Common Center Of Mass Research Articles

Modelling of W UMa-type variable stars

Most of the stars in the sky are binary or multiple star systems. In only a small percentage of binary systems are the two stars far enough apart to be able to resolve the individual stars. The binary nature of close systems can be inferred from the periodic Doppler shifts seen in the spectral lines of the stars as they orbit their common centre of mass, or, if the orbital plane is inclined at an angle to the observer so that one star passes in front of the other, by variations in the observed brightness of the stars. These stellar systems are referred to as eclipsing binaries. The vast majority of eclipsing binaries have been found by searching for stars whose brightness varies periodically. From Newton’s Law of Universal Gravitation it can be shown that the square of the period P of a binary system is proportional to the sum of the masses m1 and m2 of the stars, i.e. P 2 ∝ (m1 + m2).

Period analysis of the eclipsing binary AI Dra

The eclipsing binary system AI Dra reveals changes of its orbital period. These variations could be described as a result of orbiting the eclipsing pair around a common center of mass with two unseen companions with the periods about 18 and 43 years together with a steady period increase. Fourteen new minima observations were carried out by the authors.

Effects of Mutual Transits by Extrasolar Planet–Companion Systems on Light Curves

Abstract We consider the effects of mutual transits by extrasolar planet–companion systems (in a true binary or a planet–satellite system) on light curves. We show that induced changes in light curves depend strongly on a ratio between a planet–companion’s orbital velocity around their host star and a planet–companion’s spin speed around their common center of mass. In both the slow and fast-spin cases (corresponding to long and short distances between them, respectively), a certain asymmetry appears in light curves. We show that, especially in the case of short distances, occultation of one faint object by the other, while the transit of the planet–companion system occurs in front of its parent star, causes an apparent increase in light curves, and characteristic fluctuations appear as important evidence of mutual transits. We show also that extrasolar mutual transits provide a complementary method for measuring the radii of two transiting objects, their separation and masses, and consequently for identifying the system as a true binary, a planet–satellite system, or others. Monitoring 10$^5$ stars for 3 yr with Kepler may lead to the discovery of a second Earth–Moon-like system if the fraction of such systems for an averaged star is larger than 0.05, or we may put an upper limit on the fraction as $f$$\lt$ 0.05.

The possible existence of cloud-like clusters of microparticles at the libration points of a binary star

The possible existence of clusters of microscopic gas-dust particles forming gigantic clouds is demonstrated in the framework of the photogravitational three-body problem. These clouds are pulsating formations representing heterogeneous ensembles of particles of various sizes, densities, and susceptibilities to the radiation pressure, with each of the particles moving along its own trajectory. The conditions for the existence of co-linear and triangular libration points are derived by analyzing the dynamical equations describing the motion of a test particle in the gravitational-repulsive field of two gravitating and radiating bodies moving in an elliptical orbit about their common center of mass. The stability of these libration points is studied for various eccentricities e, mass parameters µ, and reduction coefficients characterizing the action of the stellar radiation on particles, and the results generalized in diagrams. We demonstrate the formation of clouds of particles located at multiple stable libration points. The extent of these clouds and their distances from the binary components are estimated. Scenarios for the subdivision of the clouds based on variations of e and µ are presented. The results of computations for a binary star with characteristics similar to those for α Cen are presented.

Breather states in magnetic domain wall racetrack memory samples

Magnetic domain wall racetrack memory samples allow for the controlled motion of isolated magnetic domain walls in a quasi one-dimensional geometry. Here we consider the possibility of the dynamical formation of bound states of domain walls that can be prepared via a suitably chosen external field. Upon switching off the external field, these domain walls oscillate around their common center of mass, with a frequency depending on the relative initial handedness of the domain wall. Such breather states may be observed by detecting the resulting magnetization oscillations.

Charged particle dynamics in the combined field of two rotating magnetic dipoles: A numerical investigation of the parametric effect on the equatorial motions

In this contribution we study some aspects of the dynamics of a charged particle in the field produced by two magnetic dipoles that rotate in circular orbits around their common center of mass under their mutual Newtonian attraction. More precisely, we numerically investigate the evolution of the regions of the particle motion on the equatorial plane of each dipole and we explore their parametric variation. We focus our investigation on those problem parameters that are related with the magnetic fields and the masses of the primaries. The obtained preliminary results show that for each particular set of the above parameters and for certain values of energy these regions are bounded, and therefore the motion of the particle is confined inside them.

