Variations in the orbital periods of the Algol-type eclipsing binaries RZ Cas and Z Dra

A detailed study of variations of the orbital periods of the Algol-type eclipsing binary systems RZ Cas and Z Dra is presented. The fairly complex variations of the periods of both systems can be represented as a superposition of a secular increase of the period, slow periodic fluctuations, and quasiperiodic oscillations with a small amplitude occurring on timescales of decades. The secular increase of the period can be explained by the steady mass transfer from the less massive to the more massive component with conservation of the total angular momentum. The mass-transfer rate is 5.7 × 10^?9M_⊙/yr for RZ Cas and 3.0×10^?8M_⊙/yr for Z Dra. To explain the long-period cyclic variations of the orbital periods of RZCas and Z Dra, it must be assumed that the eclipsing binaries move in long-period orbits. RZ Cas moves with a period of 133 yr around a third body withmass M₃ > 0.55M_⊙, while Z Dra moves with a period of 60 yr around a third body with mass M₃ > 0.7M_⊙. The residual fluctuations of the periods may be due to a superposition of variations due to magnetic cycles and non-stationary ejections of matter.     

The Light-time Effect in the Eclipsing Binaries with Early-type Components U CrB and RW Tau

A detailed study of the orbital-period variations of the Algol-type eclipsing binaries with earlyspectral- type primary components U CrB and RW Tau has been performed. The period variations in both systems can be described as a superposition of secular and cyclic variations of the period. A secular period increase at a rate of 2.58^d × 10^?7/year is observed for U CrB, which can be explained if there is a uniform flow of matter from the lower-mass to the higher-mass component, with the total angular momentum conserved. RW Tau features a secular period decrease at a rate of ?8.6^d × 10^?7/year; this could be due to a loss of angular momentum by the binary due to magnetic braking. The cyclic orbital-period variations of U CrB and RWTau can be explained by the motion of the eclipsing binary systems along their long-period orbits. In U CrB, this implies that the eclipsing binary moves with a period of 91.3 years around a third body with mass M₃ > 1.13M_⊙; in RW Tau, the period of the motion around the third body is 66.6 years, and the mass of the third body is M₃ > 1.24M_⊙. It also cannot be ruled out that the variations are due to the magnetic cycles of the late-type secondaries. The residual period variations could be a superposition of variations due to non-stationary ejection of matter and effects due to magnetic cycles.     

The probable quadruple systems FK Aql and FZ Del

Orbital-period variations of the eclipsing binaries FK Aql and FZ Del are analyzed. For each of the systems, a superposition of two cyclic variations of their orbital periods is found. FK Aql may be a quadruple system that contains two more bodies, besides the eclipsing binary, with masses M ₃ ? 1.75M _⊙ and M ₄ ? 1.47M _⊙, and the corresponding periods 15 and 82 yrs. This could also be a triple system with a third body of mass M ₃ ? 1.75M _⊙ and a period of the long-period orbit P ₃ = 15 yrs, or with a third body of mass M ₃ ? 1.30M _⊙ and a period of the long-period orbit P ₃ = 82 yrs. FZ Del may be a quadruple system with the additional componentmasses M ₃ ? 0.2M _⊙ and M ₄ ? 0.3M _⊙, with the periods 10.2 and 53.7 yrs. This could also be a triple system with a third-body mass M ₃ ? 0.2M _⊙ and a period of the long-period orbit P ₃ = 10.2 yrs. In both systems, the residual period variations could be due to magnetic cycles of the secondary. The period variations of the eclipsing binary FZ Del could also be due to apsidal motion, together with the influence of a third body or the effects of magnetic activity.     

Orbital-period variations of the close binaries with late-type components TY Del and RY Cnc

A detailed study of orbital-period variations was performed for TY Del and RY Cnc, which are both Algol-type eclipsing binaries with late-type second aries; for RY Cnc, this is the first study of this kind. The period variations of both stars can be considered a superposition of a secular period increase and cyclic changes of this period. The secular period increase can be explained as the effect of a uniform transfer of mass from the lower-mass to the higher-mass component, with the total angular momentum conserved. The mass-transfer rate is about 1.25 × 10^⊙ M _⊙/year for TY Del and (0.68?1.02) × 10^?8 M _⊙/year for RY Cnc. The cyclic period variations of the eclipsing binaries TY Del and RY Cnc could be due to either the presence of a third body in the system or the influence of magnetic activity of the secondary.     

