Современные методы синтеза кривых блеска и кривых лучевых скоростей позволяют определять физические пара- метры двойных систем различных типов. Нами предложен новый алгоритм синтеза кривых блеска систем, которые содержат два компонента со звездными ветрами. Проведенные численные расчеты показали сильную зависимость кривых блеска от параметров ветров. Это необходимо учитывать при анализе наблюдений двойных систем, в состав которых входят звезды ранних спектральных классов, обладающие сильными ветрами, например звезды O и WR. Modern synthesis methods for solving light and radial velocity curves make it possible to determine the physical parameters of binary systems of various types. We have proposed a new algorithm for solving light curves of systems that contain two components with stellar winds. Our numerical simulations showed a strong dependence of the light curves on the wind parameters. This should be taken into account when analyzing observations of binary systems that include early-type stars with strong winds, such as O and WR stars.

Synthesis methods for light and radial velocity curves are currently one of the main tools for studying close binary systems (CBSs). The paper gives a brief review of the history and development of the methods and their implementations in Sternberg Astronomical Institute of Moscow State University (SAI MSU), where a set of computer programs has been created to analyze observations of CBSs of various types. As a demonstration, we present the results of the analysis by our algorithms for three interesting CBSs at different evolutionary stages. An analysis of the unusual light curves of the recently discovered pre-cataclysmic binary GPX-TF16E-48 was performed using the Roche model with spots on the normal star. The X-ray light curves of the microquasar SS433 were analyzed using a precessing accretion disk model. The highly elliptical Wolf‒Rayet binary WR22 was studied in the frame of the Roche model accounting for the absorption by the powerful wind of the Wolf–Rayet star using space-based photometric observations. As a result of this detailed analysis of the light curves and involving spectroscopic information, the parameters of the CBSs and their components were found. This paper is based on a presentation made in the astrophysical memorial seminar “Novelties in Understanding the Evolution of Binary Stars”, dedicated to the 90th anniversary of Professor M.A. Svechnikov.

ABSTRACT WR22 = HD 92740 is a bright (V = 6.4 mag), intrinsically luminous, double-line WN7h + O9III-V binary exhibiting one sharp 8 per cent deep eclipse near periastron in its elliptical (e = 0.6) 80-day orbit, when the WR-star passes in front of the O star, with no secondary eclipse. We apply two models (L96, A13) to probe the optical space-based light curves from BRITE-Constellation, including three separate, complete eclipses, that show increased (o-c) scatter compared to the rest of the observations outside the eclipses, likely due to O-star light encountering WR wind-clumps. L96 is a simple atmospheric-eclipse model, often applied to close WR + O binaries, where the O-star is considered a point-source. A13 considers a finite-disk O-star and allows for atmospheric, photospheric and reflection components to the eclipse, permitting a better characterization of its shape through a more physically realistic description of the structures for both stars in WR22. Nevertheless, A13 is still susceptible to uncertainties in the luminosity of the O-star before unique values for the orbital inclination and WR mass-loss rate can be estimated. We present solutions for the two extremes of the O-star, O9V and O9III. As photometry alone cannot allow us to discriminate between these, we compared our results to the spectral models found in the literature and determined the correct solution to be O9V. Our best-fitting A13 Model 1 gives i = 83.5 ± 0.4°, with $\dot{M}_{\rm WR} = (1.86 \pm 0.2) \times 10^{-5} \dot{M}_{\odot }/yr$. The flux ratio in the red BRITE band in this model is FO/FWR = 0.064 ± 0.002.