High spatial resolution observations of the T Tau system — I. Astrometry in the near-infrared

T Tauri is an example how our knowledge about an object improves with spatial resolution: About 60 years ago, it was considered to be the prototypical T Tauri star. 25 years ago, it was discovered to be a close binary with an infrared companion at 0.7arcsec distance. Ten years ago, the infrared companion was itself resolved into a binary with just 50 mas separation. We collected astrometric data from the literature and from archived VLT observations. Additionally, we present a new measurement obtained on February 1, 2008. Fits of orbit models to the data yield estimates for the orbital elements of the close binary. In most other binaries, we can observe only the relative motion of both components around each other, which can be used to determine the total mass of the pair. The presence of the third component in the T Tauri system gives us the rare opportunity to observe also the motion of both components of the close binary around their common center of mass, allowing to determine dynamical masses of the individual stars. We find that the period of the best model for the orbit of T Tau Sa and Sb is 28+12-4 years. The mass of Sa is 2.28 ± 0.22 M⊙ and the mass of Sb is 0.41 ±0.19M⊙.

3D reconstruction and visualization of astrophysical wind volumes using physical models

This article reports on the application of a framework used to model, simulate and visualize the 3D structure of astrophysical wind volumes. The modeling methodology is similar to multidirectional medical tomography in that the spatial structure of an extended target can be reconstructed from a sequence of images obtained by scanning that target from several directions. Even though the controlled environment realized in diagnostic radiology cannot be replicated in the study of astrophysical phenomena, strong candidates for astrophysical tomography do exist in hot, close double stars locked in orbits around a common center of mass. As the Keplerian orbit is traced out, the geometry presented to the observer varies so that each star constitutes an analyzer upon its companion's wind and probes its structure. Since these targets are too far to be resolved spatially, we study and model the UV spectral lines of prominent wind ions, which scatter photospheric UV light so that line shapes vary as the stars revolve and as inhomogeneities form, propagate, and evolve in the composite wind. The framework presented is applied to two hot close binaries near the applicability limits of the discussed methodology. Two novel custom-made tools that aid the analysis of the spectra and the visualization of the results are also presented. The first of these, the Spectrum Analyzer and Animator , automates the derivation of light curves from the observed spectra and the generation of synthetic binary wind-line profiles, which reproduce the morphologies and variabilities of the observed wind profiles. After the composite wind structure of a binary has been recovered, the second tool, the Binary 3D Renderer —also authored in IDL—aids the visualization of the results by simulating the motion of the system (stars, winds and wind-interaction effects) around the binary's center of mass. The Binary 3D Renderer thus repackages the end product of a lengthy physical modeling process to generate physically sound, realistic multimedia content and increase the effectiveness and communication impact of the research results.

Ejection of Supermassive Black Holes from Galaxy Cores

[Abridged] Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks and the effects on the stellar distribution using high-accuracy direct N-body simulations. Following the kick, the motion of the SMBH exhibits three distinct phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via dynamical friction each time it passes through the core. Chandrasekhar's theory accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda < 3 and if the changing core density is taken into account. (2) When the amplitude of the motion has fallen to roughly the core radius, the SMBH and core begin to exhibit oscillations about their common center of mass. These oscillations decay with a time constant that is at least 10 times longer than would be predicted by naive application of the dynamical friction formula. (3) Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate the time for the SMBH's oscillations to damp to the Brownian level in real galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection of SMBHs also results in a lowered density of stars near the galaxy center; mass deficits as large as five times the SMBH mass are produced for kick velocities near the escape velocity. We compare the N-body density profiles with luminosity profiles of early-type galaxies in Virgo and show that even the largest observed cores can be reproduced by the kicks, without the need to postulate hypermassive binary SMBHs. Implications for displaced AGNs and helical radio structures are discussed.

On the planar inertial motion of a system of three coupled bodies

Numerous papers are devoted to studying the motion of a system (coupling) of two bodies in the Earth’s satellite orbit ([1–4] and others). The problem on the planar inertial motion of three bodies, coupled by a non-extensible weightless string having the form of an unfastened chain, is considered in the paper. Such a configuration can be represented, for example, by a system of two coupled spacecraft rotating around their common center of mass (in order to simulate the gravity force) in long-term space missions, when the third body (the lift) is located on a connecting cable. The bodies are considered to be the material points (particles).

Collision between galaxy clusters unveils striking evidence of dark matter

The nonbaryonic matter generally assumed to dominate large aggregates of stars and gas almost always shares a common center of mass with the ordinary matter we can see. But a titanic collision can force them apart.

