Dynamical effects of mass exchange in close binary systems

The problem of mass exchange in a close binary system is studied from the point of view of the evolution of the orbital elements. It is assumed that the original orbit is nearly circular and one of the components has expanded and fills the area inside the equipotential surface passing through the inner Lagrangian pointL ₁, losing mass to the other component. The mass is assumed to be ejected along the tangent to the equipotential surface passing throughL ₁ in retrograde orbits.It is proved that the eccentricity remains very small. The semimajor axis increases in almost all cases where the mass is being transferred from the less massive to the more massive component, and decreases when the mass is being transferred from the more massive to the less massive component. It is also shown that if the more massive star evolves first and loses mass to its companion, the process of mass exchange continues automatically until the originally more massive component becomes the less massive one and the binary system remains in an almost static condition for long intervals of time, the less massive component occupying the area inside the equipotential surface passing throughL ₁ and surrounding the star.     

The dimensions of gaseous rings in Close Binary Systems

The observational data seem to indicate that the upper limit of the dimensions of gaseous rings in Close Binary Systems coincides with the upper boundary of the domain of stability of singly periodic orbits around the component in question. As was shown by Kruszewski, the lower limit is determined by the amount of angular momentum carried by the mass particles ejected near the Lagrangian pointL ₁ from the surface of the companion.     

Stability of fictitious Trojan planets in extrasolar systems

Our work deals with the dynamical possibility that in extrasolar planetary systems a terrestrial planet may have stable orbits in a 1:1 mean motion resonance with a Jovian like planet. We studied the motion of fictitious Trojans around the Lagrangian points L₄/L₅ and checked the stability and/or chaoticity of their motion with the aid of the Lyapunov Indicators and the maximum eccentricity. The computations were carried out using the dynamical model of the elliptic restricted three‐body problem that consists of a central star, a gas giant moving in the habitable zone, and a massless terrestrial planet. We found 3 new systems where the gas giant lies in the habitable zone, namely HD99109, HD101930, and HD33564. Additionally we investigated all known extrasolar planetary systems where the giant planet lies partly or fully in the habitable zone. The results show that the orbits around the Lagrangian points L₄/L₅ of all investigated systems are stable for long times (10⁷ revolutions). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of Co-Orbital Motion in Exoplanetary Systems

The stability of co-orbital motions is investigated in such exoplanetary systems, where the only known giant planet either moves fully in the habitable zone, or leaves it for some part of its orbit. If the regions around the triangular Lagrangian points are stable, they are possible places for smaller Trojan-like planets. We have determined the nonlinear stability regions around the Lagrangian point L₄ of nine exoplanetary systems in the model of the elliptic restricted three-body problem by using the method of the relative Lyapunov indicators. According to our results, all systems could possess small Trojan-like planets. Several features of the stability regions are also discussed. Finally, the size of the stability region around L₄ in the elliptic restricted three-body problem is determined as a function of the mass parameter and eccentricity.     

Effects of local thermodynamics and of stellar mass ratio on accretion disc stability in close binaries

Inflow kinematics at the inner Lagrangian point L1, gas compressibility, and physical turbulent viscosity play a fundamental role on accretion disc dynamics and structure in a close binary (CB). Physical viscosity supports the accretion disc development inside the primary gravitational potential well, developing the gas radial transport, converting mechanical energy into heat. The Stellar‐Mass‐Ratio (SMR) between the compact primary and the secondary star (M₁/M₂) is also effective, not only in the location of the inner Lagrangian point, but also in the angular kinematics of the mass transfer and in the geometry ofthe gravitational potential wells. In this work we pay attention in particular to the role ofthe SMR, evaluating boundaries, separating theoretical domains in compressibility‐viscosity graphs where physical conditions allow a well‐bound disc development, as a function ofmass transfer kinematic conditions. In such domains, the lower is the gas compressibility (the higher the polytropic index γ), the higher is the physical viscosity (α) requested. In this work, we show how the boundaries of such domains vary as a function of M₁/M₂. Conclusions as far as dwarf novae outbursts are concerned, induced by mass transfer rate variations, are also reported. The smaller M₁/M₂, the shorter the duration of the active‐to‐quiet and vice‐versa transitional phases. Time‐scales are of the order of outburst duration of SU Uma, OY Car, Z Cha and SS Cyg‐like objects. Moreover, conclusions as far as active‐quiet‐active phenomena in a CB, according to viscous‐thermal instabilities, in accordance to such domains, are also reported (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mass-luminosity relation for massive stars

A catalog of massive (⩾10 M _⊙) stars in binary and multiple systems with well-known masses and luminosities has been compiled. The catalog is analyzed using a theoretical mass-luminosity relation. This relation allows both normal main-sequence stars and stars with peculiarities: with clear manifestations of mass transfer, mass accretion, and axial rotation, to be identified. Least-squares fitting of the observational data in the range of stellar masses 10M _⊙ ⩽ M ≲ 50 M _⊙ yields the relation L ∼ M ^2.76. An erratum to this article is available at .     