We study near-infrared ( JHK ) and X-ray light curves of Cyg X-3 obtained with the 2.5 m telescope of the Caucasian Mountain Observatory of MSU SAI and collected from the RXTE ASM and MAXI archives. The light curves in the X-ray and IR domains are strongly affected by irregular variations. However, the mean curves are remarkably stable and qualitatively similar in both domains. This means that the IR flux of the system originates not only from the free–free radiation of the Wolf–Rayet (WR) wind but also from a compact IR source located near the relativistic companion. The shape of the mean X-ray and IR light curves suggest the existence of two additional structures in the WR wind—a bow shock near the relativistic companion and a so-called “clumpy trail.” Modeling of the mean X-ray and IR light curves allowed us to obtain important system parameters: the orbital phase of the superior conjunction of the relativistic companion ϕ 0 = −0.066 ± 0.006, the orbital inclination angle i = 29.°5 ± 1.°2, and the WR mass-loss rate M ̇ = ( 0.96 ± 0.14 ) × 10 − 5 M ⊙ yr − 1 . By using relations between M ̇ and the rate of the period change and between M ̇ and the WR mass, we estimated the probable mass of the relativistic companion M C ≃ 7.2 M ⊙ , which points toward the black hole hypothesis. However, this estimate is based on the assumption of a smooth WR wind. Considering the uncertainty associated with clumping, the mass-loss rate can be lower, which leaves room for the neutron star hypothesis.

INTEGRAL IBIS/ISGRI 18-60 keV observations of SS433 performed in 2003-2011 enabled the hard X-ray phase-resolved orbital and precessional light curves and spectra to be constructed. The spectra can be fitted by a power-law with photon index $\simeq 3.8$ and remain almost constant while the X-ray flux varies by a factor of a few. This suggests that the hard X-ray emission is produced in an extended quasi-isothermal hot 'corona' surrounding central parts of a supercritical accretion disc. A joint analysis of the broadband 18-60 keV orbital and precessional light curves was performed in the model assuming a significant Roche lobe overfilling by the optical star, up to its filling the outer Lagrangian surface enabling mass loss through the outer Lagrangian L$_2$ point. From this modeling, the relativistic-to-optical component mass ratio $q=M_x/M_v\gtrsim0.4\div 0.8$ is estimated. An analysis of the observed long-term stability of the orbital period of SS433 with an account of the recent observations of SS433 by the VLTI GRAVITY interferometer enabled an independent mass ratio estimate $q>0.6$. This estimate in combination with the radial velocity semi-amplitude for stationary He II emission, $K_x=168\pm 18$ km/s (Hillwig et al 2004) suggests the optical component mass in SS433 $M_v>12 M_\odot$. Thus, the mass of the relativistic component in SS433 is $M_x>7 M_\odot$, which is close to the mean mass of black holes in X-ray binaries ($\sim 8 M_\odot$). The large binary mass ratio in SS433 allows us to understand why there is no common envelope in this binary at the secondary mass transfer evolutionary stage and the system remains semi-detached (van den Heuvel et al. 2017). We also discuss unsolved issues and outline prospects for further study of SS433.

ABSTRACT We report the discovery of a relatively bright eclipsing binary system, which consists of a white dwarf (WD) and a main-sequence K7 star with clear signs of chromospheric and spot activity. The light curve of this system shows ∼0.2 mag ellipsoidal variability with a period of 0.297549 d and a short total eclipse of the WD. Based on our analysis of the spectral and photometric data, we estimated the parameters of the system. The K7V star is tidally deformed but does not fill its Roche lobe (the filling factor is about 0.86). The orbital inclination is i = $73{_{.}^{\circ}}1 \pm 0{_{.}^{\circ}}2$, and the mass ratio is q = M2/M1 ≈ 0.88. The parameters of the K7V star are M2 ≈ 0.64 M⊙, R2 = 0.645 ± 0.012R⊙, and T2 ≈ 4070 K. The parameters of the WD are M1 ≈ 0.72 M⊙, R1 = 0.013 ± 0.003R⊙, and T1 = 8700 ± 1100 K. Photometric observations in different bands revealed that the maximum depth of the eclipse is in the SDSS r filter, which is unusual for a system of a WD and a late main-sequence star. We suspect that this system is a product of the evolution of a common-envelope binary star, and that the WD accretes the stellar wind from the secondary star (the so-called low-accretion-rate polar, hereafter LARP).

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.

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.

