Theoretical models for wide binary evolution

Summary Wide binary evolution under the influence of stars, giant molecular clouds, and the galactic tidal field is reviewed. Recent results show that binary lifetimes ata≳0.1 pc are determined by an interplay between relatively gentle evolution due to stellar encounters and catastrophic collisions with cloud subclumps. It is emphasized that binary semimajor axis distributions may not be understood from lifetimes alone. To determine the theoretical distribution binary ‘birthrate functions’ must be convolved with probability distributions for the evolution of an ensemble of binaries from given initial separations. Simple models show no sharp breaks below the tidal cut-off imposed by the Galaxy.     

Orbital separation amplification in fragile binaries with evolved components

The secular stellar mass loss causes an amplification of the orbital separation in fragile, common proper motion, binary systems with separations of the order of 1000 A.U. In these systems, companions evolve as two independent coeval stars as they experience negligible mutual tidal interactions or mass transfer. We present models for how post-main sequence mass-loss statistically distorts the frequency distribution of separations in fragile binaries. These models demonstrate the expected increase in orbital separation resulting from stellar mass-loss, as well as a perturbation of associated orbital parameters. Comparisons between our models and observations resulting from the Luyten survey of wide visual binaries, specifically those containing MS and white-dwarf pairs, demonstrate a good agreement between the calculated and the observed angular separation distribution functions.     

Orbital evolution and orbital phase resolved spectroscopy of the HMXB pulsar 4U 1538-52 with RXTE-PCA and BeppoSAX

We report here results from detailed timing and spectral studies of the high mass X-ray binary pulsar 4U 1538-52 over several binary periods using observations made with the Rossi X-ray Timing Explorer (RXTE) and BeppoSAX satellites. Pulse timing analysis with the 2003 RXTE data over two binary orbits confirms an eccentric orbit of the system. Combining the orbitial parameters determined from this observation with the earlier measurements we did not find any evidence of orbital decay in this X-ray binary. We have carried out orbital phase resolved spectroscopy to measure changes in the spectral parameters with orbital phase, particularly the absorption column density and the iron line flux. The RXTE-PCA spectra in the 3–20 keV energy range were fitted ∼6.4 keV, whereas the BeppoSAX spectra needed only a power law and Gaussian emission line at ∼6.4 keV in the restricted energy range of 0.3–10.0 keV. An absorption along the line of sight was included for both the RXTE and BeppoSAX data. The variation of the free spectral parameters over the binary orbit was investigated and we found that the variation of the column density of absorbing material in the line of sight with orbital phase is in reasonable agreement with a simple model of a spherically symmetric stellar wind from the companion star.     

The Restricted Three-Body Problem: Comments on the Rotational Effect

The synchronization between the orbital motion and axial rotation of the two component stars of a binary system is reviewed. Some previous published papers are mentioned and the general conclusion is outlined: If we shall use a rotating coordinate system synchronous with one of the two stellar axial rotations, it is not possible to obtain a Jacobi integral and the Roche geometry cannot be further analyzed. In addition, a theoretical approach is summarized in order to use the axial rotations of the two component stars, even if the constants of the stellar structure (k₂)₁, (k₂)₂must be taken into consideration. So it is found that if the stellar angular velocities are higher than the corresponding Keplerian angular velocity (ω_i≫ ω_k, i= ), the problem of the rotational effect could be of practical consideration. Finally, a theoretical relationship between the two constants (k₂)₁and (k₂)₂of the stellar structure is established.     

On synchronism between axial rotation and orbital motion in close binary systems

In this paper we examine the possible outcome of the tidal evolution of a close binary system using a method from which the outline has already been given by Counselman (1973). If the value of the total angular momentum of the system is sufficiently large, two equilibrium states corresponding to synchronism between stellar rotation and orbital motion are possible. In one of these states the total energy attains no extreme value. The considered evolution can be visualized geometrically by the motion of a point along a hyperbolic cylinder in three-dimensional space. A comparison with some observational data reveals that most of the synchronously rotating detached systems have attained a stable equilibrium state of minimum total energy for the given value of total angular momentum.     

