Eleonora A. Antokhina

Radial-Velocity Curves and Theoretical Spectral-Line Profiles of the Components of Low-Mass Close X-ray Binary Systems

We present the results of calculations of theoretical absorption-line profiles and radial-velocity curves for optical components in X-ray binary systems. Tidal distortion of the optical star and X-ray heating by incident radiation from the relativistic object are taken into account. An emission component forms whose intensity varies with orbital phase in the absorption-line profile in the presence of significant X-ray heating. As a result, the width of the line decreases rather than increases at quadrature. The line profiles and equivalent widths and the radial-velocity curves depend substantially on the parameters of the binary systems. This provides the possibility of directly determining component masses and orbital inclinations from high-resolution spectroscopic observations of X-ray binary systems.

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.

Estimate of the Black-Hole Mass and Orbital Inclination from the Radial-Velocity Curve of the X-Ray Binary Cyg X-1

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 component mx on the mass of the optical component mv is obtained in a Roche model. A method for estimating the orbital inclination from the radial-velocity curve is described. In contrast to the situation for a pointlike optical star, both the amplitude and shape of the radial-velocity curve changes as a function of the orbital inclination i in the case of a tidally deformed star with a complex temperature distribution over its surface. Thus, high-accuracy radial-velocity curves can be used to impose constraints on the mass and orbital inclination of the black hole: i<45°. Using the information on the optical light curve, radius, and luminosity of the optical star, we estimate 31°

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 Hγ absorption line: mx = 1.8 M⊙ and mv = 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 mx = 0.85 ± 0.15 M⊙ and mv = 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 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, mv and mx, 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 mv ≃ 2.9 M⊙), we concluded that mx ≃ 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 mv ≃ 0.65−0.75 M⊙, the compact object’s mass is close to the standard mass of a neutron star, mx ≃ 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.

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 = mx/mv. 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° andmx = 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°, mx = 9.0–13.2 M⊙).

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 mx on the mass of the optical component mv 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=mx/mv=16.7 found from the rotational broadening of the spectral lines, we obtain ms=10.65±1.95M⊙ for the mass of the black hole.

Gravitational Darkening Coefficients of the Stars in the Semidetached Binary V Puppis

We have analyzed high-precision vby light curvesfor the semi-detached binary V Pup in a Roche model. They are consistent with the standard gravitational darkening coefficient for hot stars, β = 0.25, rather than the value β = 1.36 ± 0.04 derived by Kitamura and Nakamura [1] using a simpler model. We rigorously estimate the confidence intervals for the allowed gravitational darkening coefficients for a star filling its Roche lobe to be β = (−0.24, +1.29) for the 99% confidence level and β = (−0.21, +1.26) for the 67% confidence level.