Dynamic status of the wide multiple system α Centauri + Proxima

We study the dynamics of a wide multiple system α Centauri + Proxima. The total energy of the system was estimated according to the available observational data on masses, coordinates, proper motions, and radial velocities of its components. To account for the effect of the observational data errors on the result, we have implemented the Monte Carlo method. From N = 10⁶ statistical tests we show that with the probability of about 90% the motion is hyperbolic, i.e., α Cen AB and Proxima will after a while diverge from each other by a considerable distance. We also perform numerical modeling of dynamic evolution of the wide pair α Cen AB + Proxima in the regular field of the Galaxy. The trajectory of relative motion is constructed. The components diverge from each other by a distance of 20 pc over the time scale of about 200 Myr. The critical parameter for determining the dynamic status of the system is the radial velocity of the C component (Proxima), known with an error of 200 ms^?1. For a reliable determination of the nature of motions in the system, we have to decrease the radial velocity error by at least an order of magnitude.     

The pulsation period of theβ Cephei-star NU Centauri

The radial velocity measurements of the single line spectroscopic binary and Cephei star NU Centauri made during 1985, 1987, and 1988 are presented. New ephemeris with a pulsation period of 0^d.1696401 has been derived by combining the three season data. The new ephemeris also fits well for the earlier data published in the literature.     

On the stability of circular ‘asteroid’ orbits in anN-planetary system

The restricted problem of the motion of a point of negligible mass (asteroid) in anN-planetary system is considered. It is assumed that all the planets move about the central body (Sun) along circular orbits in the same plane and the mean motions of the asteroid and the planets are incommensurable. The asteroid orbit evolution is described as a first approximation by secular equations with the perturbing function averaged by the mean longitudes of the asteroid and the planets. For small values of the asteroid orbit eccentricity an expression for the secular part of the perturbing function has been obtained. This expression holds for the arbitrary values of the asteroid orbit semiaxis which are different from those of the planet orbit radii. The stability of the asteroid circular orbits in a linear approximation with respect to the eccentricity is studied. The critical inclinations for a Solar system model are calculated.     

On possible circumbinary configurations of the planetary systems of α Centauri and EZ Aquarii

Possible configurations of the planetary systems of the binary stars α Cen A–BandEZAqr A–C are analyzed. The P-type orbits—circumbinary ones, i.e., the orbits around both stars of the binary, are studied. The choice of these systems is dictated by the fact that α Cen is closest to us in the Galaxy, while EZ Aqr is the closest system whose circumbinary planets, as it turns out, may reside in the “habitability zone.” The analysis has been performed within the framework of the planar restricted three-body problem. The stability diagrams of circumbinary motion have been constructed: on representative sets of initial data (in the pericentric distance–eccentricity plane), we have computed the Lyapunov spectra of planetary motion and identified the domains of regular and chaotic motion through their statistical analysis. Based on present views of the dynamics and architecture of circumbinary planetary systems, we have determined the most probable planetary orbits to be at the centers of the main resonance cells, at the boundary of the dynamical chaos domain around the parent binary star, which allows the semimajor axes of the orbits to be predicted. In the case of EZ Aqr, the orbit of the circumbinary planet is near the habitability zone and, given that the boundary of this zone is uncertain, may belong to it.     

Escape dynamics and fractal basin boundaries in the planar Earth–Moon system

The escape of trajectories of a spacecraft, or comet or asteroid in the presence of the Earth–Moon system is investigated in detail in the context of the planar circular restricted three-body problem, in a scattering region around the Moon. The escape through the necks around the collinear points \(L_1\) and \(L_2\) as well as the leaking produced by considering collisions with the Moon surface, taking the lunar mean radius into account, were considered. Given that different transport channels are available as a function of the Jacobi constant, four distinct escape regimes are analyzed. Besides the calculation of exit basins and of the spatial distribution of escape time, the qualitative dynamical investigation through Poincaré sections is performed in order to elucidate the escape process. Our analyses reveal the dependence of the properties of the considered escape basins with the energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. Finally, we observe the plentiful presence of stickiness motion near stability islands which plays a remarkable role in the longest escape time behavior. The application of this analysis is important both in space mission design and study of natural systems, given that fractal boundaries are related with high sensitivity to initial conditions, implying in uncertainty between safe and unsafe solutions, as well as between escaping solutions that evolve to different phase space regions.     

