar, strongly peaked, metallicity distribution functions, reinforcing the hypothesis of common origin. Furthermore, we show that HAC and VOD are indistinguishable from the prototypical GSE population within all chemical-abundance spaces analyzed. All these evidences combined provide a clear demonstration that the GSE merger is the main progenitor of the stellar populations found within these halo overdensities.

The eccentricity distribution of giant planets and their relation to super-Earths in the pebble accretion scenario

Observations of the population of cold Jupiter planets (r &gt;1 AU) show that nearly all of these planets orbit their host star on eccentric orbits. For planets up to a few Jupiter masses, eccentric orbits are thought to be the outcome of planet–planet scattering events taking place after gas dispersal. We simulated the growth of planets via pebble and gas accretion as well as the migration of multiple planetary embryos in their gas disc. We then followed the long-term dynamical evolution of our formed planetary system up to 100 Myr after gas disc dispersal. We investigated the importance of the initial number of protoplanetary embryos and different damping rates of eccentricity and inclination during the gas phase for the final configuration of our planetary systems. We constrained our model by comparing the final dynamical structure of our simulated planetary systems to that of observed exoplanet systems. Our results show that the initial number of planetary embryos has only a minor impact on the final orbital eccentricity distribution of the giant planets, as long as the damping of eccentricity and inclination is efficient. If the damping is inefficient (slow), systems with a larger initial number of embryos harbour larger average eccentricities. In addition, for slow damping rates, we observe that scattering events are already common during the gas disc phase and that the giant planets that formed in these simulations match the observed giant planet eccentricity distribution best. These simulations also show that massive giant planets (above Jupiter mass) on eccentric orbits are less likely to host inner super-Earths as they get lost during the scattering phase, while systems with less massive giant planets on nearly circular orbits should harbour systems of inner super-Earths. Finally, our simulations predict that giant planets are not single, on average, but they live in multi-planet systems.

Unbiased Distribution of Binary Parameters from LAMOST and Kepler Observations

Abstract The parameter distribution of binaries is a fundamental knowledge of the stellar systems. A statistical study on the binary stars is carried out based on the LAMOST spectral and Kepler photometric database. We presented a catalog of 1320 binary stars with plentiful parameters, including period, binary subtype, atmosphere parameters (T eff, [Fe/H], and ), and the physical properties, such as mass, radius, and age, for the primary component stars. Based on this catalog, the unbiased distribution, rather than the observed distribution, was obtained after the correction of selection biases by the Monte Carlo method considering comprehensive affecting factors. For the first time, the orbital eccentricity distribution of the detached binaries is presented. The distribution differences between the three subtypes of binaries (detached, semidetached, and contact) are demonstrated, which can be explained by the generally accepted evolutional scenarios. Many characteristics of the binary stars, such as huge mass transfer on semidetached binaries, period cutoff on contact binaries, period–temperature relationship of contact binaries, and the evolved binaries, are reviewed by the new database. This work supports a common evolutionary scenario for all subtypes of binary stars.

Constraining planetary migration and tidal dissipation with coeval hot Jupiters

We investigate the constraints on the formation of, and tidal dissipation processes in, hot Jupiters (HJs) that can be inferred based on reliable knowledge of the age of a system or population. Particular attention is paid to the role of young systems (such as those in open clusters or star-forming regions) in such studies. For an ensemble of coeval HJ (or proto-HJ) systems, we quantify the effect of age on the distribution of orbital eccentricities with respect to orbital periods as well as the location of the observed "pile-up" feature. We expect the effects of pre-main-sequence stellar evolution to be important only if a substantial fraction of HJs approach their current orbits early in protostellar contraction (ages less than 10 Myr). Application to the HJs presently known in the cluster M67 yields constraints on the dissipation roughly consistent with those gleaned from planets in the field; for those in the Hyades and Praesepe, our results suggest a higher degree of dissipation at early times than that inferred from other populations.