Orbital period variations of the eclipsing binaries TU Cnc,VZ Leo,and OS Ori

Variations of the orbital periods of the eclipsing binaries TU Cnc, VZ Leo, and OS Ori are analyzed. Secular period decreases were earlier believed to occur in these systems. It is demonstrated that the period variations of TU Cnc can be represented using the light-time effect corresponding to the orbital motion of the eclipsing binary with a period of 78.6 years around the center ofmass of the triple system, with the mass of the third body being M ₃ > 0.82M _⊙. With the same accuracy, the period variations of VZ Leo and OS Ori can be represented either solely using the light-time effect, or a superposition of a secular period decrease and the light-time effect. For VZ Leo, the period of the long-term orbit is 63.8 years in the former case and 67.9 years in the latter case. Similar masses for the third body are indicated in both cases: M ₃ > 0.55M _⊙ and M ₃ > 0.61M _⊙. For OS Ori, the period of the long-term orbit is 46 years and M ₃ > 0.5M _⊙ in the former case, and the period is 36 years and M ₃ > 0.6M _⊙ in the latter case.     

The physical parameters and orbit of the eclipsing binary system GSC 4596 1254 = SAO 3282

We have obtained the first U BV R photoelectric light curves for a recently discovered eclipsing binary with a period of 9.33 ^d and an appreciable eccentricity (e = 0.08). We have used these data to determine the photometric elements of the system for a model with two spherical stars with linear limb darkening. The high accuracy of the observations enabled determination of the absolute parameters of the components using available calibrations. The masses of the components are 1.28 and 1.08 M _⊙, and their ages are two billion years. The present orientation of the orbital ellipse is unfavorable for studies of the apsidal rotation, which is essentially due to relativistic effects.     

Neutron stars in close binaries with elliptical component orbits

We consider the evolution of close binaries in which the initial secondary component is a nondegenerate helium star with mass M_He = 0.4–60 M_⊙, while the initially more massive primary has evolved into a black hole, neutron star, or degenerate dwarf. The neutron star is assumed to originate as a result of the evolution of a helium star with a mass of 2.5 M_⊙ ≤ M_He ≤ 10 M_⊙ after the explosion of a type Ib,c supernova. If the axial rotation of the helium star before the explosion is rigid-body and synchronized with the orbital rotation, for P_orb ≤ 0.16 day, the rotational energy of the young neutron star will exceed the energy of an ordinary supernova. If the magnetic field of the neutron star is sufficiently strong, the necessary conditions for a magnetic-rotational supernova are provided. The initial rotational period of a young neutron star originating in a system with an orbital period shorter than ～50 days is shorter than ～4 s, which, according to observations, is required for the appearance of a radio pulsar. A helium star whose mass exceeds ～10 M_⊙ in a close binary with an orbital period shorter than one day and with the axial rotation of the helium presupernova synchronous with the orbital rotation evolves into a Kerr black hole, whose formation is likely to be accompanied by a gamma-ray burst with a duration longer than two seconds. In particular, we consider close binaries in which the second supernova results in the formation of a neutron star that remains in the binary. The theoretical distribution of orbital periods and eccentricities for such systems is consistent with that observed for radio pulsars in the Galactic disk in binaries with compact components and orbital eccentricities exceeding ～0.09, providing an explanation for the observed correlation between the orbital eccentricities and orbital periods for these systems.     