The helium content of the peculiar Oosterhoff type I globular cluster ω Centauri

An investigation of the observational properties for RR Lyrae variables in the galactic globular cluster Centauri is reported. The results show that Centauri belongs to the Oosterhoff Group I, notwithstanding the large, Oo II-like value of the average of the periods of ab-type RR Lyrae. The helium content is derived for this cluster from the analysis of the variables in the (A-logT _e) plane. It is shown that the helium abundance is very close to the value Y=0.30, about 0.05 larger than the value derived for the normal Oo I globular cluster M3.     

A motivating exploration on lunar craters and low-energy dynamics in the Earth–Moon system

It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L ₂ of the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four-Body Problem. In the former case, as main outcome, we observe a more relevant bombardment at the apex of the lunar surface, and a percentage of impact which is almost constant and whose value depends on the assumed Earth–Moon distance d_EM. In the latter, it seems that the Earth–Moon and Earth–Moon–Sun relative distances and the initial phase of the Sun θ ₀ play a crucial role on the impact distribution. The leading side focusing becomes more and more evident as d_EM decreases and there seems to exist values of θ ₀ more favorable to produce impacts with the Moon. Moreover, the presence of the Sun makes some trajectories to collide with the Earth. The corresponding quantity floats between 1 and 5 percent. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth–Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.     

Clausius’ virial vs. total potential energy in the dynamics of a two-component system

In a gravitational virialized bound system built up of two components, one of which is embedded in the other, the Clausius’ virial energy of one subcomponent is not, in general, equal to its total potential energy, as occurs in a single system without external forces. This is the main reason for the presence, in the case of two non-coinciding concentric spheroidal subsystems, of a minimum (in absolute value) in the Clausius’ virial of the inner component B, when it assumes a special configuration characterized by a value of its semi-major axis we have named tidal radius. The physical meaning, connected with its appearance, is to introduce a scale length on the gravity field of the inner subsystem, which is induced from the outer one. Its relevance in the galaxy dynamics has been stressed by demonstrating that some of the main features of Fundamental Plane may follow as consequence of its existence. More physical insight into the dynamics of a two-component system may be got by looking at the location of this scale length inside the plots of the potential energies of each subsystem and of the whole system and by also taking into account the trend of the anti-symmetric residual-energy, that is the difference between the tidal and the interaction-energy of each component. Some thermodynamical arguments related to the inner component are also added to prove how special is the tidal radius configuration. Moreover, the role of the divergency at the center of the two subsystems in obtaining this scale length is considered. For the sake of simplicity the analysis has been performed in the case of a frozen external component even if this constraint does not appear to be too relevant in order to preserve the main results.     

Computation of weak stability boundaries: Sun–Jupiter system

We compute the weak stability boundary in the planar circular restricted three-body problem starting from the algorithmic definition, and its generalization by García and Gómez. In addition, we consider a new set of primaries, Sun–Jupiter, to replace the case of Earth–Moon considered in previous studies. Numerical enhancements are described and compared to previous methods. This includes defining the equations of motion in polar coordinates and a modified numerical scheme for the derivation of both stable sets and their boundaries. These enhancements decrease the computational time. New results are obtained by considering the Sun–Jupiter case which we compare to the Earth–Moon case.     

