A plea for better astrophysical and astrometric data in case of double stars of peculiar interest

Summary TheIAU Symposium No. 61 (Perth, 1973, “New Problems in Astrometry’) makes clear that radiosources will play an important role for astrometry in view of the linkage of reference systems. The purposes developed later were to link the various systems from the earth and the solar system to the most inertial possible one. Extragalactic radiosources are the most reliable objects but they are faint. So, intermediate objects are needed. Among them the radiostars, optical objects having radioemission at a certain level and for given frequencies have a fundamental and key position. Most of such radiostars are double or multiple ‘binaries’ as it can be seen from the list of reference stars issued by the Working Group of Commission 24, Working Group created in 1978. The last issue of the core list of radiostars was presented by Ch. de Vegt (Chairman of the WG) on the occasion of the last General Assembly of the IAU (November 1985). A recent study of the system α Scorpii (Antares) has shown that the data concerning the magnitude and the spectral type are not accurate enough, according to the accuracy obtained for the astrometric position (±0 _. ^s 003 for an astrolabe campaign in right ascension). There is also a need for better knowledge about the orbits. In the case of the astrolabe observations, if the distance between the components in <3″ the astrometric position concerns the photocenter and accurate physical properties are needed for comparison with the radio position. Better astrophysical properties are strongly needed for all radiostars to be used as references, during the time the astrometrists have to improve the accuracy of their measurements both in optical and radio fields. Presented by S. Débarbat.     

Simulation of the full two rigid body problem using polyhedral mutual potential and potential derivatives approach

Herein we investigate the coupled orbital and rotational dynamics of two rigid bodies modelled as polyhedra, under the influence of their mutual gravitational potential. The bodies may possess any arbitrary shape and mass distribution. A method of calculating the mutual potential’s derivatives with respect to relative position and attitude is derived. Relative equations of motion for the two body system are presented and an implementation of the equations of motion with the potential gradients approach is described. Results obtained with this dynamic simulation software package are presented for multiple cases to validate the approach and illustrate its utility. This simulation capability is useful both for addressing questions in dynamical astronomy and for enabling spacecraft missions to binary asteroid systems.     

Substructure of the core of the perseus supercluster of galaxies

The hierarchical substructure of the core of the Perseus cluster of galaxies (A426, A262, A347, N507, and N383) is investigated using the method of S-tree diagrams. In the main system M (100 galaxies), two substructures AM (35 galaxies) and BM (13 galaxies) are determined. The group AM can be identified with the cluster A262 and the group N507; BM can be identified with the group N383; A426 and A347 are in the main system. The axis of symmetry of the system M passes through the Seyfert galaxy N1275 and is parallel to the axis of symmetry of the group AM, which is the core of increased density of the cluster of galaxies. Radial segregation of galaxies by morphological types is observed in the systems M and AM. The distribution of galaxies by position angles is uniform. Translated from Astrofizika, Vol. 41, No. 1, pp. 65–72, January-March, 1998.     

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.     

Hα Photometry of Two Contact Binaries

We carried out optical and Hα photometry of two contact binaries (V861 Herculis, EQ Tauri). The light curve modeling revealed stellar spots in both contact systems and strong Hα excess in the position of the observed stellar spots. A correlation was found between the V−R and R−H_α colour indices of V861 Her.     

Effect of tidal evolution in determining the ages of eclipsing-variable early main sequence close binary systems

New Claret evolutionary model-tracks, constructed for the first time for studying close binary systems (CBS) including tidal evolution constants, are used to determine the age of 112 eclipsing-variable stars in the Svechnikov-Perevozkina catalog by the method of isochrones. There is some interest in comparing the calculated ages with previous estimates obtained for these same close binary systems using evolutionary modeltracks for individual stars taking their mass loss into account. A correlation of the ages of the principal and secondary components is noted, which is most marked for massive close binaries with principal components having masses M₁ ≥ 3 M_⊙. A rejuvenating effect is found to occur for the systems studied here as calculated on the new tracks; it is most distinct for low-mass close binaries with a total mass M₁ + M₂ ≤ 3.5 M_⊙ and is predicted theoretically in terms of magnetic braking. The calculated broadband grid of isochrones, from zero-age main-sequence (ZAMS) to the age of the galaxy, can be used for estimating the ages of close binaries from other catalogs. Ages are given for the 112 eclipsing-variable close binaries with detached components lying within the main sequence. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 299–312 (May 2007).     