Orbital-period variations of the Algol-type eclipsing binaries RW CrB and AO ser

Orbital-period variations of the Algol-type eclipsing binaries RW CrB and AO Ser are analyzed. It is shown that the period variations of these systems are due mainly to the light-time effect due to the eclipsing binary’s motion in its long-period orbit. The period variations of RW CrB are reproduced by motion of the eclipsing binary with a period of 55.8 years around a third body with the mass M ₃ > 0.36M⊙. The period variations of AO Ser can be reproduced either solely with the light-time effect, or by a superposition of the light-time effect and a slow secular decrease in the period. In the former case, the period of the long-period orbit is 111.5 years; in the latter case, it is 108 years. Both cases imply the same mass for the third body in the AO Ser system: M ₃ > 0.35M⊙. The residual small-amplitude orbitalperiod variations of the two systems can be due to magnetic cycles.     

Photometry and spectroscopy of CI camelpardalis from 1998–2005

Our long-time monitoring of the B[e] star and transient X-ray source CI Cam during quiescence following the 1998 outburst demonstrates that the complex, stratified circumstellar envelope has tended to stabilize after this structure was perturbed by the passage of a shock wave from the outburst. The star’s U BV R brightness shows slow, possibly cyclic, variations with an amplitude of about 0.2^m. We determined the spectral type of the primary, B4III-V, based on the widths of the absorption wings of high-numbered Balmer lines. A Doppler shift of 460 km/s was detected for the Hell λ4686 Å emission line. The shifts in this line yield an orbital period of 19.41 days, which is also manifested itself in the photometric data as a wave with a V amplitude of 0.034^m. The orbit is elliptical, with an eccentricity of 0.62. It is most likely that the secondary is a white dwarf surrounded by an accretion disk. The primary’s mass exceeds 12 M _⊙ . The system may be at a late stage of its evolution, after the stage of mass exchange.     

The eclipsing variable CM Dra: Surface activity and orbital elements

A long series of observations of the low-mass eclipsing system CM Dra (M ₁, M _⊙<0.25M _⊙, dM4.5e, V=12.9^m, P _orb=1.27^d) was obtained in 1996–1997 as part of the international TEP (Search for Transits of Extrasolar Planets) project. The observations were obtained on the 70-cm telescope of the Astronomical Observatory of Ural State University with an automatic two-star photometer. The total duration of the data series was 155 h. We construct and analyze a master light curve, including calculation of the photometric and absolute orbital elements. Evidence for surface activity was detected. The light curve of CM Dra outside eclipses shows low-amplitude (0.024^m) brightness variations, suggesting the presence of a starspot on one of the components. The amplitude of these variations stayed the same over 20 years, but the phase of the brightness maximum shifted by one-third of the orbital period, possibly reflecting changes in the longitude or asymmetry of a single large polar spot. We detected four flares whose energies were factors of several hundred higher than those of solar flares. The derived flare rate agrees with data for CM Dra in the literature but is much lower than is typical for Population I stars in our Galaxy.     

Three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr

We present a three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr taking radiative cooling into account explicitly. The assumed mass-transfer rate through the first Lagrangian point L₁ is 3.0 × 10^?5 M _⊙/yr. A flow with a radius of 0.14–0.16 (in units of orbital separation) is formed in the vicinity of L₁. This flow forms an accretion disk with a radius close to 23 R _⊙ and a thickness of about 10 R _⊙. The accretion disk is surrounded by an outer envelope that extends beyond the computational domain. A spiral shock forms at the outer boundary of the disk at orbital phase 0.25. Geometrically, the disk is toruslike, while the outer envelope is cylinder-like. In this model, which has low temperatures inside the computational domain, no jetlike structures form in the disk. It is possible that the jetlike structure in β Lyr arises due to the interaction of radiative wind from the accretor with the flow from L₁. In the model considered, a hot region exists over the poles of the accretor at a height of about 0.21. The amount of matter lost by the system is close to 10% of the mass flowing through L₁; i.e., the mass transfer in the system is almost conservative. For a mass-transfer rate of 3.0 × 10^?5 M _⊙/yr, the orbital period varies by 40.4 s/yr. This means that the observed variation of the orbital period of 19 s/yr should correspond to a mass-transfer rate close to 1.0 × 10^?5 M _⊙/yr.     