Spectral variability of the α Sco AB binary system observed with IUE

We present ultraviolet spectra of the α Sco AB binary system taken by the International Ultraviolet Explorer during the period from 1979 to 1995. An investigation is carried out on the spectral variability of Mg II k and h emission lines arising from the chromosphere of α Sco A (Van der Hucht et al., 1979). There are absorption and emission components on the blue sides of the Mg II k and h lines, which are formed in the cool circumstellar gas shells around two stars (Bernat and Lambert, 1976).This work is based on calculations of line fluxes and line widths for the aforementioned spectral lines. We found that there is spectral variability for these physical parameters with pulsation phase, which we attribute to the changes of density and temperature of the chromosphere of α Sco A as a result of the semi-regular pulsation and the variability of mass loss of the red supergiant (Reimers et al., 2008). The observed values of the k-to-h ratio are approximately one, implying that the k and h emission lines originate from an optically thick atmosphere.     

A note on the dynamics around the Lagrange collinear points of the Earth–Moon system in a complete Solar System model

In this paper we study the dynamics of a massless particle around the L _1,2 libration points of the Earth–Moon system in a full Solar System gravitational model. The study is based on the analysis of the quasi-periodic solutions around the two collinear equilibrium points. For the analysis and computation of the quasi-periodic orbits, a new iterative algorithm is introduced which is a combination of a multiple shooting method with a refined Fourier analysis of the orbits computed with the multiple shooting. Using as initial seeds for the algorithm the libration point orbits of Circular Restricted Three Body Problem, determined by Lindstedt-Poincaré methods, the procedure is able to refine them in the Solar System force-field model for large time-spans, that cover most of the relevant Sun–Earth–Moon periods.     

Analysis of the light curves of V78 in ω Centauri in the frequency domain by automatized fourier techniques

The aim of the present paper has been to analyse the light changes of the close eclipsing system V78 in Centauri in the frequency domain. In two of his recent papers, Kopal (1977b, c) has developed new methods for the analysis of light curves using Hankel transforms of zero order. He succeeded in expressing the momentsA _2m of light curves in a closed form. The expansions, in terms of which the momentsA _2m can be expressed, converge in all circumstances. Their analytical structure presents no difficulty for automatic computation. The light variations of the eclipsing system V78 in Centauri have been studied by use of the above method. New geometrical elements are also given.     

Line variability in the spectrum of supergiant α Cam

CCD spectra taken with the PFES and CEGS echelle spectrographs attached to the 6-m Special Astrophysical Observatory (Russian Academy of Sciences) telescope and the 2-m Shamakha Astrophysical Observatory (National Academy of Sciences of Azerbaijan) telescope, respectively, were used to study the line-profile variations in the spectrum of the hot supergiant α Cam. No fast (≤1.5 h) line-profile and radial-velocity variations were found. Some of the systematic effects that cause spurious variability are considered. The Hα-profile variability appears symmetric relative to the radial velocity of the star’s center of mass and is attributable to variable blueshifted and redshifted emission and/or absorption components superimposed on a variable photospheric profile. The Hα line shows evidence of a large-scale mass ejection from the stellar surface, which is also traceable in other spectral lines. The He II 4686 line exhibits an inverse P Cyg profile, while the red wing of the He I 5876 line shows weak and variable emission. The fast (on characteristic time scales of shorter than an hour) variability of the He II 4686 profile that was previously revealed by our observations (Kholtygin et al. 2000) is called into question. A comparison of the observational data on the variability of ultraviolet and optical line profiles for the supergiant αCam suggests that nonradial motions are mainly responsible for the radial-velocity and line-profile variability.     

Discovery of high-velocity EHB stars in the globular cluster ωCentauri(NGC 5139)

We report the discovery of 45 high-velocity extreme horizontal branch(EHB) stars in the globular cluster Omega Centauri(NGC 5139).The tangential velocities of these EHB stars are determined to be in the range 93~313 km s~(-1),with an average uncertainty of ~27 km s~(-1).The central escape velocity of the cluster is determined to be in the range 60~105 km s~(-1).These EHB stars are significantly more concentrated toward the cluster core compared with other cluster members.The formation mechanisms of these EHB stars are discussed.Our conclusions can be summarized as follows:(1) A comparison of the tangential velocities of these EHB stars to the centra]escape velocity of the cluster shows that most if not all of these EHB stars are unbound to the cluster;(2) These EHB stars obtained high velocities in the central cluster region no longer than ~1 Myr ago and may be subsequently ejected from the cluster in the next ~1 Myr;(3) If the progenitors of these EHB stars were single stars,then they may have experienced a fast mass-loss process.If the progenitors were in close binaries,then they may have formed through disruptions by the intermediate-mass black hole in the cluster center.     