Tidal torque constants as a critical test for an evolution of close eclipsing binaries

Individual tidal torque λ ₂,E ₂ and apsidal-motion k ₂ constants were calculated for 112 close eclipsing binaries (CEBs) with Detached components belonging to the Main Sequence (DMS-type) from the catalogue by Svechnikov and Perevozkina (Catalogue of orbital elements, masses and luminosities of variable stars of DMS-type and some results of its statistical treatment, Ural State University Press, Yekaterinburg, pp. 1–5, 1999) and for 95 detached binaries taken from the catalogue by Torres et al. (Astron. Astrophys. Rev. 18:67, 2010) on the base of theoretical evolutionary stellar models including tidal torque constants by Claret (Astron. Astrophys. 424:919, 2004). A method of the inversion of model track grid into isochrones was formulated as a complex interpolation procedure for DMS-binaries data. Sets of isochrones were computed in k ₂–M, k ₂–R, λ ₂–M, λ ₂–R, E ₂–M, and E ₂–R planes. Calculated tidal torque constants allow to test stellar structure theory by comparing observed and estimated values of apsidal motion period and analyzing the correlation between timescales of synchronization, circularization, magnetic braking, as well as nuclear burning of DMS-components.     

A steady-state model of NEA binaries formed by tidal disruption of gravitational aggregates

We present results of a simulation of a steady-state binary near-Earth asteroid (NEA) population. This study combines previous work on tidal disruption of gravitational aggregates [Walsh, K.J., Richardson, D.C., 2006. Icarus 180, 201-216] with a Monte Carlo simulation of NEA planetary encounters. Evolutionary effects include tidal evolution and binary disruption from close planetary encounters. The results show that with the best known progenitor (small Main Belt asteroids) shape and spin distributions, and current estimates of NEA lifetime and encounter probabilities, that tidal disruption should account for approximately 1-2% of NEAs being binaries. Given the best observed estimate of a ∼15% binary NEA fraction, we conclude that there are other formation mechanisms that contribute significantly to this population. We also present the expected distribution of binary orbital and physical properties for the steady-state binary NEAs formed by tidal disruption. We discuss the effects on binary fraction and properties due to changes in the least constrained parameters, and other possible effects on our model that could account for differences between the presented results and the observed binary population. Finally, we model possible effects of a significant population of binaries migrating to the near-Earth population from the Main Belt.     

Effect of radiation on the stability of equilibrium points in the binary stellar systems: RW-Monocerotis,Krüger 60

We have studied the stability of location of various equilibrium points of a passive micron size particle in the field of radiating binary stellar system within the framework of circular restricted three body problem. Influence of radial radiation pressure and Poynting-Robertson drag (PR-drag) on the equilibrium points and their stability in the binary stellar systems RW-Monocerotis and Krüger-60 has been studied. It is shown that both collinear and off axis equilibrium points are linearly unstable for increasing value of β ₁ (ratio of radiation to gravitational force of the massive component) in presence of PR-drag for the binary systems. Further we find that out of plane equilibrium points (L _i , i=6,7) may exists for range of values of β ₁>1 for these binary systems in the presence of PR-drag. Our linear stability analysis shows that the motion near the equilibrium points L _6,7 of the binary systems is unstable both in the absence and presence of PR-drag.     

First multi-color photometric investigation of the shortest-period semi-detached binary SWASPJ222302.02+195031.8

SuperWASPJ222302.02+195031.8 is an eclipsing binary with an orbital period about 0.22517657 days that is close to the short-period limit of contact binaries. Multi-color photometric light curves of the short-period binary in B, V, R_c and I_c bands are presented and analyzed by using the Wilson–Devinney (W–D) method. It is discovered that the system is a semi-detached binary where the secondary component is already filling the critical Roche lobe, while the primary is filling just 77.1% of its Roche lobe. The temperature of the primary is about 4300 K, and the temperature difference between the two components is about 500 K. The asymmetries in the light curves are explained by the coverage of stellar dark spots on the less massive component via magnetic activity. An analysis of all available eclipse times suggests that there are no any changes in the O-C diagram. This may indicate that there are no mass transfers between the two components. The semi-detached configuration with the dark spot on the surface of the lobe-filling secondary and no variations in the orbital period make the binary an interesting target for further investigations.     