Precision Kinematics and Related Parameters of the α Persei Open Cluster

A kinematical study of the nearby open cluster α Persei is presented based on the proper motions and positions in the Tycho-2 catalog and Second USNO CCD Astrographic Catalog (UCAC2). Using the data and photometry from the Tycho-2 and ground-based catalogs, 139 probable members of the cluster are selected, 18 of them new. By the classical convergent point method, systematic motions of stars inside the cluster and velocity dispersions are estimated. As directly observed, the upper limit on the internal velocity dispersion per coordinate is 1.1 km s^(-1). The actual velocity dispersion is much smaller than that value, since all of it appears to come from the expected errors of the proper motions. The relative position of the convergent point with respect to the cluster stars yields the astrometric radial velocity, which turns out larger by a few km s^(-1) than the mean observed spectroscopic radial velocity. This implies an overall contraction of the cluster. Kinematic parallaxes are computed for each member, and an improved H-R diagram is constructed. An age of 52 Myr is determined by isochrone fitting. The star α Per itself fits an isochrone of this age computed with overshooting from the boundary of the convective zone. The theoretical mass of the star α Per is 6.65 M_⊙. With respect to the common center of mass, half of the higher mass members (earlier than G) are located within a radius of 10.3 pc. The cluster appears to be roughly twice as large, or as sparse, as the Pleiades, retaining nonetheless a similar dynamical coherence. The low rate of binaries is another feature of this cluster, where we find only about 20% of members to be known or suspected spectroscopic, astrometric, or visual binaries or multiple systems. X-ray emitters in the cluster appear to have the same dispersion of internal velocities as the rest of the membership. The cluster is surrounded by an extended, sparse halo of comoving dwarfs, which are found by combining the proper-motion data from UCAC2 with Two Micron All-Sky Survey infrared photometry. Since many of these external stars are outside the tidal radius, the cluster being in an active stage of disintegration or evaporation could be considered. This hypothesis is not supported by the weak compression and the nonmeasurable velocity dispersion found in the kinematic analysis. A search for stars ejected from the α Persei cluster is carried out by tracking a large number of nearby stars 70 Myr back in time and matching their positions with the past location of the cluster. Only one plausible ejection is found prior to 10 Myr ago. The nearby star GJ 82, an active M dwarf with a strong Hα emission, is likely a former member ejected 47 Myr ago at 5 km s^(-1).

Dark matter and galaxy formation

This first-ever double-pulsar system was discovered in 2003, consisting of two visible pulsars which orbit the common centre of mass in a slightly eccentric orbit in only 2.4 hours. One of the pulsars appears to be old and recycled with a spin period of only 22 ms. Its companion is younger and rotating slower with a period of 2.8 s, confirming the long-proposed recycling theory for millisecond pulsars. The system provides an exciting opportunity to study the workings of pulsar magnetospheres and represents a truly unique laboratory for relativistic gravitational physics. Both aspects are greatly facilitated by the very fortunate fact that the orbit is seen nearly perfectly edge on. This alignment allows the detection of the Shapiro delay in the pulse arrival times of the 22-ms pulsar when its pulses propagate through the curved space-time near the slowly rotating pulsar. In addition to updating on the continuing observations, this contribution introduces a new timing model that represents a variation of Damour-Deruelle (1986) for highly inclined orbits.

Strong-field tests of gravity with the double pulsar

This first-ever double-pulsar system was discovered in 2003, consisting of two visible pulsars which orbit the common centre of mass in a slightly eccentric orbit in only 2.4 hours. One of the pulsars appears to be old and recycled with a spin period of only 22 ms. Its companion is younger and rotating slower with a period of 2.8 s, confirming the long-proposed recycling theory for millisecond pulsars. The system provides an exciting opportunity to study the workings of pulsar magnetospheres and represents a truly unique laboratory for relativistic gravitational physics. Both aspects are greatly facilitated by the very fortunate fact that the orbit is seen nearly perfectly edge on. This alignment allows the detection of the Shapiro delay in the pulse arrival times of the 22-ms pulsar when its pulses propagate through the curved space-time near the slowly rotating pulsar. In addition to updating on the continuing observations, this contribution introduces a new timing model that represents a variation of Damour-Deruelle (1986) for highly inclined orbits. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Strong‐field tests of gravity with the double pulsar