The eclipsing binary HS hercules: Photometric elements and the evolutionary stages of its components

We used a photoelectric photometer designed by V.M. Lyutyi and the Zeiss-600 telescope of the Sternberg Astronomical Institute’s Crimean Observatory to acquire precise UBV brightness measurements (σ _obs ^V ～ 0.007^m) for the eclipsing binary system HS Her in 1984–1991. These measurements continue the homogeneous series of observations of this star commenced in 1969 by D.Ya. Martynov using the same equipment. Our detailed analysis of this homogeneous 22-year series of photoelectric observations has yielded a self-consistent set of physical and geometric parameters of the binary, and enabled us to establish the evolutionary stages of its components. The systems’s primary, M ₁ = 5 M _⊙, is at the beginning of its main-sequence evolution, whereas its secondary, M ₂ = 1.6 M _⊙, has not yet reached the main sequence. The binary’s age is estimated to be t = (17 ± 3) × 10⁶ years.     

Wolf-Rayet stars with relativistic companions

The evolution of close binary systems containing Wolf-Rayet (WR) stars and black holes (BHs) is analyzed numerically. Both the stellar wind from the donor star itself and the induced stellar wind due to irradiation of the donor with hard radiation arising during accretion onto the relativistic component are considered. The mass and angular momentum losses due to the stellar wind are also taken into account at phases when the WR star fills its Roche lobe. It is shown that, if a WR star with a mass higher than ～10M _⊙ fills its Roche lobe in an initial evolutionary phase, the donor star will eventually lose contact with the Roche lobe as the binary loses mass and angular momentum via the stellar wind, suggesting that the semi-detached binary will become detached. The star will remain a bright X-ray source, since the stellar wind that is captured by the black hole ensures a near-Eddington accretion rate. If the initial mass of the helium donor is below ～5M _⊙, the donor may only temporarily detach from its Roche lobe. Induced stellar wind plays a significant role in the evolution of binaries containing helium donors with initial masses of ～2M _⊙. We compute the evolution of three observed WR-BH binaries: Cyg X-3, IC 10 X-1, and NGC 300 X-1, as well as the evolution of the SS 433 binary system, which is a progenitor of such systems, under the assumption that this binary will avoid a common-envelope stage in its further evolution, as it does in its current evolutionary phase.     

The mass of the compact object in the low-mass X-ray binary 2S 0921-630

We interpret the observed radial-velocity curve of the optical star in the low-mass X-ray binary 2S 0921-630 using a Roche model, taking into account the X-ray heating of the optical star and screening of X-rays coming from the relativistic object by the accretion disk. Consequences of possible anisotropy of the X-ray radiation are considered. We obtain relations between the masses of the optical and compact (X-ray) components, m _v and m _x , for orbital inclinations i = 60°, 75°, and 90°. Including X-ray heating enabled us to reduce the compact object’s mass by ～0.5–1 M _⊙, compared to the case with no heating. Based on the K0III spectral type of the optical component (with a probable mass of m _v ? 2.9 M _⊙), we concluded that m _x ? 2.45?2.55 M _⊙ (for i = 75°?90°). If the K0III star has lost a substantial part of its mass as a result of mass exchange, as in the V404 Cyg and GRS 1905+105 systems, and its mass is m _v ? 0.65?0.75 M _⊙, the compact object’s mass is close to the standard mass of a neutron star, m _x ? 1.4 M _⊙ (for i = 75°?90°). Thus, it is probable that the X-ray source in the 2S 0921-630 binary is an accreting neutron star.     

