Numerical simulations of collisions in self-gravitating systems

The influence of partially elastic collisions, gravitational encounters, and different gravitational potentials is studied in terms of computer simulations involving a ring of 200 identical particles. If the masses of the particles are small, their mutual gravitational attraction is found to produce a decrease in the dispersion of velocities below the collisional equilibrium value, but for heavier particles the dispersion again begins to increase. The vertical component of the force which is produced by the self-gravitation of the ring reduces its thickness. The results of the simulations are in good agreement with the predictions of the collisional theory.     

Fast computation of satellite gravitational gradient

The computation of the Earth's potential function at high order and degree with the method of reference [1], causes overflow most of the time. The normalized method [2–6] can eliminate the overflows, but leads to formulae much more involved than those in reference [1]; besides, the programming is more complex and the computer time required larger. The method presented in this paper has the following features: each component of the satellite gravitational gradient can be computed; the formulae are short and easy to be programme; the method is much quicker than the normalization method and can be carried out with a micro‐computer, without overflow even in the case of Earth's spherical harmonics of order and degree as high as 1025 or higher. This method satisfies the present demand to compute satellite gravitational gradient with high accuracy. Furthermore, we present formulae for the fast computation, without overflow, of the gravitational gradient corresponding to Earth's spherical harmonics up to order and degree of 3170 × 3170 or higher. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scope for a small circumsolar annular gravitational contribution to the Pioneer anomaly without affecting planetary orbits

All proposed gravitational explanations of the Pioneer anomaly must crucially face the Equivalence Principle. Thus, if Pioneers 10 and 11 were influenced by anomalous gravitational effects in regions containing other Solar System bodies, then those bodies should likewise be influenced, irrespective of their shape, composition or mass. Although the lack of any observed influence upon planetary orbits severely constrains such explanations, here we aim to construct by computer modeling, hypothetical gravitating annuli having no gravitational impact on planetary orbits from Mercury to Neptune. One model has a central zone, free of radial gravitation in the annular plane, and an ‘onset’ beyond Saturn’s orbit, where sunward annular gravitation increases to match the Pioneer anomaly data. Sharp nulls are included so that Uranus and Neptune escape this influence. Such models can be proportionately reduced in mass: a 1 % contribution to the anomaly requires an annulus of approximately 1 Earth mass. It is thus possible to comply with the JPL assessment of newly recovered data attributing 80 %, or more, of the anomaly to spacecraft heat, which appears to allow small contributions from other causes. Following the possibility of an increasing Kuiper belt density at great ranges, another model makes an outward small anomalous gravitation in the TNO region, tallying with an observed slight indication of such an effect, suggesting that New Horizons may slightly accelerate in this region.     

Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids

Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.     

Dynamics of plance stellar systems

The evolution of initially balanced rotating disks of stars is investigated with a computer model for isolated disks of stars. An isolated, initially cold balanced disk is found to be violently unstable. Adding a sufficient amount of velocity dispersion will stabilize all small-scale disturbances. However, the disks are still unstable against slowly growing long wave-length modes and after about two rotations most disks tend to assume a bar-shaped structure. It is found that the final mass distribution over most of the disk can be closely approximated by an exponential variation, irrespective of the initial mass distribution. The gravitational two-stream instability is investigated by means of a modified computer model for infinite doubly periodic stellar systems.     

Possible conditions for formation of satellite from protoearth by ejection of material

Conditions for the formation of a large gaseous protoearth and the formation of a satellite are considered. The energy required is assumed to come from the gravitational contraction to form the Sun, the gravitational contraction to form the protoearth, core overturn and planetesimal impacts on the protoearth. The model is compatible with geochemical, tidal and angular momentum data.     

Proposed searches for candidate sources of gravitational waves in a nearby core-collapse supernova survey

Gravitational wave bursts in the formation of neutron stars and black holes in energetic core-collapse supernovae (CC-SNe) are of potential interest to LIGO-Virgo and KAGRA. Events nearby are readily discovered using moderately sized telescopes. CC-SNe are competitive with mergers of neutron stars and black holes, if the fraction producing an energetic output in gravitational waves exceeds about 1%. This opportunity motivates the design of a novel Sejong University Core-CollapsE Supernova Survey (SUCCESS), to provide triggers for follow-up searches for gravitational waves. It is based on the 76 cm Sejong university telescope (SUT) for weekly monitoring of nearby star-forming galaxies, i.e., M51, M81-M82 and blue dwarf galaxies from the unified nearby galaxy catalog with an expected yield of a few hundred per year. Optical light curves will be resolved for the true time-of-onset for probes of gravitational waves by broadband time-sliced matched filtering.     

