Interpretation of the light curve of the eclipsing binary V444 Cyg on the set of convexo-concave functions

The narrow-band λ4244 Å continuum light curve of the eclipsing binary V444 Cyg, which has a Wolf-Rayet component, is interpreted assuming that the brightness distribution and absorption in the WN5 star's disk are monotonic, non-increasing, convexo-concave, non-negative functions. The convex and concave parts of these functions correspond to the core of the WN5 star and its extended photosphere and atmosphere, respectively. The radius and brightness temperature of the opaque core of the WN5 star are r _WN5 ^core ? 4R _⊙ and T _br ^core >52000 K, respectively. The stellar wind is characterized by an accelerated radial outflow. Acceleration of the wind persists at large distances from the center of the star. A crude Lamers-law fit to the reconstructed velocity field in the wind yields an acceleration parameter β=1.58–1.82.     

Spatial structure of the globular cluster M15

The spatial structure of the metal-poor globular cluster M15 is studied as a function of magnitude interval ΔB and the limiting B magnitude of star counts. Astrometric and photometric measurements of two plates obtained with the 2-m reflector of the National Academy of Sciences of Bulgaria were used. Analysis of the differential and integrated apparent (ΔF(r) and F(r)) and spatial (Δf(r) and f(r)) stellar density distributions in different ΔB intervals and to different limiting magnitudes reaching B=21.5^m indicates that the cluster structure changes systematically as we consider fainter stars, beginning with the transition region between the subgiant branch and the main-sequence turnoff in the (V, B-V) diagram. This variation is manifest in two ways: a homological growth in the radii of spatial zones of the cluster and of the cluster radius in accordance with a single law, and variations in the stellar density, with the rate of increase in the number of faint stars growing toward the outer zones of the cluster. Empirical relations describing these variations and parameters determining the cluster structure are obtained.     

Kinematic structure of the atmosphere and envelope of the post-AGB star HD 56126

We present a detailed analysis of the optical spectrum of the post-AGB star HD 56126 (IRAS 07134+1005) based on observations made with the echelle spectrographs of the 6-m telescope of the Special Astrophysical Observatory with resolutions of R = 25 000 and 60 000 at 4012-8790 Å. The profiles of strong lines (HI; FeII, YII, BaII absorption lines, etc.) formed in the expanding atmosphere at the base of the stellar wind display complex and variable shapes. To study the kinematics of the atmosphere, the velocities of individual features in these profiles must be measured. Differential line shifts of up to ΔV _r = 15–30 km/s have been detected from the lines of metals and molecular fetures. The stellar atmosphere simultaneously contains both expanding layers and layers falling onto the star. A comparison of the data for different times demonstrates that both the radial velocity and the overall velocity pattern are variable. The position of the molecular spectrum is stable, implying stability of the expansion velocity of the circumstellar envelope around HD 56126 detected in observations in the C₂ and NaI lines.     

Instability of the kinematic state in the atmosphere of the hypergiant ρ Cas outside outburst

Multiple observations of the yellow hypergiant ρ Cas obtained in 2007–2011 in a wide wavelength range with spectroscopic resolving power R ≥ 60 000 have enabled studies of features of its optical spectrum in detail and brought to light previously unknown characteristics of the star’s extended atmosphere. The radial velocity measured from symmetric absorption lines of metals varies with an amplitude of about ±7 km/s around the systemic velocity V _sys = ?47 km/s, due to low-amplitude pulsations of the atmospheric layers near the photosphere. At some times, a velocity gradient was observed in deep atmospheric layers of the star. A slight velocity stratification in the stellar atmosphere was detected for the first time, manifest as a difference of 3–4 km/s in the velocities measured from absorption lines of neutral metals and of ions. The long-wavelength components of split absorption lines of BaII, SrII, TiII, and other strong lines with low excitation potentials for their lower levels are distorted by nearby emission lines. It is suggested that the short-wavelength components, whose locations correspond to the narrow velocity range V _r (blue) from approximately ?60 to ?70 km/s, are formed in a circumstellar envelope; one component of the D NaI doublet and the emission components of the FeII 6369.46 and 6432.68 Å ions are also formed there.     

The optical spectrum of an LBV candidate in the Cyg OB2 association

We have obtained the first high-spectral-resolution (R=15000 and 60000) optical spectra for the extremely luminous star No. 12, identified with the IR source IRAS 20308+4104 in the Cyg OB2 association. We have identified about 200 spectral features at 4552–7939 Å, including the interstellar NaI, KI lines and numerous DIBs, which are the strongest absorption lines in the spectrum, along with the HeI, CII, and SiII lines. A two-dimensional spectral classification indicates that the star's spectral type is B5±0.5 Ia⁺. Our analysis of the radial-velocity pattern shows the presence of a radial-velocity gradient in the stellar atmosphere, due to the infall of matter onto the star. The strong Hα emission line displays broad Thompson wings and time-variable core absorption, providing evidence that the stellar wind is inhomogeneous, and a slightly blue-shifted P Cygni absorption profile. We conclude that the wind is time-variable.     

