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_⊙).     

K-Corrections to radial-velocity curves of optical components in X-ray binaries. Massive systems with weak X-ray heating

The radial-velocity curves of optical components in X-ray binary systems can differ from the radial-velocity curves of their barycenters due to tidal distortion, gravitational darkening, X-ray heating, etc. This motivated us to investigate how the semi-amplitudes of the radial-velocity curves of these optical components can depend on the binary-system parameters in a Roche model. The K correction is taken to be the ratio of the radial velocity semi-amplitude for a star in the Roche model to the corresponding value for the stellar barycenter. K corrections are tabulated for the optical stars in the massive X-ray binaries Cen X-3, LMC X-4, SMC X-1, Vela X-1, and 4U 1538-52.     

Parameters of V404 Cyg—A black-hole binary

We present the results of spectroscopic observations of the X-ray binary V404 Cyg obtained on the 6-m telescope of the Special Astrophysical Observatory in 2001–2002. We have used a statistical approach to interpret the radial-velocity curve of V404 Cyg. We derived the dependence of the mass of the X-ray emitting component m_x on the mass of the optical component m_v via an analysis of the radial-velocity curve based on profiles of the CaI 6439.075 Å absorption line synthesized in a Roche model. Using the orbital inclination estimated from the ellipticity of the optical component, i=54°–64°, and the component-mass ratio q=m_x/m_v=16.7 found from the rotational broadening of the spectral lines, we obtain m _s =10.65±1.95M_⊙ for the mass of the black hole.     

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.     

Masses of X-ray pulsars in binary systems with OB supergiants

We describe the results of a statistical approach to analyzing the combined radial-velocity curves of X-ray binaries with OB supergiants in a Roche model, both with and without allowance for the anisotropy of the stellar wind. We present new mass estimates for the X-ray pulsars in the close binary systems Cen X-3, LMC X-4, SMC X-1, 4U 1538-52, and Vela X-1.     

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.     

A possible mechanism for the X-ray emission of Be/X stars

A new mechanism for the generation of X-ray emission in binary Be/X stars is proposed. It is shown that the mass-transfer rate through the point L₁ in a model in which the optical component of a Be/X star has an expanding envelope is sufficient to generate the observed X-ray luminosities of such stars. The results of computations indicate a dependence between the orbital periods and X-ray fluxes of these systems. The relationship between the orbital perod and the mass-transfer rate during flares obtained from modeling corresponds to the observed dependence of the maximum X-ray flux on the orbital period.     

Analysis of reflection effects in HS 2333+3927

The results of photometric and spectroscopic observations of the pre-cataclysmic variable HS 2333+3927, which is a HW Vir binary system, are analyzed. The parameters of the sdB subdwarf companion (T _eff = 37 500 ± 500 K, log g = 5.7 ± 0.05) and the chemical composition of its atmosphere are refined using a spectrum of the binary system obtained at minimum brightness. Reflection effects can fully explain the observed brightness variations of HS 2333+3927, changes in the HI and HeI line profiles, and distortions of the radial-velocity curve of the primary star. A new method for determining the component-mass ratios in HW Vir binaries, based on their radial-velocity curves and models of irradiated atmospheres, is proposed. The set of parameters obtained for the binary components corresponds to models of horizontal-branch sdB subdwarfs and main-sequence stars.     

The evolutionary status of UX CVn

We have analyzed available spectroscopic and photometric observations of the close binary UX CVn using model atmospheres. Theoretical spectra and light curves were derived from models of a precataclysmic variable and a close binary consisting of degenerate stars. We have used the 6-m telescope of the Special Astrophysical Observatory to obtain ten moderate-resolution spectra at three orbital phases. Our analysis of the radial-velocity curve shows that the orbital period of the system has been stable over 40 yrs, and the variations of the intensities of lines of various elements at different phases and radial velocities indicates an absence of the reflection effect. As a result, we have classified UX CVn as a detached close binary consisting of a hot, low-luminosity sub-dwarf primary and a white-dwarf secondary.     

Physical and dynamical parameters of the multiple system HD 222326

We present the results of our study of the physical and dynamical parameters of the multiple system HD 222326. A new method for determining the individual radial velocities of components in wide binary and multiple systems in the case of small radial-velocity differences (δV _r ≤ the FWHMfor the line profiles) is suggested and tested for both model systems and the binary HD 10009. This testing yielded the component radial velocities V _{r 1,2} for HD 10009, enabling us to derive the center-of mass velocity, V _γ, for the first time. We determined the radial velocities of the components of HD 222326 from high-resolution spectra, and refined the orbital parameters of the subsystems using speckle-interferometric observations. A combined spectroscopic and speckle interferometric analysis enabled us to find the positions of the components in the spectral type—luminosity diagram and to estimate their masses. It is likely that the components are all in various evolutionary stages after leaving the main sequence. We analyzed the dynamical evolution of the system using numerical modeling in the gravitational three-body problem and the known stability criteria for triple systems. The system is probably stable on time scales of at least 10⁶ years. The presence of a fourth component in the system is also suggested.     