Note concerning gravitation and electromagnetism

The Maxwell equations for gravitational fields previously assumed by Sciama are derived from elementary considerations. The Lagrangian for a gravitating mass in a non-inertial coordinate system yields equations of motion leading to force definitions for a gravitational field intensity and a gravitational induction field. The non-inertial velocity of the coordinate system plays the role of a vector potential contributing to the generalized momenta of bodies moving in the system. A Lagrangian density constructed from the force-defined fields then lead to the source definitions of gravitational fields. It is found that positive field energy densities require repulsive gravitational forces, whereas attractive forces imply the violation of the conservation of energy. This paradox is resolved by representing gravitational quantities as pure-imaginary entities. Thus characterized, the equations which define gravitational fields become identical to Maxwell's equations but are pure-imaginary. This suggests a combined representation for gravitational and electromagnetic fields which, in covariant form, indicates both the well known equivalence of mass and energy and a possible equivalence of charge and energy. From orthogonality considerations, it is conjectured that this latter energy is gravitational, and that, whereas gravitational fields interact with electromagnetic energy, electromagnetic fields interact with gravitational energy. Parts of this work were completed at Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A.     

Convergence of Liapunov Series for Maclaurin Ellipsoids: Real Analysis

According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in a small parameter q, in the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. In [5] the convergence radius for Liapunov series was found in case of homogeneous equilibrium figures (Maclaurin ellipsoids). Isobars were described by means of implicit functions of q. The proof was based on the analysis of these functions in a complex domain and used computer algebra tools. Here we present a much simpler proof examining the above mentioned functions in a real domain only.     

引力波、引力波源和引力波探测实验

引力波是爱因斯坦和其他物理学家提出的关于广义相对论的四大预言之一。除了PSR1 91 3 + 1 6引力辐射阻尼的观测提供了引力波存在的间接证据外 ,科学家至今仍没有在实验室中确证引力波的存在。由于人类目前的技术水平还不可能在实验室中产生强度可供探测的引力波 ,而宇宙中存在大量大质量、高速运动的天体 ,有可能产生较强的引力波 ,天体引力波源自然成为现阶段科学家研究引力波的首选。本文介绍广义相对论框架下预言的引力波性质 ,引力波探测的理论依据 ,共振型棒式天线和激光干涉仪两大类探测器的基本原理 ,引力波探测实验的现状和面临的困难 ,科学家采取的对策 ,以及爆发型和连续型两类天体引力波源。最后介绍了正在计划中的几个引力波探测空间实验     

Fast and accurate computational tools for gravitational waveforms from binary stars with any orbital eccentricity

The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationally effective (fast and accurate) tools for constructing gravitational wave templates from binary stars with any orbital eccentricity are introduced including tight estimation criteria of the pertinent truncation and approximation errors.     

A model for accretion of the terrestrial planets

One possible origin of the terrestrial planets involves their formation by gravitational accretion of particles originally in Keplerian orbits about the sun. Some implications of this theory are considered. A formal expression for the rate of mass accretion by a planet is developed. The formal singularity of the gravitational collision cross-section for low relative velocities is shown to be without physical significance when the accreting bodies are in heliocentric orbits. The distribution of particle velocities relative to an accreting planet is considered; the mean velocity increases with time. The internal temperature of an accreting planet is shown to depend simply on the accretion rate. A simple and physically reasonable approximate expression for a planetary accretion rate is proposed.     