Detection of spectral variability of the optical component of the IR source IRAS 20508+2011

Our high-resolution spectral observations have revealed variability of the optical spectrum of the cool star identified with the IR source IRAS 20508+2011. We measured the equivalent widths of numerous absorption lines of neutral atoms and ions at wavelengths 4300–7930 Å, along with the corresponding radial velocities. Over the four years of our observations, the radial velocity derived from photospheric absorption lines varied in the interval V _r⊙ = 15–30 km/s. In the same period, the Hα profile varied from being an intense bell-shaped emission line with a small amount of core absorption to displaying two-peaked emission with a central absorption feature below the continuum level. At all but one epoch, the positions of the metallic photospheric lines were systematically shifted relative to the Hα emission: ΔV _r = V _r(met) ? V _r(Hα, emis) ≈ ?23 km/s. The Na D doublet displayed a complex profile with broad (half-width ≈ 120 km/s) emission and photospheric absorption, as well as an interstellar component. We used model atmospheres to determine the physical parameters and chemical composition of the star’s atmosphere: T _eff = 4800 K, log g = 1.5, ξ_t = 4.0 km/s. The metallicity of the star differs little from the solar value: [Fe/H]_⊙ = ?0.36. We detected overabundances of oxygen [O/Fe]_⊙ = +1.79 (with the ratio [C/O] ≈ ?0.9), and α-process elements, as well as a deficit of heavy metals. The entire set of the star’s parameters suggests that the optical component of IRAS 20508+2011 is an “O-rich” AGB star with luminosity M _v ≈ ?3^m that is close to its evolutionary transition to the post-AGB stage.     

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.     

Kinematics of the envelope of the post-AGB star V510 Pup—Nucleus of a future planetary nebula

We have carried out a detailed identification of lines in the optical spectrum of the post-AGB star V510 Pup associated with the infrared source IRAS 08005-2356 based on observations with high spectral resolution. Absorption lines of the ions FeII, TiII, CrII, and YII are present at wavelengths from 4549 to 8546 Å. The absorption by YII and other s-process elements is anomalously strong, and the absorption is also strong in the circumstellar C₂ Swan bands. The profiles of most of the lines (of hydrogen and metals) display P Cygni absorption-emission profiles. All the absorption lines are shifted toward the blue, suggesting an outflow of stellar material. The expansion velocity of the envelope derived from the Swan bands arising there is V _exp =42 km/s. The highest wind velocity determined from the absorption wings of the FeII(42) P Cygni profiles reaches 240 km/s. Based on the star’s kinematic characteristics and the amount of interstellar absorption, it is at a distance of d≈3?4 kpc, which corresponds to an absolute magnitude of M_v≈?6^m.     

Variability of Hell and hydrogen line profiles in the spectrum of HD 93521

We have studied the variability of the Hell λλ 4686 and 5411 Å Hβ, and Hα lines in the spectrum of the pulsating star HD 93521. All these line profiles display the same variability pattern relative to the average profiles: a sinusoidal wave that moves systematically from the short-to the long-wavelength wing of the profile. This variability is due to non-radial pulsations. To study the pulsation movements and stratification of the radial velocity in the atmosphere of HD 93521, we analyzed the variability of the radial velocities measured individually for the blue and red halves of the absorption profile at the half-level of the line intensity. The periods and amplitudes of this radial-velocity variability are different for different lines and are well correlated with their central depths. In the transition from weak to strong lines (i.e., from lower to upper layers of the atmosphere), the period of the radial-velocity variations measured using both halves of the absorption profile increases, while its amplitude decreases. When the morphology and variability of photospheric and wind-driven lines are compared, it is clear that the variability of their absorption components is due to the same process—non-radial pulsations. In this way, the non-radial pulsations partly affect the variability of the stellar wind. The effect of the stellar wind on the profiles of strong lines is observed as a variable absorption feature that moves along the profiles synchronous with the axial rotation of the star.     