The General Method for Fixing the Gauges of Relativistic Astronomical Reference Systems

This article applies a new scheme of the first post-Newtonian theory (Damour et al., 1991–1994) to the problem of gauge in relativistic reference systems. Choosing and fixing gauge are necessary when the precision of time measurement and application needs to reach the 2PN level (10⁻¹⁶ or better). We present a general method for fixing the gauges of both the global and local coordinate systems, and for determining the expressions of gravitational potentials and coordinate transformations. The results relevant are consistent with the newest IAU resolutions, therefore they can be applied to astronomical practice.     

A Quick Method for Estimating the Propagation Direction of Coronal Mass Ejections Using STEREO-COR1 Images

We describe here a method to obtain the position of a coronal moving feature in a three-dimensional coordinate system based on height – time measurements applied to STEREO data. By using the height – time diagrams from the two SECCHI-COR1 coronagraphs onboard STEREO, one can easily determine the direction of propagation of a coronal mass ejection (i.e., if the moving plasma is oriented toward or away from the Earth). This method may prove to be a useful tool for space weather forecasting by easily identifying the direction of propagation as well as the real speed of the coronal mass ejections.     

Tidal interactions in binary stellar systems

The tidal interactions in binary stellar systems are studied under the assumption that the orbital motion of the binary is negligible in comparison with the stellar motion. By integrating over time the tidal forces acting on the stars, the energy changes are derived. These are used to obtain simple analytical expressions for the rates of disruption and merging. This method gives appropriate value for the Roche density ρ_r and it is found that the disruption rate of a satellite of density ρ changes drastically at ρ ρ_R A comparison is made with earlier results obtained under the simplifying assumption that stellar motion is negligible in comparison with the orbital motion of the binary and its implications are discussed.     

Contact Binaries: A Study of the Proximity Effects and Gravity Darkening Based on Kopal’s Fourier Method

A new method for the determination of the proximity effects and gravity darkening exponents in contact binaries of W UMa type is presented. The method is based on Kopal’s method of Fourier analysis of the light changes of eclipsing variables in the Frequency Domain. The method was applied to 36 W UMa systems for which geometric and photometric elements have been derived by the most powerful techniques. The derived values are very close to those predicted by the existing theory of radiative transfer or convective equilibrium.     

New method of orbit determination from two position vectors based on solving Gauss’s equations

The classic problem of finding the orbit of a celestial body from its two position vectors for two instants of time is considered. A solution to the problem free from uncertainties is obtained which can be applied for all three kinds of Keplerian movement. The main part of the computational procedure is reduced to solving one equation with one unknown. Formulas are derived for the initial value of the equation root, which makes the application of the Newton-Raphson method successful. The efficiency and reliability of the suggested algorithm is illustrated by examples of the orbit determination for the asteroids Adeona and Icarus, as well as for Halley’s Comet and Bowell’s Comet.     

Small virial oscillations of axisymmetric gravitating systems. II

Equations obtained in Part I of this investigation are solved and describe the gross dynamics of axisymmetric, collisionless gravitating systems for small departures from the equilibrium position. The solution obtained describes a superposition of oscillations with two eigenfrequencies. Against the background of periodic contractions and expansions, the system’s flattening varies with a period half as long. Translated from Astrofizika, Vol. 43, No. 3, pp. 483-492, July–September, 2000.     

A Spectroscopic Model of euv Filaments

We propose a new spectroscopic model for extended dark structures around Hα filaments observed in EUV lines. As in previous papers, we call these structures EUV filaments. Our model uses at least three observed EUV lines (located shortward the hydrogen Lyman-continuum limit) to compute iteratively the altitudes at which the EUV filament extensions are located. A transition-region line (O v in the present case) can be used to derive the opacity of the Lyman continuum and the other two coronal lines (e.g., Mg x and Si xii) then give two heights: the bottom and top of the EUV filament. The method takes into account self-consistently the absorption of EUV-line radiation by the Lyman continuum, as well as the volume-blocking effect potentially important for coronal lines. As an example we compute the heights of the EUV filament at one particular position, using CDS data for the 5 May 2000 filament. At this position, the EUV filament extension lies between altitudes 28 700 and 39 000 km, so that the geometrical thickness of the structure is 10300 km (we discuss also the sensitivity of our models to variations of the line intensities). These heights are consistent with the concept of twisted magnetic flux tubes, but there could be also some influence on our results due to additional low lying cool structures from parasitic polarities.     