Evolutionary Processes in Low-Mass Binary Systems

We consider the evolution of certain low-mass binaries, incorporating models of (a) internal evolution, (b) tidal friction, (c) dynamo activity driven by an elementary α,Ω dynamo, (d) stellar wind driven by the activity, and (e) magnetic braking as a consequence of wind and poloidal dynamo-generated magnetic field. In some circumstances the stellar wind is found to remove mass on a nuclear timescale, as is necessary to explain some observed systems. We can hope that various uncertainties in the model may be clarified by a careful comparison of the models with such observed quantities as rotation periods. These are modified by processes (a), (b) and (e). Assuming that stellar evolution is slow, rotation rate should in some circumstances represent a balance between magnetic braking trying to slow the star down and tidal friction trying to spin it up. Preliminary attempts are promising, but indicate that some fine tuning is necessary. When there is a third body present, in an orbit which is inclined but not necessarily of short period, the eccentricity of a close binary can be strongly modified by ‘Kozai cycles’. We show that this may complicate attempts to account for spin rates of stars in close binaries.     

Tidal dwarf galaxies in the Stephan's Quintet?

We present kinematics and photometric evidence for the presence of seven candidate tidal dwarf galaxies in Stephan's Quintet. The central regions of the two most probable parent galaxies, NGC 7319 and NGC 7318B, contain little or no gas whereas the intragroup medium and, in particular, the optical tails that seem to be associated with NGC 7318B are rich in cold and ionized gas. Two tidal dwarf candidates may be located at the edge of a tidal tail, another located within a tail, and for the four others there is no obvious stellar/gaseous bridge between them and the parent galaxy. Two of the candidates are associated with H I clouds, one of which is, in addition, associated with a CO cloud. All seven regions have low continuum fluxes and high Hα luminosity densities [F(Hα) = (1-60) × 10-14 ergs s^-1 cm^-2]. Their magnitudes (M_B = –16.1 to –12.6), sizes (∼ 3.5 h₇₅ ^-1 kpc), colors (typically B – R = 0.7), and gas velocity gradients (∼ 8 –26 h₇₅ km s^-1 kpc^-1) are typical for tidal dwarf galaxies. In addition, the ratios between their star formation rates determined from Hα and from the B-band luminosity are typical of other tidal dwarf galaxies. The masses of the tidal dwarf galaxies in Stephan's Quintet range from ∼ 2 × 10⁸ to 10¹⁰ M_⊙, and the median value for their inferred mass-to-light ratios is 7 (M/L)_⊙. At least two of the systems may survive possible ‘fallbacks’ or disruption by the parent galaxies and may already be, or turn into, self-gravitating dwarf galaxies, new members of the group. This revised version was published online in September 2006 with corrections to the Cover Date.     

Tidal disruption of stars by a massive black hole

The hydrodynamics of stellar models in the tidal field of a massive black hole is calculated numerically under certain simplifying assumptions. It is found that solar type stars are totally disrupted only when falling toward a black hole whose mass does not exceed 10⁶–10⁷ M . Red giants lose their entire envelope for all black hole masses studied.Our findings strengthen the view that tidal disruption is not an important source of gas in AGN's.     

Modulation of circumstellar extinction in a young binary system with a low-mass companion in a noncoplanar orbit

We consider a model of cyclic brightness variations in a young star with a low-mass (q = M ₂/M ₁ ≤ 0.1) companion that accretes matter from the remnants of a protostellar cloud (circumbinary disk). We assume that the orbit of the companion is circular and that its plane does not coincide with the disk plane. We have computed grids of hydrodynamic models for such a binary by the SPH method based on which we have investigated the circumstellar extinction variations produced by the streams of matter and density waves excited in the circumbinary disk by the orbital motion of the companion. We show that, depending on the inclination and orientation of the binary’s line of nodes relative to the observer, the brightness of the primary component can undergo various (in shape and depth) oscillations with a period equal to the orbital one. In contrast to the models with coplanar circular orbits, the accretion rate onto the components of a binary with a noncoplanar orbit depends on the orbital phase. The results of our computations can be used to study the cyclic activity of UX Ori stars and young eclipsing binaries with anomalously long eclipses.     

Stability of strange dwarfs. I. Static criterion for stability. Statement of the problem

This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M _0core /M _⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ _c and the energy density ρ _tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ _c and ρ _tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M ₀ (total baryon number) of the quark core and different masses of the crust. In each series, ρ _tr ranges from the value for white dwarfs to ρ _drip = 4.3∙10¹¹ g/cm³, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ _tr . Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009).     