Diagnostics for accretion disks around UX Ori stars based on Balmer, Paschen, and Brackett Lines

We have modeled the H_α, H_β, and H_γ (Balmer series), P₁₄ (Paschen series), and Br_γ (Brackett series) hydrogen lines formed in the inner regions of the accretion disk around the Herbig Ae star UX Ori. Our calculations are based on spectra obtained with the Nordic Optical Telescope (NOT) and the IRTF. We computed a grid of non-LTE models for a radiating area in the accretion disk and determined the basic parameters of the lines using the method of Sobolev. Analyzing the theoretical and observed line profiles, equivalent widths, and luminosities, we have estimated the accretion rate and electron-temperature distribution in the inner parts of the accretion disk. The accretion rate of UX Ori is about $\dot M_a = (3 - 10) \times 10^{ - 9} M_ \odot /yr$ , and the temperature distribution is consistent with the power law T(r)=T(r _*)(r/r _*)^?1/n , where the electron temperature near the stellar surface T(r _*) is 15000–20000 K and the power-law index n≈2–3 is about two to three. The resulting value for $\dot M_a $ eliminates problems connected with the application of magnetospheric accretion models to Herbig Ae/Be stars. Another important conclusion is that, at the estimated accretion rate, the energy release is substantially (about two orders of magnitude) lower than the stellar luminosity. Therefore, the optical radiation of UX Ori accretion disks cannot appreciably contribute to the observed variability of these stars, which must be determined mainly by variability in the circumstellar extinction.     

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.     

Photometric observations of R Coronae Borealis in the optical and infrared

The results of long-term photometric observations of R CrB in the UBV JHKLM bands are presented. The temporal and color characteristics of the emission of the star itself and of its extended dust envelope are analyzed in detail. No stable harmonic has been found in the semiregular variations of the optical brightness of R CrB. Two harmonics with periods P≈3.3 and 11.3 yrs have been detected in the brightness variations of the dust envelope; the minima of these variations coincided in 1999, resulting in a record decrease in the LM brightness of the envelope. This by chance coincided in time with a deep minimum of the visual brightness of the star, resulting in a unique decrease in the total brightness of the star and dust envelope. This enabled estimation of the bolometric flux of the hot dust clouds, which made up only a few per cent of the bolometric flux of the dust envelope. The brightness variations of the dust envelope are not accompanied by appreciable color changes and are associated with variations of its optical depth τ(V) in the range 0.2–0.4. The dust envelope forms at a large and fairly constant distance from the star $(r_{in} \approx 110R_* ,T_{gr} \approx 860 K)$ , from material in its stellar wind, whose intensity $(\dot M_{gas} \approx 2.1 \times 10^{ - 7} M_ \odot /year)$ obeys a Reimers law. No variations synchronous with those of the optical depth of the dust envelope, in particular, with the period P≈3.3 yrs, have been found in the optical emission of R CrB, suggesting that the stellar wind is not spherically symmetric. The dust envelope consists of small grains (a _gr≤0.01 µm), while the clouds screening the star from the observer are made up of large grains (a _gr≈0.1 µm). The activity of R CrB, whose nature is unclear, is reflected in variations of the stellar-wind intensity and the appearance of dust clouds in the line of sight: these variations are repeated by corresponding changes in the optical depth of the dust envelope with a delay of ～4 years (the time for a particle moving at V _env≈45 km/s to move from the star to the boundary of the dust envelope).     

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.     

Analysis of light curves of eclipsing systems with exoplanets: HD 189733

High-accuracy multicolor light curves of the binary system HD 189733, which contains an exoplanet, are analyzed. We have determined the radii of the star and the planet in the binary system, as well as the orbital inclination. The limb-darkening coefficients of the stellar disk were obtained in 10 filters in the wavelength interval λλ = 5500?10 500 Å. The uncertainties of the fitted parameters were estimated using the differential-correction and confidence-area methods. The wavelength dependence of the limb-darkening coefficients is compared to the corresponding theoretical function for a model thin stellar atmosphere. We confirm the wavelength dependence of the exoplanet’s radius found by Pont et al. (at the 1σ level). The exoplanet radius increases with decreasing wavelength, which seems to argue for the presence of an atmosphere around the planet.     

Photometric activity of the Herbig Be star MWC 297 over 25 years

The photometric behavior of the hot, young Herbig Be starMWC 297 on various time scales is studied using published data, as well as new observations. The series of photometric observations covers about 25 years. Over this time, the star showed low-amplitude (ΔV ≈ 0.3 ^m ) irregular variabilitymodulated by large-scale cyclic variabilitywith an amplitude close to 0.2 ^m and a period (or quasi-period) of 5.4±0.1 yr. A detailed seasonal analysis of the data shows that the light curve of MWC 297 displays two types of photometric features: low-amplitude Algol-like fading with an amplitude close to 0.2 ^m and low-amplitude flares resembling the flares of UV Ceti stars, but being more powerful and having longer durations. The variations of the stellar brightness are accompanied by variations of the B-V and V -R colors: when the brightness decreases, B-V decreases, while V -R increases (the star reddens). The reddening law is close to the standard interstellar reddening law. Although the character of the brightness variability ofMWC 297 resembles the photometric activity of UX Ori type stars, which is due to variations of their circumstellar extinction, its scale is very far from the scales observed for UX Ori stars. It is difficult to reconcile the level of photometric activity with the idea that MWC 297 is observed through its own gas-dust disk viewed almost edge-on, as has been suggested in several studies.     