引力波理论和实验的新进展

引力波的存在是爱因斯坦在广义相对论理论中提出的一个重要预言．由于目前技术水平的限制,无法在实验室产生足以被探测到的引力波,因此宇宙中大量的大质量剧烈活动的天体成为科学家研究引力波的首选,从而诞生了引力波天文学．引力波探测将开启研究宇宙的新窗口,是继电磁辐射、宇宙线和中微子探测后探索宇宙奥秘的又一重要手段,对天文学研究有着极为重要的意义.新一代应用了高灵敏度的迈克耳逊干涉仪装置的长基线引力波探测仪正在建造中．该综述从引力波理论出发,阐述了目前研究较多的可探测引力波源,给出了目前观测上的最新进展,并展望了今后的发展前景．     

Astrophysical input for gravitational wave searches

We describe several areas where the newly emerging field of gravitational wave astronomy would benefit from exploiting the expertise of the broader astrophysics community. We deal specifically with searches for long-lived gravitational wave signals from neutron stars, paying particular attention to the known radio pulsar population and supernova remnants.      

Similarity considerations and conservation laws for magneto-static atmospheres

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential A. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, we construct a model magnetostatic atmosphere in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an e-folding distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J × B force (B, magnetic field induction) and the gas pressure gradient.     

基于Shapelets基函数的引力透镜质量重构方法

引力透镜效应是探测星系团物质分布的有效方法之一.目前,利用引力透镜数据重构星系团质量分布的主流方法可以分为两大类,即参数法和非参数法.在实际研究工作中,受限于质量模型假设和计算分辨率等方面的影响,现有的重构算法仍有诸多亟需解决的问题.基于Shapelets基函数的引力透镜质量重构方法通过基函数来实现引力透镜质量重构,使用Shapelets基函数分解引力透镜势,以引力透镜中多重像的位置和背景星系椭率畸变为限制条件来迭代求解基函数系数从而得到透镜体的质量分布.通过拟合一个模拟的NFW (Navarro,Frenk and White)透镜系统测试了新方法的可行性,结果表明新方法可以在整体上重构出透镜体的质量分布,并拟合出接近真实的源位置,能够为星系团质量测量提供一套灵活且高效的重构算法.     

Novel formulation of the quadrupole equation for potential stellar gravitational‐wave power estimation

A novel formulation of the quadrupole equation for potential stellar gravitational‐wave power estimation is derived. The derivation commences with the classical Einstein quadrupole formalism and then utilizes Newton's second law to establish a simplified formulation involving the radius of gyration of a mass or system of masses involving a pair of massive stars either on orbit about one another, or otherwise separated, or a star with a dumbbell‐like or aspherical mass distribution and an impulsive force acting on the mass or masses in order to estimate the power of a gravitational wave that is generated. A numerical example, based upon the well‐known gravitational‐wave power observed to be generated by PSR 1913+16, is utilized to test the formulation. Potential applications to stellar jets, including stellar‐black‐hole produced jets, are cited as examples of the potential applications of the novel quadrupole formulation. It is suggested that the gravitational waves, generated by the applications suggested, might be detected by the proposed space‐based Laser Interferometer Space Antenna or LISA. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The gravitational instability of flow through porous medium for some systems of astrophysical interest

The gravitational instability of flow through porous medium for some hydrodynamical and hydromagnetical systems of astrophysical interest is investigated. The effects of rotation, magnetic field, viscosity and finite electrical conductivity are studied for the gravitational instability through porous medium. The effect of suspended particles on the instability is also considered. It is found that Jean's criterion remains unchanged in the presence of porosity, viscosity, finite conductivity, rotation, magnetic field and suspended particles in the medium.     

Statistical analyses for NANOGrav 5-year timing residuals

In pulsar timing, timing residuals are the differences between the observed times of arrival and predictions from the timing model. A comprehensive timing model will produce featureless residuals, which are presumably composed of dominating noise and weak physical effects excluded from the timing model(e.g. gravitational waves). In order to apply optimal statistical methods for detecting weak gravitational wave signals, we need to know the statistical properties of noise components in the residuals. In this paper we utilize a variety of non-parametric statistical tests to analyze the whiteness and Gaussianity of the North American Nanohertz Observatory for Gravitational Waves(NANOGrav) 5-year timing data, which are obtained from Arecibo Observatory and Green Bank Telescope from 2005 to2010. We find that most of the data are consistent with white noise; many data deviate from Gaussianity at different levels, nevertheless, removing outliers in some pulsars will mitigate the deviations.