Orbit Determination of Binary Asteroids

In addition to the detection of an asteroid moon or a binary asteroid, the knowledge of the satellite’s true orbit is of high importance to derive fundamental physical parameters of the binary system such as its mass and to shed light on its possible formation history and dynamical evolution (prograde/retrograde orbit, large/small eccentricity or inclination, etc.). A new methodology for preliminary orbit determination of binary asteroids – and visual binaries in general – is proposed. It is based on Thiele–Innes method combined with a ‘trial and error’ Monte-Carlo technique. This method provides the full set of solutions (bundle of orbits, with the 7 orbital elements) even for a reduced number of observations. The mass is a direct by-product of this orbit determination, from which one can next infer the bulk-density and porosity. In addition to the bundle of orbits, the method provides the marginal probability densities of the foreseen parameters. Such error analysis – since it avoids linear approximation – can be of importance for the prediction of the satellite’s position in the plane-of-sky during future stellar occultations or subsequent observations, but also for the analysis of the orbit’s secular evolution. After briefly describing the method, we present the algorithm and its application to some practical cases, with particular emphasis on asteroids binaries and applications on orbital evolution.     

Ballistic representation for kinematic access

This work uses simple two-body orbital dynamics to initially determine the kinematic access for a ballistic vehicle. Primarily this analysis was developed to assess when a rocket body might conjunct with an orbiting satellite platform. A family of access opportunities can be represented as a volume for a specific rocket relative to its launch platform. Alternately, the opportunities can be represented as a geographical footprint relative to aircraft or satellite position that encompasses all possible launcher locations for a specific rocket. A thrusting rocket is treated as a ballistic vehicle that receives all its energy at launch and follows a coasting trajectory. To do so, the rocket’s burnout energy is used to find its equivalent initial velocity for a given launcher’s altitude. Three kinematic access solutions are then found that account for spherical Earth rotation. One solution finds the maximum range for an ascent-only trajectory while another solution accommodates a descending trajectory. In addition, the ascent engagement for the descending trajectory is used to depict a rapid access scenario. These preliminary solutions are formulated to address ground-, sea-, or air-launched vehicles.     

New OB-association in Pup — CMa

A new method of determination of distances to stellar associations is proposed. This method is based on the measurements of mean thicknesses of globules of the systems of dark globules connected with that association. It is shown that the method is in good agreement with other known methods. A new grouping of OB stars in Pup-CMa is found. It is shown that this grouping has properties characteristic for OB-associations: the stars of that grouping have similar distances, similar radial velocities, the grouping is connected with molecular clouds, with Herbig-Haro objects, and cometary nebulae. All these results are in favour of this grouping to be a new OB-association. We named that association OB-association Pup-CMa. The preliminary results of¹²CO observations of molecular clouds connected with that association are also given. The radial velocities of these clouds are in good agreement with the mean radial velocity of stars in the association in Pup-CMa. Translated from Astrofizika, Vol. 42, No. 2, pp. 179–188, April–June, 1999.     

A sixth-order accurate scheme for solving two-point boundary value problems in astrodynamics

A sixth-order accurate scheme is presented for the solution of ODE systems supplemented by two-point boundary conditions. The proposed integration scheme is a linear multi-point method of sixth-order accuracy successfully used in fluid dynamics and implemented for the first time in astrodynamics applications. A discretization molecule made up of just four grid points attains a O(h ⁶) accuracy which is beyond the first Dahlquist’s stability barrier. Astrodynamics applications concern the computation of libration point halo orbits, in the restricted three- and four-body models, and the design of an optimal control strategy for a low thrust libration point mission.     

Computing periodic orbits of the three-body problem: Effective convergence of Newton’s method on the surface of section

We consider Newton’s method for computing periodic orbits of dynamical systems as fixed points on a surface of section and seek to clarify and evaluate the method’s uncertainty of convergence. Several fixed points of various multiplicities, both stable and unstable are computed in a new version of Hill’s problem. Newton’s method is applied with starting points chosen randomly inside the maximum possible—for any method—circle of convergence. The employment of random starting points is continued until one of them leads to convergence, and the process is repeated a thousand times for each fixed point. The results show that on average convergence occurs with very few starting points and non-converging iterations being wasted.