Chemo-Kinematic Properties of the Galactic Disk with SEGUE G and K Dwarfs: Constraints on Formation

AbstractWe present the derived kinematic characteristics of low-α thin-disk and high-α thick-disk stars in the Milky Way, investigated with a sample of about 32,000 G- and K-type dwarfs from the Sloan Extension for Galactic Understanding and Exploration (SEGUE). Based on the level of α-element enhancement as a function of [Fe/H], we separate our sample into thin- and thick-disk stars and then derive mean velocities, velocity dispersions, and velocity gradients for the U, V, and W velocity components, respectively, as well as the orbital eccentricity distribution. There are notable gradients in the V velocity over [Fe/H] in both populations: −23 km s−1 dex−1 for the thin disk and +44 km s−1 dex−1 for the thick disk. The velocity dispersion of the thick disk decreases with increasing [Fe/H], while the velocity dispersion gradient over [Fe/H] for the thin disk is almost flat for all velocity components, except for the W velocity dispersion of the metal-poor thin-disk stars. The eccentricity distribution exhibits a peak at a higher value, and is more symmetric as [α/Fe] increases, implying that complex formation mechanisms may be involved. Our results can be used to constrain several proposed disk-formation scenarios of the Milky Way and other large spirals.

On the fragmentation boundary in magnetized self-gravitating discs

We investigate the role of magnetic fields in the fragmentation of self-gravitating discs using 3D global ideal magnetohydrodynamic simulations performed with the "phantom" smoothed particle hydrodynamics code. For initially toroidal fields, we find two regimes. In the first, where the cooling time is greater than five times the dynamical time, magnetic fields reduce spiral density wave amplitudes, which in turn suppresses fragmentation. This is the case even if the magnetic pressure is only a tenth of the thermal pressure. The second regime occurs when the cooling time is sufficiently short that magnetic fields cannot halt fragmentation. We find that magnetised discs produce more massive fragments, due to both the additional pressure exerted by the magnetic field, and the additional angular momentum transport induced by Maxwell stresses. The fragments are confined to a narrower range of initial semimajor axes than those in unmagnetised discs. The orbital eccentricity and inclination distributions of unmagnetised and magnetised disc fragments are similar. Our results suggest the fragmentation boundary could be at cooling times a factor of two lower than predicted by purely hydrodynamical models.

Radial velocities of K–M dwarfs and local stellar kinematics

Aims. The goal of this paper is to present complete radial-velocity data for the spectroscopically selected McCormick sample of nearby K–M dwarfs and, based on these and supplementary data, to determine the space-velocity distributions of late-type stars in the solar neighborhood.Methods. We analyzed nearly 3300 measurements of radial velocities for 1049 K–M dwarfs, that we obtained during the past decade with a CORAVEL-type instrument, with a primary emphasis on detecting and eliminating from kinematic calculations the spectroscopic binaries and binary candidates. Combining radial-velocity data with Hipparcos/Tycho-2 astrometry we calculated the space-velocity components and parameters of the galactic orbits in a three-component model potential for the stars in the sample, that we use for kinematical analysis and for the identification of possible candidate members of nearby stellar kinematic groups.Results. We present the catalog of our observations of radial velocities for 959 stars which are not suspected of velocity variability, along with the catalog of U,V,W velocities and Galactic orbital parameters for a total of 1088 K–M stars which are used in the present kinematic analysis. Of these, 146 stars were identified as possible candidate members of the known nearby kinematic groups and suspected subgroups. The distributions of space-velocity components, orbital eccentricities, and maximum distances from the Galactic plane are consistent with the presence of young, intermediate-age and old populations of the thin disk and a small fraction (~3%) of stars with the thick disk kinematics. The kinematic structure gives evidence that the bulk of K–M type stars in the immediate solar vicinity represents a dynamically relaxed stellar population. The star MCC 869 is found to be on a retrograde Galactic orbit (V = −262 km s-1 ) of low inclination (4°) and can be a member of stellar stream of some dissolved structure. The Sun’s velocity with respect to the Local Standard of Rest, derived from the distributions of space-velocity components, is (U ⊙ ,V ⊙ ,W ⊙ ) = (9.0 ± 1.4,13.1 ± 0.6,7.2 ± 0.8) km s-1 . The radial solar motion derived via the Stromberg’s relation, V ⊙ = 14.2 ± 0.8 km s-1 , agrees within the errors with the value obtained directly from the V distribution of stars on nearly circular orbits.