There is a mismatch between modelled and observed distributions of optical stars masses in BH LMXB. Companion masses in BH LMXB are found in the mass range 0.1 - 1.6 M_⊙ with the peak at 0.6 M_⊙. The standard evolutionary scenarios require the donor mass distribution peaks to be at least ∼ 1 M_⊙ to eject a massive envelope of the black hole progenitor. Imperfect of the methods of optical stars masses determination may cause this difference. Two common used approximations of real Roche lobe filling star as distortion sources have been tested. On the one hand, there is the a approximation of real Roche lobe filling optical stars as sphere. We tested rotational broadening of absorption lines based on an exact calculation of CaI λ 6439.075 Å absorption profiles in the spectra of Roche lobe filling optical stars. There is overestimation of projected equatorial rotational velocity V_rotsin i and, accordingly, underestimation of mass ratio q=M_x/M_v in the spherical star model. On the other hand, the approximation of a real Roche lobe filling star as disk with uniform local profile and linear limb darkening law is more rough. In this case overestimation of projected equatorial rotational velocity V_rotsin i is ∼ 20%. Such overestimation of V_rotsin i can result in significant underestimation of mass ratio q=M_x/M_v at hight value of q=M_x/M_v. Refined value of q does not affect the mass of a black hole, but the mass of an optical star has shrunk 1.5 times. Hence, the masses of optical stars in BH LMXB must be corrected downward, despite the contradictions to the standard evolutionary scenarios.

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].

We have analyzed photometric UBV light curves of the massive eclipsing binary system V729 Cyg which lies in the Cyg OB2 stellar association. The observations were made at the Abastumani Astrophysical Observatory in 1983–2003 as part of a program for studying binary systems of early types. The system V729 Cyg is a spectroscopic binary and consists of Of-stars. Effects associated with the collision of stellar winds are observed in it. Various researchers have assumed previously that the binary system is at an evolutionary stage of conversion into a WR+O system. The light curves have been analyzed by a synthesis method in terms of a Roche model using our own computer code analogous to the standard Wilson-Devinney code. This analysis shows that the binary system has a contact configuration and an orbital inclination of about 66 degrees. The absolute parameters of the components are estimated to be M 1 = 30.4M ⨀ , M 2 = 9.2M ⨀, R 1 = 24.6 R ⨀ , and R 2 = 13.8R ⨀ .

Physically-based distributed modelling under changing climatic conditions has been carried out for the Northern Dvina River basin using the ECOMAG (ECOlogical Model for Applied Geophysics). The parameters of the model have been adjusted through calibration against runoff hydrographs observed for the period 2000–2009. Validation of the model has been performed for the period of 1970–1989. Both sensitivity analysis and scenario approaches (based on the CMIP3 projections) have been applied to assess possible hydrological consequences of climate change in the basin. It has been shown that for greenhouse gases emissions A2 scenario, averaged for 11 climate models, annual runoff will not change significantly for the future 50 years. But due to increasing of winter precipitation by up to 15%, the volume of flow in the flood period could increase by up to 20%. Earlier beginning of the flood season is expected because of rising of the air temperature.

An exact calculation of CaI λ6439 Å absorption profiles in the spectra of optical stars in low-mass X-ray binary systems is carried out. The calculations are used to revise a formula relating the rotational broadening of lines and the component-mass ratio. In the case of modest (substantial) X-ray heating, failure to take into account the tidal-rotational deformation of the figure of the star leads to overestimation (underestimation) of the mass of the relativistic object. The radial-velocity curves of optical stars are modeled for binary systems with various parameters and X-ray heating powers k x ; corresponding tables ofK corrections are presented. Refined values for the component-mass ratio q = 23 ± 1, black-hole mass M x = 8.4 ± 0.5, and optical-star mass M v = 0.36 ± 0.07 for the GS 2023+338 (V404 Cyg) system are presented.

Individual probability-density distributions for the masses of compact objects in 20 X-ray binary systems have been constructed. The mass distributions were modeled using Monte-Carlo simulations. The closeness of the components in systems with massive optical stars was taken into account using K corrections. The parameters of the resulting black-hole mass distributions were obtained using nonparametric statistical methods. The presence of a statistically significant mass gap in the range 3–5 M ⊙ is confirmed. The currently observed probability-density distributions of the compact-object masses are stable against small amounts of data contamination.