Chaos in a quartic dynamical model

We study the orbital characteristics of a time independent, two dimensional quartic dynamical model with two exact periodic orbits that displays always closed zero velocity curves. It is shown that the stability of the periodic orbits depends on the value of the coupling parameter . Computer calculations suggest that the degree of stochasticity is small for the values of in the range 1<<3 while it grows rapidly when >3. We also compute the Lyapunov characteristic exponents for different values of the coupling parameter.     

Escape from a Crisis in Fokker-Planck Models

Recent N-body simulations have shown that there is a serious discrepancy between the results of N-body simulations and the results of Fokker-Planck simulations for the evolution of globular and rich open clusters under the influence of the galactic tidal field. In some cases, the lifetime obtained from Fokker-Planck calculations is more than an order of magnitude smaller than those from N-body simulations. In this paper we show that the principal cause for this discrepancy is an over-simplified treatment of the tidal field used in previous Fokker-Planck simulations. We performed new Fokker-Planck calculations using a more appropriate implementation for the boundary condition of the tidal field. The implementation is only possible with anisotropic Fokker-Planck models, while all previous Fokker-Planck calculations rely on the assumption of isotropy. Our new Fokker-Planck results agree well with N-body results. Comparison of the two types of simulations gives a better understanding of the evolution of such clusters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Escape from a gravitational system of positive energy

It is proved in this article that under the condition defined in Equation (6), whent, at least two particles must escape from a Newtonian gravitational system of positive energy.     

A Map for a Group of Resonant Cases in a quartic Galactic Hamiltonian

We present a map for the study of resonant motion in a potential made up of two harmonic oscillators with quartic perturbing terms. This potential can be considered to describe motion in the central parts of non-rotating elliptical galaxies. The map is based on the averaged Hamiltonian. Adding on a semi-empirical basis suitable terms in the unperturbed averaged Hamiltonian, corresponding to the 1:1 resonant case, we are able to construct a map describing motion in several resonant cases. The map is used in order to find thex − p _x Poincare phase plane for each resonance. Comparing the results of the map, with those obtained by numerical integration of the equation of motion, we observe, that the map describes satisfactorily the broad features of orbits in all studied cases for regular motion. There are cases where the map describes satisfactorily the properties of the chaotic orbits as well.     

Escape from planetary neighbourhoods

In this paper we use recently developed phase-space transport theory coupled with a so-called classical spectral theorem to develop a dynamically exact and computationally efficient procedure for studying escape from a planetary neighbourhood. The 'planetary neighbourhood' is a bounded region of phase space where entrance and escape are only possible by entering or exiting narrow 'bottlenecks' created by the influence of a saddle point. The method therefore immediately applies to, for example, the circular restricted three-body problem and Hill's lunar problem (which we use to illustrate the results), but it also applies to more complex, and higher-dimensional, systems possessing the relevant phase-space structure. It is shown how one can efficiently compute the mean passage time through the planetary neighbourhood, the phase-space flux in, and out, of the planetary neighbourhood, the phase-space volume of initial conditions corresponding to trajectories that escape from the planetary neighbourhood, and the fraction of initial conditions in the planetary neighbourhood corresponding to bound trajectories. These quantities are computed for Hill's problem. We study the dependence of the proportions of these quantities on energy and dimensionality (two-dimensional planar and three-dimensional spatial Hill's problem). The methods and quantities presented are of central interest for many celestial and stellar dynamical applications such as, for example, the capture and escape of moons near giant planets, the formation of binaries in the Kuiper belt and the escape of stars from star clusters orbiting about a galaxy.     

Escape of asteroids from the Hecuba gap

The dynamics of the 2/1 mean-motion asteroidal resonance with Jupiter is studied by numerical integration of the equations of motion of the Sun-Jupiter-Saturn-asteroid system. The measurement of the fundamental asteroidal frequencies by means of Fourier and wavelet analyses allows us to construct the web of the secular, secondary and Kozai resonances inside the 2/1-resonance boundaries. The structure of the phase space of the 2/1 resonance is discussed with emphasis on the acting depletion mechanisms due to presence of these inner resonances. Special attention is paid to the study of the middle-eccentricity depleted region. The importance of the great inequality of the Jupiter-Saturn system in the acceleration of the diffusion processes in this region is pointed out. The existence of a group of asteroids like (3789) Zhongguo, inside the 2/1 resonance, is also discussed.     

Comparative case study of two methods to assess the eruptive potential of selected active regions

Solar eruptive events,like flares and coronal mass ejections,are characterized by the rapid release of energy that can give rise to emission of radiation across...     

Escape or retention in the three-body problem

Sufficient conditions for escape and for retention in the three-body problem are derived which, for escape, are more stringent than those previously derived and, for retention, avoid the difficulty of containing the inverse of the mass of the escaping particle.     