Analytic formulas for the mass-transfer rate and the evolution of a close binary system of neutron (degenerate) stars

We derive approximate analytic relations between the mass-transfer rate in a close binary system described in terms of the Roche potential and its basic parameters, such as the total mass of the binary, the radius of its circular orbit, the mass of the mass-losing component, and the degree of its Roche lobe overfilling. Using simplifying assumptions (conservative mass transfer, a short relaxation time of matter on the mass-gaining component compared to the mass-transfer time scale, adiabaticity and quasi-stationarity of the mass flow through the Lagrangian point L ₁) allows the evolution of a binary system of neutron (degenerate) stars to be described in terms of two ordinary differential equations. This makes it possible to qualitatively analyze the evolution process, which is useful in those cases where the evolution of a close binary system must be investigated in general terms, for example, in terms of the scenario for the transformation of the collapse of a rotating presupernova core into a supernova explosion proposed by Imshennik and Nadyozhin (1992) and Imshennik (1992).     

Case a evolution of massive close binary systems

The evolution of three close binary systems of total mass 20.4M in and after the phase of mode Br mass-transfer in caseA of mass exchange is investigated. In every case a secondary component evolves to interfere with the progress of primary's evolution and the system overflows the outer critical surface before the primary completes its nuclear-burning evolution. This strongly indicates the importance of simultaneous calculation of both components. A summary of evolution of the systems considered in this series of papers up to the stage ofL ₂-overflow is given. The observational aspects of the numerical models are also discussed.     

CK Bootis: a W UMa system with a small mass ratio

We present an analysis of BV R light curves of an eclipsing binary CK Bootis, a system with a very small mass ratio. The light curves appear to exhibit a typical O'Connell effect. The light curves are analyzed by means of the latest version of the WD program. The asymmetry of the light curves is explained by a cool star spot model. The simultaneous BV R synthetic light curve analysis gives a tiny mass ratio of 0.12, an extremely large fill‐out factor of 0.65, and a very small difference between the component temperatures of 90 K. The absolute parameters of the system were also derived by combining the photometric solutions with the radial velocity data. The mass of the secondary is very low (0.15 M_⊙) and it continues losing mass. Thirty seven new times of minimum are reported. It is found that the orbital period of the system has a quasi periodic variation, superimposed on a period increase. The long‐term period increase rate is deduced to be dP/dt = 3.54x10^–7 d yr^–1, which can be interpreted as being due to mass transfer from the less massive star to the more massive component. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The elliptical three-body problem. Triangular solution

The restricted three-body problem with eccentric orbit is reviewed and the positions of the triangular Lagrangian points (L₄, L₅) are determined. It is put in evidence the fact the fact L₄ and L₅ are situated at the corners of an isoscales triangle: AB = BC = 1 − e²/)1 + e cos ν )4/3 and AC = 1 − e²/)1 + e cos ν )     

First light curve and period study of LO Andromedae

New BV light curves and times of minimum light for the short period W UMa system LO And were analyzed to derive the preliminary physical parameters of the system. The light curves were obtained at Ankara University Observatory during 5 nights in 2003. A new ephemeris is determined for the times of primary minimum. The analysis of the light curves is made using the Wilson‐Devinney 2003 code. The present solution reveals that LO And has a photometric mass ratio q = 0.371 and is an A‐type contact binary. The period of the system is still increasing, which can be attributed to light‐time effect and mass transfer between the components. With the assumption of coplanar orbit of the third body the revealed mass is M₃ = 0.21M_⊙. If the period change dP/dt = 0.0212 sec/yr is caused only by the mass transfer between components (from the lighter component to the heavier) the calculated mass transfer rate is dm/dt = 1.682×10⁻⁷M_⊙/yr. The absolute radii and masses estimated for the components, based on our photometric solution and the absolute parameters of the systems which have nearly same period are R₁ = 1.30R_⊙, R₂ = 0.85R_⊙, M₁ = 1.31M_⊙, M₂ = 0.49M_⊙ respectively for the primary and secondary components. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Further confirmations of mass transfer in Algol type binary U Sagittae

This paper describes how a new photometric V light curve solution of Algol type binary U Sge was obtained using Wilson–Devinney code. I also discuss how the physical and orbital parameters, along with absolute dimensions of the system, were determined. The Roche lobe configurations of the system indicate that the secondary component has filled its Roche lobe and therefore is losing mass at the rate of 6.15×10⁻⁷ M _sun yr⁻¹. The conservative mass flow is the most likely process in this system.     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

V 361 Lyrae: An exotic binary system with a “Hot Spot” between the components?

