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.     

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 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.     

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.     

Radial pulsations of helium stars and a model for BX CIR

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.     

Photometric elements and apsidal motion of the eclipsing binary ES Lac

We have obtained high-accuracy photoelectric measurements of ES Lac, an eclipsing binary with an elliptical orbit (B9III + B9III; P = 4.459^d, e = 0.198) in 1985–2004 at the Sternberg Astronomical Institute’s Tien Shan High-Altitude Observatory. Our detailed analysis of the 19-year uniform series of measurements has yielded the first photometric elements for this system, as well as a self-consistent set of physical and geometrical parameters for the binary. The virtually identical components (M ₁ = M ₂ = 3.0 M _⊙; R ₁ = R ₂ = 4.12 R _⊙) are appreciably separated from the main sequence, and are located on the giant branch: their age is t = (3.5 ± 0.2) × 10⁸ yrs. An analysis of our observations together with previously published times of minima has enabled a considerable refinement of the period of the apsidal motion, U = 355 ± 20 years, and a first determination of the apsidal parameter reflecting the radial density distributions for the components stars: k ₂ ^obs = 0.00213(18). This value is in a good agreement with the value expected theoretically for current evolutionary models of such stars: k ₂ ^th = 0.00257(15).     

Evolution of the masses of neutron stars in binary systems

We study the growth of the masses of neutron stars in binary systems due to the accumulation of mass from the optical donors accreted onto the neutron-star surface. Possible scenarios for this accretion are considered. The masses and magnetic-field strengths of radio pulsars derived using population-synthesis methods are compared to the observational data. The population-synthesis analysis indicates that a neutron star can increase its mass from the standard value of m _x ? 1.35M_⊙ to the Oppenheimer-Volkoff limit, m _x ? 2.5M_⊙, via accretion from a companion.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 25 Mon and HR 7389

An analysis of high-resolution CCD spectra of the giant 25 Mon, which shows signs of metallicity, and the normal giant HR 7389 is presented. The derived effective temperatures, gravitational accelerations, and microturbulence velocities are T_eff = 6700 K, log g = 3.24, and ξ _t = 3.1 km/s for 25 Mon and T_eff = 6630 K, log g = 3.71, and ξ _t = 2.6 km/s for HR 7389. The abundances (log ε) of nine elements are determined: carbon, nitrogen, oxygen, sodium, silicon, calcium, iron, nickel, and barium. The derived excess carbon abundances are 0.23 dex for 25 Mon and 0.16 dex for HR 7389. 25 Mon displays a modest (0.08 dex) oxygen excess, with the oxygen excess for HR 7389 being somewhat higher (0.15 dex). The nitrogen abundance is probably no lower than the solar value for both stars. The abundances of iron, sodium, calcium (for HR 7389), barium, and nickel exceed the solar values by 0.22–0.40 dex for both stars. The highest excess (0.62 dex) is exhibited by the calcium abundance for 25 Mon. Silicon displays a nearly solar abundance in both stars—small deficits of ?0.03 dex and ?0.07 dex for 25 Mon and HR 7389, respectively. No fundamental differences in the elemental abundances were found in the atmospheres of 25 Mon and HR 7389. Based on their T_eff and log g values, as well as theoretical calculations, A. Claret estimated the masses, radii, luminosities, and ages of 25 Mon (M/M_⊙ = 2.45, log(R/R_⊙) = 0.79, log(L/L_⊙) = 1.85, t = 5.3 × 10⁸ yr) and HR 7389 (M/M_⊙ = 2.36, log(R/R_⊙) = 0.50, log(L/L_⊙) = 1.24, t = 4.6 × 10⁸ yr), and also of the stars 20 Peg (M/M_⊙ = 2.36, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.79, t = 4.9 × 10⁸ yr) and 30 LMi (M/M_⊙ = 2.47, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.88, t = 4.8 × 10⁸ yr) studied by the author earlier.     

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.     