Masses of stellar black holes and testing theories of gravitation

The paper analyzes the mass distribution of stellar black holes derived from the light and radial-velocity curves of optical stars in close binary systems using dynamical methods. The systematic errors inherent in this approach are discussed. These are associated primarily with uncertainties in models for the contribution from gaseous structures to the optical brightness of the systems under consideration. The mass distribution is nearly flat in the range 4–15M _⊙. This is compared with the mass distribution for black holes in massive close binaries, which can be manifest as ultrabright X-ray sources (L _x >10³⁹ erg/s) observed in other galaxies. If the X-ray luminosities of these objects correspond to the Eddington limit, the black-hole mass distribution should be described by a power law, which is incompatible with the flat shape derived dynamically from observations of close binaries in our Galaxy. One possible explanation of this discrepancy is the rapid evaporation of stellar-mass black holes predicted in recent multi-dimensional models of gravity. This hypothesis can be verified by refining the stellar black-hole mass spectrum or finding isolated or binary black holes with masses below ～3M _⊙.     

The mass of the black hole in the X-ray binary M33 X-7 and the evolutionary status of M33 X-7 and IC 10 X-1

We have analyzed the observed radial-velocity curve for the X-ray binary M33 X-7 in a Roche model. We have analyzed the dependence between the component masses and the degree of filling of the optical star’s Roche lobe to obtain the ratio of the masses of the optical star and compact object. For the most probable mass of the optical star, m _v = 70 M⊙, the mass of the compact object is m _x = 15.55 ± 3.20 M⊙. It has been shown that black holes with masses of mx = 15 M⊙ and even higher can form in binaries. We present characteristic evolutionary tracks for binary systems passing through an evolutionary stage with properties similar to M33 X-7-type objects. According to population-synthesis analyses, such binaries should be present in galaxies with masses of at least 10¹¹ M⊙. The present number of such systems in M33 should be of the order of unity. We have also studied the evolutionary status of the X-ray binary IC 10 X-1 with a Wolf-Rayet component, which may contain a massive black hole. The final stages of the evolution of the M33 X-7 and IC 10 X-1 systems should be accompanied by the radiation of gravitational waves.     

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_⊙.     

Estimate of the black-hole mass and orbital inclination from the radial-velocity curve of the X-ray binary Cyg X-1

Astronomy Reports - The results of a statistical approach to interpreting a master radial-velocity curve for the X-ray binary Cyg X-1 are presented. The dependence of the mass of the X-ray...     

Analysis of optical spectra of V1357 Cyg≡Cyg X-1

Optical spectra and light curves of the massive X-ray binary V1357 Cyg are analyzed. The calculations were based on models of irradiated plane-parallel stellar atmospheres, taking into account reflection of the X-ray radiation, asphericity of the stellar surface, and deviations from LTE for several ions. Comparison of observed spectra obtained in 2004?C2005 at the Bohyunsan Observatory (South Korea) revealed variations of the depths of HI lines by up to 18% and of HeI and heavy elements lines by up to 10%. These variations are not related to the orbital motion of the star, and are probably due to variations of the stellar wind intensity. Perturbations of the thermal structure of the atmosphere due to irradiation in various states of Cyg X-1 (including outburst) do not lead to the formation of a hot photosphere with an electron temperature exceeding the effective temperature. As a result, variations of the profiles of optical lines of HI, HeI, and heavy elements due to the orbital motion of the star and variations of the irradiating X-ray flux do not exceed 1% of the residual intensities. Allowing for deviations from LTE enhances the HI and HeI lines by factors of two to three and the MgII lines by a factor of nine, and is therefore required for a fully adequate analysis of the observational data. Analysis of the HI, HeI, and HeII lines profiles yielded the following set of parameters for theOstar at the observing epoch: T _eff = 30 500±500 K, log g = 3.31±0.05, [He/H] = 0.42 ± 0.05. The observed HeI line profiles have emission components that are formed in the stellar wind and increase with the line intensity. The abundances of 11 elements in the atmospheres of V1357 Cyg and ?? Cam, which has a similar spectral type and luminosity class, are derived. The chemical composition of V1357 Cyg is characterized by a strong excess of helium, nitrogen, neon, and silicon, which is related to the binarity of the system.     