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].     

Hydrodynamical modeling of mass transfer in the close binary system <Emphasis Type="Italic">β</Emphasis> Lyr

We present results of two-dimensional hydrodynamical simulations of mass transfer in the close binary system β Lyr for various radii of the accreting star and coefficients describing the interaction of the gaseous flow and the main component (primary). We take the stellar wind of the donor star into account and consider various assumptions about the radiative cooling of the gaseous flow. Our calculations show that the initial radius of the flow corresponding to our adopted mass-transfer rate through the inner Lagrange point (L₁) of (1–4) × 10^?5M_⊙/yr is large: 0.22–0.29 (in units of the orbital separation). In all the models, the secondary loses mass through both the inner and outer (L₁ and L₂) Lagrange points, which makes the mass transfer in the system nonconservative. Calculations for various values of the primary radius show a strong dependence on the coefficient fv that models the flow-primary interaction. When the radius of the primary is 0.5, there is a strong interaction between the gas flow from L1 and the flow reflected from the primary surface. For other values of the primary radius (0.1 and 0.2), the flow does not interact directly with the primary. The flow passes close to the primary and forms an accretion disk whose size is comparable to that of the Roche lobe and a dense circum-binary envelope surrounding both the disk and the binary components. The density in the disk varies from 10¹² to 10¹⁴ cm^?3, and is 10¹⁰–10¹² cm^?3 in the circum-binary envelope. The temperature in the accretion disk ranges from 30000 to 120000 K, while that in the circum-binary envelope is 4000–18000 K. When radiative cooling is taken into account explicitly, the calculations reveal the presence of a spiral shock in the accretion disk. The stellar wind blowing from the secondary strongly interacts with the accretion disk, circum-binary envelope, and flow from L₂. When radiative cooling is taken into account explicitly, this wind disrupts the accretion disk.     

Light curve analysis for eclipsing systems with exoplanets. The system HD 209458

We have analyzed precision light curves for HD 209458, a binary with an exoplanet. The parameters obtained at different epochs and different wavelengths are in good mutual agreement when confidence regions are used to calculate the uncertainty intervals. We demonstrate the effectiveness and reliability of our new method for estimating the uncertainty intervals. Reliable estimates are provided for the linear and quadratic limb-darkening coefficients of the star and their confidence intervals (uncertainties). We find that the wavelength dependence for the limb-darkening coefficients at λ = 3201?9708 Å differs significantly from the corresponding theoretical relation based on thin model stellar atmospheres.     

The formation and evolution of the most massive stars

We consider the formation of massive stars under the assumption that a young star accretes material from the protostellar cloud through its accretion disk while losing gas in the polar directions via its stellar wind. The mass of the star reaches its maximum when the intensity of the gradually strengthening stellar wind of the young star becomes equal to the accretion rate. We show that the maximum mass of the forming stars increases with the temperature of gas in the protostellar cloud T ₀, since the rate at which the protostellar matter is accreted increases with T ₀. Numerical modeling indicates that the maximum mass of the forming stars increases to ～900 M _⊙ for T ₀ ～ 300 K. Such high temperatures of the protostellar gas can be reached either in dense star-formation regions or in the vicinity of bright active galactic nuclei. It is also shown that, the lower the abundance of heavy elements in the initial stellar material Z, the larger the maximum mass of the star, since the mass-loss rate due to the stellar wind decreases with decreasing Z. This suggests that supermassive stars with masses up to 10⁶ M _⊙ could be formed at early stages in the evolution of the Universe, in young galaxies that are almost devoid of heavy elements. Under the current conditions, for T ₀ = (30–100) K, the maximum mass of a star can reach ～100M _⊙, as is confirmed by observations. Another opportunity for the most massive stars to increase their masses emerges in connection with the formation and early stages of evolution of the most massive close binary systems: the most massive stars can be produced either by coalescence of the binary components or via mass transfer in such systems.     

A method for determining stellar parameters from multicolor photometry

Amethod for determining the most probable spectral types, color excesses E _B-V , and distances of stars from multicolor photometry is described. The main idea of the method is modeling the photometric data using various models for the stellar spectra and the interstellar extinction law, and applying the maximum likelihood method. The reliability of the method is estimated using stars with known spectral types and WBVR photometry, based on the empirical library of stellar spectra of Pickles and the model for the interstellar extinction law developed by Fluks et al.