The impact of reflection effects on the parameters of the old pre-cataclysmic variables MS Peg and LM Com

We have determined the main parameters of the old precataclysmic variable stars MS Peg and LM Com. The radial velocities of the components, reflection effects in the spectra, and light curves of the systems are studied based on model stellar atmospheres subject to external irradiation. Forty-seven moderate-resolution spectra for MS Peg and 57 for LM Com obtained with the 6-m telescope of the Special Astrophysical Observatory are used to derive the refined orbital periods of 0.1736660 days and 0.2586873 days, respectively; the orbital eccentricities do not exceed e=0.04. The mass (M _w =0.49e_⊙) and radius (e _w =0.015R_⊙) of the MS Peg primary calculated using the gravitational redshift correspond to those for a cooling carbon white dwarf with a thin hydrogen envelope. The parameters of the red dwarf (M _r =0.19M_⊙, T_eff=3560 K, R _r =0.18R_⊙) are close to those derived from evolutionary tracks for main-sequence M stars with solar chemical composition. The radius (R _r =0.22R_⊙) and temperature (T_eff=3650 K) of the LM Com secondary exceed theoretical estimates for main-sequence stars with masses of M _r =0.17M_⊙. The luminosity excess of the red dwarf in LM Com can be explained by a prolonged (T>5×10⁶ yrs) relaxation of the M star to its normal state after the binary leaves the common-envelope stage. For both systems, theoretical U, B, V, and R light curves and spectra calculated using the adopted sets of parameters are generally consistent with the observations. This confirms the radiative origin of the hot spots, the unimportance of horizontal radiative transport, and the absence of large-scale velocity fields with high values (V_trans>50 km/s) at the surfaces of the secondaries. Most of the emission lines in the spectra of these objects are formed under conditions close to thermalization, enabling modeling of their pro files in an LTE approximation. A strong λ3905 Å emission line has been identified as the 3s²3p4s 1P⁰-3s²3p² 1S SiI λ3905.52 Å line formed in the atmosphere of the hot spot. The observed intensity can be explained by non-LTE “superionization” of SiI atoms by soft UV radiation from the white dwarf. We suggest a technique for identifying binaries whose cool components are subject to UV irradiation based on observations of λ3905 Å emission in their spectra.     

The mass of the compact object in the X-ray binary 4U 1700-37

The results of a systematic analysis of master radial-velocity curves for the X-ray binary 4U 1700-37 are presented. The dependence of the mass of the X-ray component on the mass of the optical component is derived in a Roche model based on a fit of the master radial-velocity curve. The parameters of the optical star are used to estimate the mass of the compact object in three ways. The masses derived based on information about the surface gravity of the optical companion and various observational data are 2.25 _?0.24 ^+0.23 M_⊙ and 2.14 _?0.56 ^+0.50 M_⊙. The masses based on the radius of the optical star, 21.9R_⊙, are 1.76 _?0.21 ^+0.20 M_⊙ and 1.65 _?0.56 ^+0.78 M_⊙. The mass of the optical component derived from the mass-luminosity relation for X-ray binaries, 27.4M_⊙, yields masses for the compact object of 1.41 _?0.08 ⁺ M_⊙ and 1.35 _?0.18 ^+0.18 M_⊙.     

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.     

Physical properties of molecular clouds as functions of their Galactocentric distance from CS and C<Superscript>34</Superscript>S observations

Twenty-eight CS molecular clouds toward HII regions with Galactocentric distances from ～ 4 to 20 kpc have been studied based on observations obtained in the J=2→1 lines of CS and C³⁴S on the 20-meter radio telescope of the Onsala Space Observatory (Sweden) in March 2001. All 28 clouds have been mapped with an angular resolution of ～40″. The peak intensity in the C³⁴S line has been measured for 20 objects. An LTE analysis has been performed and the parameters of the molecular cloud cores derived. The core sizes are d_A=0.3–4.8 pc, with a median value of ～1.6 pc. The mean hydrogen densities in the cloud cores are n_H2=3.5×10²–3.7 × 10⁴ cm^?3, with a median value of ～7.2×10³ cm^?3. The value of n_H2 ends to decrease with increasing Galactocentric distance of the cloud. The masses of most clouds are 10²?6×10³M_⊙, with the most probable value being M_CS～10³M_⊙. The data follow the dependence M_CS ∝d _A ^(2.4–3.2) . As a rule, the cloud masses are lower than the virial masses for M_CS<10³M_⊙.     

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_⊙).     