Kinematics of the Galactic disc from a LAMOST dwarf sample

Based on the LAMOST survey and Sloan Digital Sky Survey (SDSS), we use low-resolution spectra of 130,043 F/G-type dwarf stars to study the kinematics and metallicity properties of the Galactic disk. Our study shows that the stars with poorer metallicity and larger vertical distance from Galactic plane tend to have larger eccentricity and velocity dispersion. After separating the sample stars into likely thin-disk and thick-disk sub-sample, we find that there exits a negative gradient of rotation velocity $V_{\phi}$ with metallicity [Fe/H] for the likely thin-disk sub-sample, and the thick-disk sub-sample exhibit a larger positive gradient of rotation velocity with metallicity. By comparing with model prediction, we consider the radial migration of stars appears to have influenced on the thin-disk formation. In addition, our results shows that the observed thick-disk stellar orbital eccentricity distribution peaks at low eccentricity ($e \sim 0.2$) and extends to a high eccentricity ($e \sim 0.8$). We compare this result with four thick-disk formation simulated models, and it imply that our result is consistent with gas-rich merger model.

Properties of thick discs formed in clumpy galaxies

We examine a possible formation scenario of galactic thick discs with numerical simulations. Thick discs have previously been argued to form in clumpy disc phase in the high-redshift Universe, which host giant clumps of <10^9 M_sun in their highly gas-rich discs. We performed SPH simulations using isolated galaxy models for the purpose of verifying whether dynamical and chemical properties of the thick discs formed in such clumpy galaxies are compatible with observations. The results of our simulations seem nearly consistent with observations in dynamical properties such as radial and vertical density profiles, significant rotation velocity lag with height and distributions of orbital eccentricities. In addition, the thick discs in our simulations indicate nearly exponential dependence of azimuthal and vertical velocity dispersions with radius, nearly isothermal kinematics in vertical direction and negligible metallicity gradients in radial and vertical directions. However, our simulations cannot reproduce altitudinal dependence of eccentricities, metallicity relations with eccentricities or rotation velocities, which shows striking discrepancy from recent observations of the Galactic thick disc. From this result, we infer that the clumpy disc scenario for thick-disc formation would not be suitable at least for the Milky Way. Our study, however, cannot reject this scenario for external galaxies if not all galaxies form their thick discs by the same process. In addition, we found that a large fraction of thick-disc stars forms in giant clumps.

BLACK HOLES IN YOUNG STELLAR CLUSTERS

We present theoretical models for stellar black hole (BH) properties in young, massive star clusters. Using a Monte Carlo code for stellar dynamics, we model realistic star clusters with $N\simeq 5\times10^5$ stars and significant binary fractions (up to 50%) with self-consistent treatments of stellar dynamics and stellar evolution. We compute the formation rates and characteristic properties of single and binary BHs for various representative ages, cluster parameters, and metallicities. Because of dynamical interactions and supernova (SN) kicks, more single BHs end up retained in clusters compared to BHs in binaries. We also find that the ejection of BHs from a cluster is a strong function of initial density. In low-density clusters (where dynamical effects are negligible), it is mainly SN kicks that eject BHs from the cluster, whereas in high-density clusters (initial central density $\rho_c(0) \sim 10^5 \, M_\odot\, {\rm pc}^{-3} $ in our models) the BH ejection rate is enhanced significantly by dynamics. Dynamical interactions of binary systems in dense clusters also modify the orbital period and eccentricity distributions while also increasing the probability of a BH having a more massive companion.

Parametrizing the exoplanet eccentricity distribution with the Beta distribution

Abstract It is suggested that the distribution of orbital eccentricities for extrasolar planets is well described by the Beta distribution. Several properties of the Beta distribution make it a powerful tool for this purpose. For example, the Beta distribution can reproduce a diverse range of probability density functions (PDFs) using just two shape parameters (a and b). We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis. The Beta distribution is also uniquely defined over the interval zero to unity, meaning that it can serve as a proper prior for eccentricity when analysing the observations of bound extrasolar planets. Using nested sampling, we find that the distribution of eccentricities for 396 exoplanets detected through radial velocity with high signal-to-noise is well described by a Beta distribution with parameters a = 0.867${^{+ 0.044}_{- 0.044}}$ and b = 3.03${^{+ 0.17}_{- 0.16}}$. The Beta distribution is shown to be 3.7 times more likely to represent the underlying distribution of exoplanet eccentricities than the next best model: a Rayleigh + exponential distribution. The same data are also used in an example population comparison utilizing the Beta distribution, where we find that the short- and long-period planets are described by distinct Beta distributions at a confidence of 11.6σ and display a signature consistent with the effects of tidal circularization.