A phenomenological model for V 361 Lyr is proposed. Probably it is a binary system which consists of a mass accreting primary star with mass of about M₁ ≈ 0·81 M⊙ and radius R₁ ≈ (6.1 ± 0·4) · 10¹⁰ cm and a mass losing secondary with about M₂ ≈ 0·77 M⊙ and R₂ ≈ 5.8 · 10¹⁰ cm. The secondary fills its Roche lobe, but the primary is something smaller than this lobe, contrary to the models of W UMa-type systems. So the hot spot appears in the atmosphere of the primary, but not in a disk, like in cataclysmic variables. The luminosity of the hot spot, L = (6-15) · 10³² erg/s, is large enough to be the main emission source of the system in visible light. So phenomenologically the object may be somewhat between W UMa-type stars and cataclysmic variables.     

A new light on the L 1, L 2 Lagrangian points

The relation between the locations of L ₁, L ₂ Lagrangian points and the boundary to their respective satellite system is brought forth, in that, the Lagrangian points L ₁, L ₂ are seen to lie just on the boundary to their respective satellite system.     

Doppler tomography of Algols

The technique of Doppler tomography has been influential in the study of mass transfer in Algol‐type interacting binaries. The Algols contain a hot blue dwarf star with a magnetically‐active late‐type companion. In the close Algols, the gas stream flows directly into the photosphere of the blue mass‐gaining star because it does not have enough room to avoid impact with that star. Doppler tomograms of the Algols have been produced from over 2500 time‐resolved spectra at wavelengths corresponding to Hα, Hβ, He I (6678 Å), Si II (6371 Å) and Si IV (1394 ° A). These tomograms display images of accretion structures that include a gas stream, accretion annulus, accretion disk, stream‐star impact region, and occasionally a source of chromospheric emission associated with the cool, mass‐losing companion. Some Algol systems alternate between streamlike and disk‐like states, and provide direct evidence of active mass transfer within the Algols. This work produced the very first images of the gas stream for the entire class of interacting binaries, and demonstrated that the Algols are far more active than formerly believed, with variability on time scales of weeks to months. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The origin of the emission lines shown by RW Tauri and other binary systems

It is proposed that the observed double-component emission lines originate from the triangular Lagrangian points, L4 and L5, of the restricted three-body problem. The light curves of many close binary systems show absorption dips at ±60° of the primary (and sometimes also the secondary) minimum, indicating appreciable accumulation of matter at these points. The orbital velocity of L4 and L5 is derived as a function of period and the masses of the component stars. This equation is an independent relationship for determining the two stellar masses. It also reproduces Struve's empirical finding ofV ³P ^–1. The observed emission line velocity is consistently higher than the calculated orbital velocity of L4 and L5. This is due to the serious erosion of the low velocity sides of the emission components by the stellar and shell absorption lines. There are observational evidences which indicate the intermittent high velocity radial ejection of matter to be a mode of mass loss from the secondary. And the energy of mass motion from this ejection is sufficient, and may be responsible, for heating the gas at L4 and L5. The ionizing radiation emitted by the primary of the Algol systems is many orders of magnitude below that required by the observed strength of the emission lines. Some related discussion is also given to nova and dwarf nova systems.     

The effect of solar radiation pressure on the Lagrangian points in the elliptic restricted three-body problem

In this paper the effect of solar radiation pressure on the location and stability of the five Lagrangian points is studied, within the frame of elliptic restricted three-body problem, where the primaries are the Sun and Jupiter acting on a particle of negligible mass. We found that the radiation pressure plays the rule of slightly reducing the effective mass of the Sun and changes the location of the Lagrangian points. New formulas for the location of the collinear libration points were derived. For large values of the force ratio β, we found that at β=0.12, the collinear point L₃ is stable and some families of periodic orbits can be drawn around it.     

Accretion in Strong Gravity: from Galactic to Supermassive Black Holes

The galactic black hole binary systems give an observational template showing how the accretion flow changes as a function of increasing mass accretion rate, or L/L_Edd. These data can be synthesised with theoretical models of the accretion flow to give a coherent picture of accretion in strong gravity, in which the major hard-soft spectral transition is triggered by a change in the nature and geometry of the inner accretion flow from a hot, optically thin plasma to a cool, optically thick accretion disc. However, a straightforward application of these models to AGN gives clear discrepancies in overall spectral shape. Either the underlying accretion model is wrong, despite its success in describing the Galactic systems and/or there is additional physics which breaks the simple scaling from stellar to supermassive black holes.