Hydrodynamical models for W Vir pulsating variables

We have calculated a grid of hydrodynamical models for W Vir pulsating variable stars with mass M = 0.6M _⊙ and bolometric luminosity 200 ≤ L _bol/L _⊙ ≤ 1.2 × 10³. The positions of the blue edge of the instability strip and the boundary separating the domains of periodic and semi-regular pulsation in the H-R diagram were determined. These two boundaries converge for L _bol ≈ 10³ L _⊙. Two different groups of models can be distinguished in the region of periodic solutions, characterized by oscillations with alternating amplitude and duration of the pulsation cycle. For the first group of models, the alternation of the pulsations occurs over a time interval of two periods of the fundamental mode; this is due to the 2П₀=3П₁ resonance between the fundamental mode and first overtone. The models of the second group have larger luminosities and are located near the boundary separating the domains of periodic and semiregular pulsations. A discrete Fourier transformation analysis shows that, as we approach the region of semiregular pulsations, additional peaks appear in the spectra of the oscillatory moment of inertia and kinetic energy. These peaks correspond to period doubling bifurcations (a Feigenbaum sequence) of order n≤4. Approximate formulas are presented for the pulsation constant Q as a function of the mass-to-radius ratio (M/M _⊙)/(R/R _⊙) and the luminosity of the star L _bol.     

The mass of the compact object in the X-ray binary her X-1/HZ her

We have obtained the first estimates of the masses of the components of the Her X-1/HZ Her X-ray binary system taking into account non-LTE effects in the formation of the H _γ absorption line: m _x = 1.8 M _⊙ and m _v = 2.5 M _⊙. These mass estimates were made in a Roche model based on the observed radial-velocity curve of the optical star, HZ Her. The masses for the X-ray pulsar and optical star obtained for an LTE model lie are m _x = 0.85 ± 0.15 M _⊙ and m _v = 1.87 ± 0.13 M _⊙. These mass estimates for the components of Her X-1/HZ Her derived from the radial-velocity curve should be considered tentative. Further mass estimates from high-precision observations of the orbital variability of the absorption profiles in a non-LTE model for the atmosphere of the optical component should be made.     

Evolution of Stars Paired with Intermediate-Mass Black Holes

Under certain conditions, stars close to intermediate-mass black holes (IMBHs) can form close binary systems with these objects, in which the Roche lobe can be filled by the star and intense accretion of the star’s matter onto the IMBH is possible. Recently, accreting IMBHs have been associated with hyperluminous X-ray sources (HLXs), whose X-ray luminosities can exceed 10⁴¹ erg/s. In this paper, the evolution of star—IMBH binary systems is investigated assuming that the IMBH mainly accretes the matter of its companion star, and that the presence of gas in the vicinity of the IMBH does not appreciably affect changes in the orbit of the star. The computations take into account all processes determining the evolution of ordinary binary systems, as well as the irradiation of a star by hard radiation during the accretion of its matter onto the IMBH. The absorption of external radiation in the stellar envelope was calculated applying the same formalism that is used to calculate the opacity of the stellar matter. The computations also assumed that, if the characteristic time for the mass transfer is less than the thermal time scale of the star, there is no exchange betwween the orbital angular momentum of the system and the angular momentum of the matter flowing onto the IMBH.

Numerical simulations have shown that, under these assumptions, three types of evolution are possible for such a binary system, depending on the mass of the IMBH and the star, as well as on the star’s initial distance from the IMBH. The first type ends with the destruction of the star. For low-mass main sequence (MS) stars, only this option is realized, even in the case of large initial distances from IMBH. For massive MS stars, the star is also destroyed if the mass of the IMBH is high and the initial distance of the star from the IMBH is sufficiently small.

The second type of evolution can occur for massive MS stars, which are initially located farther from the IMBH than in the first type of evolution. In this case, the massive star fills its Roche lobe during its evolutionary expansion, after which a stage of intense mass transfer begins. It is in this phase of the evolution that the star- IMBH system can manifest itself as a HLX, when its X-ray luminosity L_X exceeds 10⁴¹ erg/s for a fairly long time. Numerical simulations show that the initial mass of the donor star in systems with M_BH = (10³?10⁵)M_⊙ must be close to ～10 M_⊙ in this case. The characteristic duration of the HLX stage is 30 000–70 000 years. For smaller initial donor masses close to ～5M_⊙, L_X does not reach 10⁴¹ erg/s in the stage of intense mass transfer, but can exceed 10⁴⁰ erg/s. The duration of this stage of evolution is 300 000–800 000 years. A characteristic feature of this second type of evolution is an increase in the orbital period of the system over time. As a result, after a period of intense mass loss, the star “retreats” inside the Roche lobe. A remnant of the star in the form of a white dwarf is left behind, and can end up fairly far from the IMBH.