Effect of Orbital Distance on the Atmospheric Escape of Exoplanets

Atmospheric escape is an important sector in the evolution of planetary atmosphere, and its energy is mainly originated from the radiation of the host star at the high energy band. The radiation flux drops dramatically with the increase of orbital distance, there is a large difference of planetary atmospheric escape in different orbits, so it is necessary to study the impact of orbital distance on the atmospheric escape of an exoplanet. We consider the radiation transfer and the photochemical reactions of multiple kinds of particles to study the variation of planetary atmospheric escape with the orbital distance by using a 1-D hydrodynamic model. Due to the large differences of the spectra of host stars in different evolution stages, the Astrophysical Plasma Emission Code (APEC) in the X-Ray Spectral Fitting Package (XSPEC) is used to obtain the spectra of solar-type stars with different ages as the input spectra of the model. The results indicate that the escape rates of the exoplanets in different orbits are different significantly, and the escape mechanism is converted from the drastic hydrodynamic escape into the moderate Jeans escape as the orbital distance increases, the smaller the planetary gravitational potential, the younger the star-planet system, the larger the distance of this conversion. The correlation between the escape rate and the radiation flux decreases for the short-period exoplanets in a younger star-planet system. It is shown that the classical energy-limited escape theory is not suitable for this kind of exoplanets. These results have enriched the studies on the atmospheric escape of exoplanets, especially, extended the studies on the escape mechanism and energy conversion under different orbital distances and stellar ages.     

Helicity of solar active regions from a dynamo model

We calculate helicities of solar active regions based on the idea that poloidal flux lines get wrapped around a toroidal flux tube rising through the convection zone, thereby giving rise to the helicity. We use our solar dynamo model based on the Babcock-Leighton α-effect to study how helicity varies with latitude and time.     

Internal motions of HII regions and giant HII regions

We report new echelle observations of the kinematics of 30 HII regions in the LMC, including the 30 Doradus giant HII region. All of the HII regions possess supersonic velocity dispersions, which can be attributed to a combination of turbulent motions and discrete velocity splitting produced by stellar winds and/or embedded supernova remnants (SNRs). The core of 30 Dor is unique, with a complex velocity structure that parallels its chaotic optical morphology. We use our calibrated echelle data to measure the physical properties and energetic requirements of these velocity structures. The most spectacular structures in 30 Dor are several fast expanding shells, which appear to be produced at least partially by SNRs.     

An Estimation of the Galactic Escape Velocity From High-Velocity Metal-Poor Stars

A large number of high-velocity stars was included in the Hipparcos Input Catalogue for the purpose of determining the galactic escape velocity in the solar vicinity. However, the `fastest' stars known, listed by Carney et al. (1994, CLLA) were not included because they are too faint. In the intersection between the CLLA list and the Hipparcos Catalogue (770 common stars), the metal-deficient stars with the most reliable parallaxes (fracσ_ππ)_HIP ≤ 0.15) are used for recalibrating CLLA absolute magnitudes and photometric parallaxes, using metallicities and VandenBerg et al. (1998) isochrones. In this way, about twenty non-Hipparcos stars get improved parallaxes and are added to our primary sample of Hipparcos high-velocity stars, for a better determination of the escape velocity from the Galaxy. This revised version was published online in July 2006 with corrections to the Cover Date.     

类地行星的形成、内部结构与大气逃逸

截止到2014年4月21日,已发现了1490多颗系外行星和3705颗Kepler候选体。这从观测角度证明了行星在银河系中是普遍存在的。对系外行星的研究丰富并加深了人们对行星形成与演化的认识。另外,新的观测与发现也不断提出新的科学问题。本论文开展了类地行星的形成演化、内部结构以及大气逃逸的研究。     

Stability regions in the vicinity of a periodic Ducati orbit

One- and two-dimensional sections of the region of initial conditions in the vicinity of a periodic Ducati orbit have been studied in detail in the plane equal-mass three-body problem. A continuous stability region generated by the periodic Ducati orbit has been revealed. In addition, a number of other stability regions that are probably related to stable hierarchical triple systems have been found. Several specific trajectories from the stability regions and in the boundary zones are analyzed.     

Reversed-polarity regions

We present results of a statistical study of reversed-polarity regions, RPRs, collected over the past 11 years, 1969–1979.The 58 RPRs we studied have a lifespan comparable to normal active regions and have no tendency to rotate toward a more normal alignment. They seem to have stable configurations with no apparent evidence suggesting stress due to their anomalous magnetic alignment. Magnetic complexity in RPRs is the key to flare productivity just as it is in normal regions: Our weak field RPRs produce no flares and regions with complex spots produce more flares than regions with non-complex spots by a factor of 5.The RPRs however, differ from normal regions in the frequency of having complex spots, particularly the long-lived complex spots, in them. Less than 17% of normal ARs have complex spots; less than 1.8% have long-lived complex spots. In contrast, 41% of RPRs have complex spots and 24% have long-lived complex spots.     

Observational appearance of circumstellar ionized regions and ultracompact HII regions

Im Rahmen eines entwickelten theoretischen Modells, das die Dynamik von Protosternhüllen während der Entstehung massereicher Sterne dar-stellt, werden die Hauptentwicklungsstufen von HII-Gebieten bestimmt. Es sollen charakteristische Besonderheiten der Entwicklung von HII-Gebieten um entstehende Sterne mit Leuchtkräften von und besprochen werden.     

Active regions

A summary of data on the occurrence of flares and the development of active regions, based on cinematographic data is given. It is shown that flare frequency is determined by the orientation of the magnetic axis relative to the direction of solar rotation and the morphology of the magnetic field as seen in H. In particular, flares are most numerous in simple round spots with reversed polarity nearby, although they may also be frequent in complex spots with polarity reversal.Important solar active regions are shown to evolve principally along two lines; typically they appear as bright regions with loops and grow rapidly to stable bipolar magnetic form. Important activity will occur as the result of later growth of following polarity ahead of the main spots, or some other source of reversal. However, some groups appear as reversed polarity regions and grow rapidly to a level of extreme activity.A series of papers giving case histories is promised.