ACCRETION RATES OF MOONLETS EMBEDDED IN CIRCUMPLANETARY PARTICLE DISKS

We examine the gravitational capture probability of colliding particles in circumplanetary particle disks and accretion rates of small particles onto an embedded moonlet, using analytic calculation, three-body orbital integrations, and N-body simulations. Expanding our previous work, we take into account the Rayleigh distribution of particles' orbital eccentricities and inclinations in our analytic calculation and orbital integration and confirm agreement between them when the particle velocity dispersion is comparable to or larger than their mutual escape velocity and the ratio of the sum of the physical radii of colliding particles to their mutual Hill radius () is much smaller than unity. As shown by our previous work, the capture probability decreases significantly when the velocity dispersion is larger than the escape velocity and/or . Rough surfaces of particles can enhance the capture probability. We compare the results of three-body calculations with N-body simulations for accretion of small particles by an embedded moonlet and find agreement at the initial stage of accretion. However, when particles forming an aggregate on the moonlet surface nearly fill the Hill sphere, the aggregate reaches a quasi-steady state with a nearly constant number of particles covering the moonlet, and the accretion rate is significantly reduced compared to the three-body results.

The orbital eccentricity distribution of solar-neighbourhood halo stars

We present theoretical calculations for the differential distribution of stellar orbital eccentricity for a sample of solar-neighbour halo stars. Two types of static, spherical gravitational potentials are adopted to define the eccentricity e for given energy E and angular momentum L, such as an isochrone potential and a Navarro-Frenk-White potential that can serve as two extreme ends covering in-between any realistic potential of the Milky Way halo. The solar-neighbour eccentricity distribution \Delta N(e) is then formulated, based on a static distribution function of the form f(E,L) in which the velocity anisotropy parameter \beta monotonically increases in the radial direction away from the galaxy center, such that beta is below unity (near isotropic velocity dispersion) in the central region and asymptotically approaches \sim 1 (radially anisotropic velocity dispersion) in the far distant region of the halo. We find that \Delta N(e) sensitively depends upon the radial profile of \beta, and this sensitivity is used to constrain such profile in comparison with some observational properties of \Delta N_{obs}(e) recently reported by Carollo et al. (2010). Especially, the linear e-distribution and the fraction of higher-e stars for their sample of solar-neighbour inner-halo stars rule out a constant profile of \beta, contrary to the opposite claim by Bond et al. (2010). Our constraint of \beta \lesssim 0.5 at the galaxy center indicates that the violent relaxation that has acted on the inner halo is effective within a scale radius of \sim 10 kpc from the galaxy center. We discuss that our result would help understand the formation and evolution of the Milky Way halo.

ORIGIN OF CHEMICAL AND DYNAMICAL PROPERTIES OF THE GALACTIC THICK DISK

We adopt a scenario in which the Galactic thick disk was formed by minor merging between the first generation of the Galactic thin disk (FGTD) and a dwarf galaxy about 9 Gyr ago and thereby investigate chemical and dynamical properties of the Galactic thick disk. In this scenario, the dynamical properties of the thick disk have long been influenced both by the mass growth of the second generation of the Galactic thin disk (i.e., the present thin disk) and by its non-axisymmetric structures. On the other hand, the early star formation history and chemical evolution of the thin disk was influenced by the remaining gas of the thick disk. Based on N-body simulations and chemical evolution models, we investigate the radial metallicity gradient, structural and kinematical properties, and detailed chemical abundance patterns of the thick disk. Our numerical simulations show that the ancient minor merger event can significantly flatten the original radial metallicity gradient of the FGTD, in particular, in the outer part, and also can be responsible for migration of inner metal-rich stars into the outer part (R>10kpc). The simulations show that the central region of the thick disk can develop a bar due to dynamical effects of a separate bar in the thin disk. The simulated orbital eccentricity distributions in the thick disk for models with higher mass-ratios (~0.2) and lower orbital eccentricities (~ 0.5) of minor mergers are in good agreement with the corresponding observations. The simulated V_{phi}-|z| relation of the thick disk in models with low orbital inclination angles of mergers are also in good agreement with the latest observational results. Our Galactic chemical evolution models can explain both the observed metallicity distribution functions (MDFs) and correlations between [Mg/Fe] and [Fe/H] for the two disks in a self-consistent manner.