The third type of evolution can occur for massive MS stars that are initially even farther from the IMBH, as well as for massive stars that are already evolved at the initial time. In this case, conservative mass exchange in the presence of intense stellar wind leads to the star moving away from the IMBH, without filling its Roche lobe at all. For massive stars with sufficiently strong stellar winds (for example, stars with masses ～50M_⊙), the accretion rate of matter onto the IMBH in this case can reach values that are characteristic of HLXs. As in the case of the second type of evolution, the stellar remnant can remain at a fairly large distance from the IMBH.

     

A Double Wave in the Orbital-period Variations of the Eclipsing Binary RT Per

Orbital-period variations of the low-mass, semi-detached eclipsing binary RT Per are analyzed. In addition to the secular variation of the orbital period determined by the mass transfer between the components, cyclic variations are also present. Both the light-time effect and magnetic oscillations can describe the cyclic orbital-period variations of RT Per. The secular period increase can be explained by a uniform flow of matter from the lower-mass to the higher-mass component at a rate of 0.60 × 10⁻⁸M-/year, with the total angular momentum being conserved. The period variations can be represented equally accurately by either a superposition of two cyclic variations or a superposition of a secular period increase and two cyclic variations. Approximately the same parameters are derived for the lower-period (36.8 year) variations when the times of minima are fitted with a linear or a quadratic formula. For the longer-period variation, a period of 275 years and amplitude of 0.104 days are found using the linear formula, or 89 years and 0.045 days using the quadratic formula.

     

Dependence of the absorption-line profiles and radial-velocity curve of the optical star in an X-ray binary on the orbital inclination and component-mass ratio

Theoretical absorption-line profiles and radial-velocity curves for tidally deformed optical stars in X-ray binary systems are calculated assuming LTE. The variations in the profile shapes and radial-velocity curve of the optical star are analyzed as a function of the orbital inclination of the X-ray binary system. The dependence of the shape of the radial-velocity curve on the orbital inclination i increases with decreasing component-mass ratio q = m _x /m _v . The integrated line profiles and radial-velocity curves of the optical star are calculated for the Cyg X-1 binary, which are then used to estimate the orbital inclination and mass of the relativistic object: i < 43° andm _x = 8.2–12.8 M_⊙. These estimates are in good agreement with earlier results of fitting the radial-velocity curve of Cyg X-1 using a simpler model (i < 45°, m _x = 9.0–13.2 M_⊙).     

The evolution of close binary systems with intermediate-mass black holes and ultra-luminous X-ray sources

The results of numerical studies of the evolution of a close binary system containing a black hole with a mass of ～3000M_⊙ are presented. Such a black hole could form in the center of a sufficiently rich and massive globular cluster. The secondary could be a main-sequence star, giant, or degenerate dwarf that fills or nearly fills its Roche lobe. The numerical simulations of the evolution of such a system take into account the magnetic wind of the donor together with the wind induced by X-ray irradiation from the primary, the radiation of gravitational waves by the system, and the nuclear evolution of the donor. Mass transfer between the components is possible when the donor fills its Roche lobe, and also via the black hole’s capture of some material from the induced stellar wind. The computations show that the evolution of systems with solar-mass donors depends only weakly on the mass of the accretor. We conclude that the observed ultra-luminous X-ray sources (L _X ? 10³⁸ erg/s) in nearby galaxies could include accreting black holes with masses of 10²?10⁴M_⊙. Three scenarios for the formation of black holes with such masses in the cores of globular clusters are considered: the collapse of superstars with the corresponding masses, the accretion of gas by a black hole with a stellar initial mass (<100M_⊙), and the tidal accumulation of stellar black holes. We conclude that the tidal accumulation of stellar-mass black holes is the main scenario for the formation of intermediate-mass black holes (10²?10⁴M_⊙) in the cores of globular clusters.