AbstractThis first‐ever double‐pulsar system was discovered in 2003, consisting of two visible pulsars which orbit the common centre of mass in a slightly eccentric orbit in only 2.4 hours. One of the pulsars appears to be old and recycled with a spin period of only 22 ms. Its companion is younger and rotating slower with a period of 2.8 s, confirming the long‐proposed recycling theory for millisecond pulsars. The system provides an exciting opportunity to study the workings of pulsar magnetospheres and represents a truly unique laboratory for relativistic gravitational physics. Both aspects are greatly facilitated by the very fortunate fact that the orbit is seen nearly perfectly edge on. This alignment allows the detection of the Shapiro delay in the pulse arrival times of the 22‐ms pulsar when its pulses propagate through the curved space‐time near the slowly rotating pulsar. In addition to updating on the continuing observations, this contribution introduces a new timing model that represents a variation of Damour‐Deruelle (1986) for highly inclined orbits.

A Random Polymer Model of the Statistical Significance of Structure Alignment

A theory for assessing the statistical significance of structure alignment is developed using a random or Gaussian chain model. In this model, we consider the statistical distribution of the root mean square distance (rmsd) of the alignment between two random chains of equal length and common center of mass (referred to as Case 1). We demonstrate that the rmsd2 is distributed as a sum of independent Gamma variables. Analytic results on the mean and variance of the rmsd2 are presented. Since rmsd is strongly dependent on the length, we define the dimensionless quantity, reduced rmsd, as the rmsd divided by the radius of gyration. We find that the reduced rmsd can be accurately approximated by an extreme value distribution (EVD) that is independent of chain length and of bond length. The parameters of the EVD can be calculated from the mean and the variance of the rmsd2. We also consider the case of two chains with a common center of mass that are then rotated to minimize the rmsd (Case 2). In this case, the distribution of reduced rmsd can again be accurately approximated by an EVD, which is independent of the chain length and expected bond length. This distribution is used to calculate the p-value for a given reduced rmsd. Performing an analogous comparison for proteins, we find that <rmsd> approximately M(nu) and nu = 0.28 and 0.32 for Case 1 and Case 2, respectively, where M is the chain length. This result for Case 2 exactly matches with previous scaling results and suggests that rmsd/M(nu)is an appropriate metric for protein structure alignment and will be independent of chain length. We also find that the new score roughly follows the EVD.

Rotating regular solutions in Einstein–Yang–Mills–Higgs theory

We construct new axially symmetric rotating solutions of Einstein–Yang–Mills–Higgs theory. These globally regular configurations possess a nonvanishing electric charge which equals the total angular momentum, and zero topological charge, representing a monopole–antimonopole system rotating around the symmetry axis through their common center of mass.

Motion of a Planet with a Complex Structure

The motion of a planet consisting of a mantle and a core (solid bodies) connected by a viscoelastic layer and interacting with each other and an external point mass by the law of gravitation is considered. The mutual motions of the core and mantle are investigated assuming that the centers of mass of the planet and external point mass moves along undisturbed Keplerian orbits around the common center of mass of the system. The planetary core and mantle have an axial symmetry and different principal moments of inertia, which leads to a displacement of the center of mantle relative to the center of core and to their mutual rotations. The results obtained on the basis of averaged equations are illustrated by the example of the Earth–Moon system.

Translational–Rotational Motion of a Viscoelastic Sphere in Gravitational Field of an Attracting Center and a Satellite

We study the translational–rotational motion of a planet modeled by a viscoelastic sphere in the gravitational fields of an immovable attracting center and a satellite modeled as material points. The satellite and the planet move with respect to their common center of mass that, in turn, moves with respect to the attracting center. The exact system of equations of motion of the considered mechanical system is deduced from the D'Alembert–Lagrange variational principle. The method of separation of motions is applied to the obtained system of equations and an approximate system of ordinary differential equations is deduced which describes the translational–rotational motion of the planet and its satellite, taking into account the perturbations caused by elasticity and dissipation. An analysis of the deformed state of the viscoelastic planet under the action of gravitational forces and forces of inertia is carried out. It is demonstrated that in the steady-state motion, when energy dissipation vanishes, the planet's center of mass and the satellite move along circular orbits with respect to the attracting center, being located on a single line with it. The viscoelastic planet in its steady-state motion is immovable in the orbital frame of reference. It is demonstrated that this steady-state motion is unstable.

The planar n-body problem: regular polygon solutions

In this paper, the planar n-body problem under central force fields is considered. By introducing appropriate matrices and under determinated central force fields, we prove that n masses ( n⩾4) at the vertices of a regular polygon, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the n-body problem if and only if the masses are equal.