Multicolor photoelectric WBVR observations of the close binary system HZ Her = Her X-1 in 1986–1988. Method and observations

We present results of four-color (WBVR) photoelectric observations of the close binary HZ Her = Her X-1 in 1986–1988. As a rule, the duration of the observations exceeded two 35-day X-ray orbital periods in the 1986–1988 observing seasons. The accuracy and length of the photoelectric observations facilitated multi-faceted studies, which enabled us to define several fine photometric effects in the light curves of the binary more precisely and attempt to interpret them in a model for the matter flow from the optical component to the accretion disk around the neutron star. This model provides a satisfactory explanation for the inhomogeneity of the gas flow and “hot spot,” as well as the existence of distinct “splashes” moving in their own Keplerian orbits around the outer parts of the Keplerian disk. We present series of light curves for all the observing seasons, as well as color-color diagrams that reflect the physics of various photometric effects. The transformation coefficients for each of the instrumental systems for the three observatories at which the observations were carried out are given. Atmospheric extinction was taken into account duringmulti-color observations of the object, with subsequent correction for atmospheric effects with accuracies ranging from 0.003 ^m to 0.005 ^m for air masses up to M(z) = 2.     

Estimation of the accuracy of methods for determining component masses for low-mass X-ray binary systems

Modern modeling of the population of low-mass X-ray binary systems containing black holes applying standard assumptions leads to a lack of agreement between the modeled and observed mass distributions for the optical components, with the observed masses being lower. This makes the task of estimating the systematic errors in the derived component masses due to imperfect models relevant. To estimate the influence of systematic errors in the derived masses of stars in X-ray binary systems, we considered two approximations for the tidally deformed star in a Roche model. Approximating the star as a sphere with a volume equal to that of the Roche lobe leads to slight overestimation of the equatorial rotational velocity V _rot sin i, and hence to slight underestimation of the mass ratio q = M _x /M _v . Approximating the star as a flat, circular disk with constant local line profiles and a linear limb-darkening law (a classical rotational broadeningmodel) is an appreciably cruder approach, and leads to overestimation of V _rot sin i by about 20%. In the case of high values of q = M _x /M _v , this approximation leads to substantial underestimation of the mass ratio q, which can reach several tens of percent. The mass of the optical star is overestimated by a factor of 1.5 in this case, while the mass of the black hole is changed only slightly. Since most estimates of component mass ratios for X-ray binary systems are carried out using a classical rotational broadening model for the lines, this leads to the need for appreciable corrections to (reductions of) previously published masses for the optical stars, which enhances the contradiction with the standard evolutionary scenario for low-mass X-ray binaries containing black holes.     

Variability of the HeI line profiles in the spectrum of the hot O9.5V star HD 93521

CCD spectra acquired with the PFES echelle spectrograph on the 6 m telescope of the Special Astrophysical Observatory (Russian Academy of Sciences) were used to study short-term variations in the HeI-line profiles in the spectrum of HD 93521. For all the lines, the variability pattern relative to the mean profile is the same, and can be described as a sinusoidal wave passing through the profiles, from the blue to the red wings. The variability amplitudes and time scales are different for different HeI lines. We studied variations of the radial velocities at the level of 0.5 R ₀ of the line residual intensity, for the absorption bisector and the blue and red halves of the absorption profile. The variation time scales and amplitudes for the line halves differ from one HeI line to another, and show good correlations with the line central depths. Going from the weak to the strong lines, the time scale of the radial-velocity variations measured for both halves of the absorption profile increases, and the amplitude decreases. The time scale of the radial-velocity variations for weak lines is, on average, twice the time scale for strong HeI lines. A variable absorption feature was detected in the profiles of strong HeI lines, which moves across the profile synchronously with the star’s axial rotation. Generally, the observed line variations are probably due to nonradial photospheric pulsations, together with the influence of the stellar wind on the profiles of the strong lines.     

The mass of the black hole in the X-ray binary LMC X-1

A dynamical estimate of the mass of the black hole in the LMC X-1 binary system is obtained in the framework of a Roche model for the optical star, based on fitting of the He I 4471 Å and He II 4200 Å absorption lines assuming LTE. The mass of the black hole derived from the radial-velocity curve for the He II 4200 Å line is m_x = 10.55 M_⊙, close to the value found earlier based on a model with two point bodies [1].     

The Hydrogen and Helium Lines of the Symbiotic Binary Z And during Its Brightening at the End of 2002

High resolution observations in the region of the Hα, HeII λ 4686, and Hγ lines in the spectrum of the symbiotic binary Z And were performed during a small-amplitude flare at the end of 2002. The profiles of the hydrogen lines were double-peaked, and suggest that the lines may be emitted mainly by an optically thin accretion disk. Since the Hα line is strongly contaminated by emission from the envelope, the Hγ line is used to investigate the properties of the accretion disk. The Hα line has broad wings, believed to be determined mostly by radiation damping, although the high-velocity stellar wind from the compact object in the system may also contribute. The Hγ line has a broad emission component, assumed to be emitted mainly from the inner part of the accretion disk. The HeIIλ 4686 line also has a broad emission component, but is believed to arise in a region of high-velocity stellar wind. The outer radius of the accretion disk can be calculated from the shift between the peaks. Assuming that the orbital inclination can range from 47° to 76°, we estimate the outer radius to be 20–50 R_⨀. The behavior of the observed lines can be interpreted in the model proposed for the line spectrum during the first large 2000–2002 flare of this binary.