Dynamical capture in the Pluto–Charon system

This paper explores the possibility that the progenitors of the small satellites of Pluto got captured in the Pluto?CCharon system from the massive heliocentric planetesimal disk in which Pluto was originally embedded into. We find that, if the dynamical excitation of the disk is small, temporary capture in the Pluto?CCharon system can occur with non- negligible probability, due to the dynamical perturbations exerted by the binary nature of the Pluto?CCharon pair. However, the captured objects remain on very elliptic orbits and the typical capture time is only ~ 100?years. In order to explain the origin of the small satellites of Pluto, we conjecture that some of these objects got disrupted during their Pluto-bound phase by a collision with a planetesimal of the disk. This could have generated a debris disk, which damped under internal collisional evolution, until turning itself into an accretional disk that could form small satellites on circular orbits, co-planar with Charon. Unfortunately, we find that objects large enough to carry a sufficient amount of mass to generate the small satellites of Pluto have collisional lifetimes orders of magnitude longer than the capture time. Thus, this scenario cannot explain the origin of the small satellites of Pluto, which remains elusive.     

Free collisions in a microgravity many-particle experiment – II: The collision dynamics of dust-coated chondrules

The formation of planetesimals in the early Solar System is hardly understood, and in particular the growth of dust aggregates above millimeter sizes has recently turned out to be a difficult task in our understanding (Zsom, A., Ormel, C.W., Güttler, C., Blum, J., Dullemond, C.P. [2010]. Astron. Astrophys., 513, A57). Laboratory experiments have shown that dust aggregates of these sizes stick to one another only at unreasonably low velocities. However, in the protoplanetary disk, millimeter-sized particles are known to have been ubiquitous. One can find relics of them in the form of solid chondrules as the main constituent of chondrites. Most of these chondrules were found to feature a fine-grained rim, which is hypothesized to have formed from accreting dust grains in the solar nebula. To study the influence of these dust-coated chondrules on the formation of chondrites and possibly planetesimals, we conducted collision experiments between millimeter-sized, dust-coated chondrule analogs at velocities of a few cm s^?1. For 2 and 3 mm diameter chondrule analogs covered by dusty rims of a volume filling factor of 0.18 and 0.35–0.58, we found sticking velocities of a few cm s^?1. This velocity is higher than the sticking velocity of dust aggregates of the same size. We therefore conclude that chondrules may be an important step towards a deeper understanding of the collisional growth of larger bodies. Moreover, we analyzed the collision behavior in an ensemble of dust aggregates and non-coated chondrule analogs. While neither the dust aggregates nor the solid chondrule analogs show sticking in collisions among their species, we found an enhanced sicking efficiency in collisions between the two constituents, which leads us to the conjecture that chondrules might act as “catalyzers” for the growth of larger bodies in the young Solar System.     

Polarimetry in Planetary Science—A Step Forward with the VLT and a Need for the ELTs

We present a brief review of polarimetric measurements of solar system objects, both linear and circular, obtained with the FORS1 instrument at the Very Large Telescope VLT over the past years. A number of first and new results have been obtained by using this unique observing mode at an 8 m class telescope, among them polarimetry of faint planetary bodies like near-Earth asteroids, Kuiper Belt objects and cometary nuclei, spectropolarimetry of cometary coma material and of the Earthshine of the Moon (in order to verify that life exists on Earth!). We outline the science cases for planetary polarimetry at a future Extremely Large Telescope ELT and provide high level requirements for polarimetric equipment to be used at the ELTs for the study of the science cases described.