Nonlinear radial pulsations of Wolf-Rayet stars

The evolution of Population I stars with initial masses 60 M _⊙ ≤ M _ZAMS ≤ 120 M _⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y _c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T _eff ～ 10⁵ K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T _eff ≈ 10⁵ K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M _⊙ to M = 6 M _⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 10⁵ K.     

The evolution of GRS 1915+105—an X-ray binary with a black hole

A brief review of the observed parameters of binary systems with black holes is presented. We discuss in detail the evolutionary status of the X-ray binary GRS 1915+105, which contains a massive black hole. Numerical simulations of the evolution of GRS 1915+105 at the X-ray stage indicate that the most probable initial mass of the optical component (donor star) is (1.5–)M_⊙. Two possible scenarios are suggested for the evolution of the system prior to the formation of the black hole. If the initial mass of the optical component was (2.5–)M_⊙, the system underwent a common-envelope phase; in this case, the initial mass of the black hole progenitor did not exceed ～50M_⊙. If the initial mass of the donor was (1.5–2.5)M_⊙, a scenario without a common envelope is possible, with the initial mass of the black hole progenitor being smaller than ～50M_⊙. The lack of information about the initial mass-ratio distribution for binary components for small q and the uncertainty of the system parameters make it impossible to give preference to a particular scenario for the system's prior evolution.     

Evolution of close binaries and gamma-ray bursts

We analyze the late stages of evolution of massive (M ₀ ? 8 M _⊙) close binaries, from the point of view of possible mechanisms for the generation of gamma-ray bursts. It is assumed that a gamma-ray burst requires the formation of a massive (～1 M _⊙), compact (R ? 10 km) accretion disk around a Kerr black hole or neutron star. Such Kerr black holes are produced by core collapses of Wolf-Rayet stars in very close binaries, as well as by mergers of neutron stars and black holes or two neutron stars in binaries. The required accretion disks can also form around neutron stars that were formed via the collapse of ONeMg white dwarfs. We estimate the Galactic rate of events resulting in the formation of rapidly rotating relativistic objects. The computations were carried out using the “Scenario Machine.”     

Masses of the visual components and black holes in X-ray novae: Effects of proximity of the components

It is shown that the approximation of the complex, tidally distorted shape of a star as a circular disc with local line profiles and a linear limb-darkening law, which is usually applied when deriving equatorial stellar rotation velocities from line profiles, leads to overestimation of the equatorial velocity V _rot sin i and underestimation of the component mass ratio q = M _x /M _v . A formula enabling correction of the effect of these simplifying assumptions on the shape of a star is used to re-determine the mass ratios q and the masses of the black holes M _x and visual components M _v in low-mass X-ray binary systems containing black holes. Taking into account the tidal–rotational distortion of the stellar shape can significantly increase the mass ratios q = M _x /M _v , reducing M _v , while M _x changes only slightly. The resulting distribution of M _v attains its maximum near M _v ? 0.35M _⊙, in disagreement with the results of population synthesis computations realizing standard models for Galactic X-ray novae with black holes. Possible ways to overcome this inconsistency are discussed. The derived distribution of M _x also differs strongly from the mass distribution for massive stars in the Galaxy.     

Interpretation of the light curves of “quiescent” X-ray novae in a model with a noncollisional interaction between the flow and disk. The XTE J1118+480 system

We have analyzed the orbital light curve of the X-ray nova XTE J1118+480 in a “disk + hot line” model based on three-dimensional gas-dynamical computations of gas flows in interacting binary systems. As a result, we have been able to derive reliable parameters for the system: i = 80 _?4 ⁺⁴ degrees, _MBH = 7.1 _?0.1 ^+0.5 M_⊙, M _opt = 0.39 _?0.07 ^+0.15 M_⊙.     

Evolution of close stellar binaries with black holes under the action of gravitational radiation and magnetic and induced stellar winds of the donor

We show that semi-detached close binary systems with massive (4–25M_⊙) black holes are formed in the evolution of massive stellar binaries in which the initial mass of the primary exceeds ～25M_⊙. The mass exchange in such systems is maintained by the nuclear evolution of the donor and by its magnetic and induced stellar winds. The donor in such systems can be a main-sequence star, subgiant, non-degenerate helium star, or white dwarf. The evolution of corresponding systems with black-hole masses of 10M_⊙ is investigated.