Equilibrium Structures of Differentially Rotating Primary Components of Binary Stars

In this paper a method is proposed for computing the equilibrium structures and various other observable physical parameters of the primary components of stars in binary systems assuming that the primary is more massive than the secondary and is rotating differentially about its axis. Kippenhahn and Thomas averaging approach (1970) is used in a manner earlier used by Mohan, Saxena and Agarwal (1990) to incorporate the rotational and tidal effects in the equations of stellar structure. Explicit expressions for the distortional terms appearing in the stellar structure equations have been obtained by assuming a general law of differential rotation of the typeω² = b ₀+b ₁ s ²+b ₂ s ⁴, where ω is the angular velocity of rotation of a fluid element in the star at a distance s from the axis of rotation, and b ₀, b ₁, b ₂ are suitably chosen numerical constants. The expressions incorporate the effects of differential rotation and tidal distortions up to second order terms. The use of the proposed method has been illustrated by applying it to obtain the structures and observable parameters of certain differentially rotating primary components of the binary stars assuming the primary components to have polytropic structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of periodic perturbations in the multiple system ADS 15571

The visual binary star ADS 15571 has been observed with the 26″ refractor at Pulkovo since 1960. Periodic perturbations in the relative motion of the components are studied in this paper. The visible motion of the component B was resolved into orbital motion of the barycenter relative to component A and an elliptical motion of the photocenter relative to the barycenter. The visible ellipse of the photocenter motion is used to determine the elements of the orbit by the direct geometric method of A. A. Kiselev and estimate the perturbing mass. The minimum mass of the invisible companion is 0.62 M_⊙. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 467–474 (August 2006).     

The cyclical reversible transitions of the universe’s evolution

In this work we propose cyclical reversible transitions as the scenario in which the universe evolves, through a series consisting of reversible expansion, temporary stability, and contraction. Our model is based on the comparison between local and global time-dependent densities {ρ ₀(τ ₀),ρ(τ)} instead of the critical density ρ _c, local and global time-dependent Hubble parameters {H ₀(τ ₀),H(τ)}, and the variations {Δρ(τ),ΔH(τ)} due to cosmological chaotic fluctuations, which are generally ignored in certain oscillating models. By taking into account all these factors, a rate equation in the form of (H ₀/H)² ∝(ρ ₀/ρ) has been established, and from it we derive some others, to provide a mechanism that is responsible for the cyclical reversible transitions. Also, the problems of singularities, black hole overproduction, and the second law of thermodynamics arising in oscillating universe models are conceptually resolved.     

Robe’s problem: its extension to 2+2 bodies

In the problem of 2+2 bodies in the Robe’s setup, one of the primaries of mass m^*₁m^{*}_{1} is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ ₁. The second primary is a mass point m ₂ outside the shell. The third and the fourth bodies (of mass m ₃ and m ₄ respectively) are small solid spheres of density ρ ₃ and ρ ₄ respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal. We assume m ₂ is describing a circle around m^*₁m^{*}_{1}. The masses m ₃ and m ₄ mutually attract each other, do not influence the motion of m^*₁m^{*}_{1} and m ₂ but are influenced by them. We also assume masses m ₃ and m ₄ are moving in the plane of motion of mass m ₂. In the paper, the equations of motion, equilibrium solutions, linear stability of m ₃ and m ₄ are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are unstable for all values of the mass parameters μ,μ ₃,μ ₄. There exist an infinite number of non collinear equilibrium solutions each for m ₃ and m ₄, lying on circles of radii λ,λ′ respectively (if the densities of m ₃ and m ₄ are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ ₃,μ ₄, φ, φ′. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon.     

The chromospherically active binary star EI Eridani: I. Absolute dimensions

We present a detailed determination of the astrophysical parameters of the chromospherically active binary star EI Eridani. Our new radial velocities allow to improve the set of orbital elements and reveal long‐term variations of the barycentric velocity. A possible third‐body orbit with a period of ≈19 years is presented. Absolute parameters are determined in combination with the Hipparcos parallax. EI Eri's inclination angle of the rotational axis is confined to 56°.0 ± 4°.5, ist luminosity class IV is confirmed by its radius of 2.37 ± 0.12 R_⊙. A comparison to theoretical stellar evolutionary tracks suggests a mass of 1.09 ± 0.05 M_⊙ and an age of ≈ 6.15 Gyr. The present investigation is the basis of our long‐term Doppler imaging study of its stellar surface (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)