Stability in the Full Two-Body Problem

Stability conditions are established in the problem of two gravitationally interacting rigid bodies, designated here as the full two-body problem. The stability conditions are derived using basic principles from the N-body problem which can be carried over to the full two-body problem. Sufficient conditions for Hill stability and instability, and for stability against impact are derived. The analysis is applicable to binary small-body systems such as have been found recently for asteroids and Kuiper belt objects.     

数据挖掘中关联规则的探讨

介绍了数据挖掘中关联规则的概念及经典的Apriori算法,以及在Apriori算法基础上的改进算法和数据挖掘的应用领域.     

Evolution of massive binary stars in the LMC and its implications for radio pulsar population

The Hertzsprung-Russell diagram of the Large Magellanic Cloud compiled recently by Fitzpatrick & Garmany (1990) shows that there are a number of supergiant stars immediately redward of the main sequence although theoretical models of massive stars with normal hydrogen abundance predict that the region 4.5 ≤ logT _eff ≤ 4.3 should be un-populated (“gap”). Supergiants having surface enrichment of helium acquired for example from a previous phase of accretion from a binary companion, however, evolve in a way so that the evolved models and observed data are consistent — an observation first made by Tuchman & Wheeler (1990). We compare the available optical data on OB supergiants with computed evolutionary tracks of massive stars of metallicity relevant to the LMC with and without helium-enriched envelopes and conclude that a large fraction (≈ 60 per cent) of supergiant stars may occur in binaries. As these less evolved binaries will later evolve into massive X-ray binaries, the observed number and orbital period distribution of the latter can constrain the evolutionary scenarios of the supergiant binaries. The distributions of post main sequence binaries and closely related systems like WR + O stars are bimodal-consisting of close and wide binaries in which the latter type is numerically dominating. When the primary star explodes as a supernova leaving behind a neutron star, the system receives a kick and in some cases can lead to runaway O-stars. We calculate the expected space velocity distribution for these systems. After the second supernova explosion, the binaries in most cases, will be disrupted leading to two runaway neutron stars. In between the two explosions, the first born neutron star’s spin evolution will be affected by accretion of mass from the companion star. We determine the steady-state spin and radio luminosity distributions of single pulsars born from the massive stars under some simple assumptions. Due to their great distance, only the brightest radio pulsars may be detected in a flux-limited survey of the LMC. A small but significant number of observable single radio pulsars arising out of the disrupted massive binaries may appear in the short spin period range. Most pulsars will have a low velocity of ejection and therefore may cluster around the OB associations in the LMC.     

Period changes and photometric solution of AP Leonis

The results of BV photometry of AP Leonis are presented. Photometric analysis is carried out by using the Wilson-Devinney program. The solution shows that the system is an over-contact binary with an over-contact degree of 23.5% and its mass ratio q equal to 0.301. A starspot group is found in the low latitude region on the secondary component. The average temperature of the spot is about 1220 K lower than that of surrounding photosphere.

The light minimum times observed over ninety years are collected. The O-C curve of minima reveals that the period of AP Leo changes with the time in a pseudo-sinusoidal pattern and there is probably a third body in the system.     

The chromospherically active solar-type spectroscopic binary HD 191262

HD 191262 is a double-lined spectroscopic binary consisting of two slightly unequal solar-type stars in an orbit’ with a period of 5.43435 days. The system is both synchronized and circularized and is probably at least as old as the Sun. The inclination of the system is about 45°     

Photometric elements,apsidal motion,and a third body in the eclipsing binary HP Aur

Highly accurate W BV R photometric measurements of the eclipsing binary HP Aur were performed in 2002–2003 with the 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Observatory to determine the rate of apsidal motion. A consistent system of physical and geometrical parameters of the components and the binary as a whole has been constructed for the first time by analyzing these new measurements together with other published data: we determined their radii (R₁ = 1.05R_⊙, R₂ = 0.82R_⊙) and luminosities (L₁ = 1.10L_⊙, L₂ = 0.46L_⊙), spectral types (G2V + G8V) and surface gravities (log g₁ = 4.38, log g₂ = 4.51), age (t = 9.5 × 10⁹ yr), and the distance to the binary (d = 197 pc). We detected an ultraviolet excess in the spectra of both components, \(\Delta (W - B) \simeq - 0\mathop .\limits^m 25\), that is probably attributable to a metal deficiency in the atmospheres of these stars. In this system of two solar-type stars, we found a third body with the mass M₃ sin i ₃ ³ = 0.17_M⊙ that revolved with the period P₃ = 13.7 yr around the eclipsing binary in a highly eccentric elliptical orbit: e₃ = 0.70 and A₃ sin i₃ ? 7 AU. The orbit of the eclipsing binary itself was shown to be also elliptical, but with a low eccentricity (e = 0.0025(5)), while apsidal motion with a period U_obs > 80 yr was observed at a theoretically expected period U_th ≈ 92 yr. At least 20 to 30 more years of photoelectric measurements of this star will be required to reliably determine U_obs.     

Orbit of an Astrometric Binary System

We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based on the material available for an observer, for example relative positions at a given time of the couple in the “plane of sky”, namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one hand, the geometric problem is solved using the first Kepler’s law from a single observing run and, on the other hand, dynamical parameters are then inferred from the fit of the Kepler’s equation. At last, the final stage consists in determining the main physical parameters involved in the secular evolution of the system, that is the spin axis and the J₂ parameter of the primary if we assume that it is a quasi-spherical body. As a matter of fact there is no need to make too restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by a non-linear least-squares Levenberg–Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto–Charon system parameters from observations collected in the literature since 1980.     

Wide Binaries from Few-Body Interactions

The orbital properties of wide binaries are modified by stellar encounters during their lifetimes as field stars. The few body process is particularly efficient right after the star formation in star clusters. In this article we review the orbital parameters which we expect from the few-body process. First, the solutions of the General Three-Body Problem are described, and then a detailed discussion of the theory relevant to binaries follows. Among other things, Öpik's law of the distribution of semi- major axes of the binaries is derived. In addition, we summarize recent results from the few-body problem of extended bodies which may be relevant to the early dynamical evolution of protostellar clouds.     

The orbit of the double-line spectroscopic binary system HR 7112

We present velocity observations, obtained with the E. W. Fick Observatory 0.6 m telescope, of the 7th magnitudeK1 star HR 7112. Our observations show that HR 7112 is a double-line spectroscopic binary system composed of almost equal mass stars with a period of 215.6 days. The orbit has an eccentricitye = 0.142 and the stars orbit each other with a mean semi-major axis distance of approximately 0.4sin(i) AU. The masses of the stars are consistent with the classification as giant stars. Tidal effects are known to circularise the orbits of giant stars and this process is apparently underway in this system.     

密近双星自转的测量和研究（Ⅱ）──自转同步性的计算

本文继续研究文（Ⅰ）中的密近双星系统。文中收集了不同作者给出的、或由此而推出的各子星的基本物理参量，加权平均后作为计算自转参数和统计工作的依据，计算了同步自转速度（Ｖｓｉｎｉ）ｓｙｎ，对于非圆形轨道在近星点时的即时同步自转速度Ｖ_ｅ，以及反映自转同步性的参量（Ｆ－１）．统计分析表明，绝大多数系统的自转接近同步，但对分离系统，（Ｆ－１）分布范围很宽。