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.     

Photometry and spectroscopy of the system V4641 sagittarii in quiescence

We present the results of our CCD photometric and moderate-dispersion spectroscopic observations of the binary system V4641 Sgr, which contains a black hole of mass ≈9.5M_⊙ and a normal B9III star. The photometric light curve reveals an ellipticity effect with very high amplitudes in V and R, 0.40^m and 0.37^m, and the color curve shows that the surface temperature is nonuniform. All this testifies to tidal distortion of the normal star's surface due to the massive companion and to a high inclination of the orbit to the line of sight. In June and July 2002, during quiescence, we obtained data during three flares with amplitudes up to 0.26^m. In particular, spectroscopic observations were acquired near the time of the black hole's inferior conjunction. One hour before conjunction, a depression by EW=0.5 Å was observed in the red wing of the Hα absorption line, interpreted as absorption by gas flowing in the direction from the observer toward the normal star. This flow is apparently associated with a rarefied gas disk around the black hole, and the conjunction grazes the stellar surface if the orbital inclination is close to 70.7°. The maximum velocity along a circular Keplerian orbit is 650 km/s at a distance of R=0.15–0.20a from the black hole (where a is the component separation). Thus, we find the mass of the black hole to be M _BH =7.1–9.5M_⊙, confirming the model of Orosz et al. (2001).     

The eclipsing binary HS hercules: Photometric elements and the evolutionary stages of its components

We used a photoelectric photometer designed by V.M. Lyutyi and the Zeiss-600 telescope of the Sternberg Astronomical Institute’s Crimean Observatory to acquire precise UBV brightness measurements (σ _obs ^V ～ 0.007^m) for the eclipsing binary system HS Her in 1984–1991. These measurements continue the homogeneous series of observations of this star commenced in 1969 by D.Ya. Martynov using the same equipment. Our detailed analysis of this homogeneous 22-year series of photoelectric observations has yielded a self-consistent set of physical and geometric parameters of the binary, and enabled us to establish the evolutionary stages of its components. The systems’s primary, M ₁ = 5 M _⊙, is at the beginning of its main-sequence evolution, whereas its secondary, M ₂ = 1.6 M _⊙, has not yet reached the main sequence. The binary’s age is estimated to be t = (17 ± 3) × 10⁶ years.     

Orbital-period variations in the eclipsing binary Y Cam

We have studied the time behavior of the orbital period and the primary’s pulsation period for the eclipsing binary system Y Cam, whose secondary fills its Roche lobe and whose primary is a δ Scuti star. The times of minima available for this eclipsing binary cover 120 years. δ Scuti pulsations of the primary have been observed over the last 50 years, with the period of these pulsational brightness variations remaining virtually unchanged during the entire observed time interval. The large-amplitude cyclic variations of the orbital period of Y Cam cannot be explained solely by the presence of a third body in the system. It is possible to explain the period variations of Y Cam with magnetic oscillations or a superposition of a stationary matter flow from the lower-mass to the higher-mass component together with magnetic oscillations, similar to the case of AB Cas. A good agreement with observations is provided by a model assuming a stationary matter flow from the secondary filling its Roche lobe to the primary, at the rate of 2.85 × 10^?7 M _⊙/year, superposed with irregular period jumps that can be explained by instabilities in the matter flow. We have detected cyclic variations of the orbital period of Y Cam with an amplitude of 0.011^d, which can be understood if the binary moves in a long-period orbit (with a period of 38.6 years) around a third body with mass M ₃ s> 0.30M _⊙. These cyclic period variations of the eclipsing binary agree with the observed small period variations of the δ Scuti pulsations.     

PN G068.1+11.0: A young pre-cataclysmic variable with an extremely hot primary

An analysis of spectroscopic and photometric data for the young pre-cataclysmic variable (PCV) PN G068.1+11.0, which passed through its common-envelope stage relatively recently, is presented. The spectroscopic and photometric data were obtained with the 6-m telescope and Zeiss-1000 telescope of the Special Astrophysical Observatory. The light curves show sinusoidal brightness variations with the orbital-period time scale and brightness-variation amplitudes of Δm = 1_.^m41, 1_.^m62, and 1_.^m57 in the B, V, and R bands, respectively. The system’s spectrum exhibits weak HI (Hβ–Hδ) andHeII λλ4541, 4686, 5411 Å absorption lines during the phases of minimum brightness, as well as HI, HeII, CIII, CIV, NIII, and OII emission lines whose intensity variations are synchronized with variations of the integrated brightness of the system. The emission-line formation in the spectra can be fully explained by the effects of fluorescence of the ultraviolet light from the primary at the surface of the cool star. All the characteristics of the optical light of PN G068.1+11.0 confirm that it is a young PCV containing sdO subdwarf. The radial velocities were measured from a blend of lines of moderately light elements, CIII+NIII λ4640 Å, which is formed at the surface of the secondary due to reflection effects. The ephemeris of the system has been improved through a joint analysis of the radial-velocity curves and light curves of pre-cataclysmic variable, using modelling of the reflection effects. The fundamental parameters of PN G068.1+11.0 have been determined using two evolutionary tracks for planetary-nebula nuclei of different masses (0.7 M_⊙and 0.78M_⊙). The model spectra for the system and a comparison with the observations demonstrate the possibility of refining the components’ effective temperatures if the quality of the spectra used is improved.     

IR photometry of the symbiotic star BF Cyg: Detection of the red giant’s ellipsoidal brightness variability

We present the results of our IR photometric observations of the classical symbiotic star BF Cyg acquired in 1978–2003. The variability range in the J and K bands was ～0.2^m. A periodic component in the cool star’s brightness variations is clearly visible, its period being half the orbital one and its J amplitude being ～0.15^m. This component is associated with the ellipsoidal shape of the red giant, which model calculations show fills its Roche lobe. This is required in order to reproduce ellipsoidal brightness variability with such a large amplitude: the calculated amplitude for a red giant filling 90% of its Roche lobe is half the observed value. At the same time, it was not possible to confidently chose the optimum component-mass ratio, q = M _giant /M_hot, and orbital inclination, i, from possible values in the ranges q = 2–4, i = 70°–90°. Including the contribution from the hot radiation sources (the hot component and ionized envelope), which vary with a period equal to the orbital period, has a considerable influence on the estimated parameters associated with the red giant’s ellipsoidal brightness variations, and this contribution cannot be neglected. The deviations of the observed from the calculated light curve are irregular, with the rms deviation being σ(O-C) ≈ 0.04^m.     

The nature of the unique precataclysmic variable V664 Cas with two-peaked Balmer lines in its spectrum

We analyze photometric and spectroscopic observations of the close binary system V664 Cas. All the characteristics of its radiation are consistent with the star being a cataclysmic variable with powerful reflection effects. The orbital period is refined (P=0.5816475 d) and the ephemerides of the system determined. The U, B, V, R light curves of V664 Cas display sinusoidal variations with similar amplitudes near Δm=1.1^m. This suggests that a hot spot on the surface of the secondary always dominates the optical radiation of the system. The spectra contain emission lines, two-peaked hydrogen lines, and narrow lines of helium and heavy elements in high ionization states, whose intensities vary synchronously with the brightness. The HeII λ4686 Å line has broad absorption wings that form in the atmosphere of the O subdwarf. The mass function, f(m)=0.007M_⊙, is the lowest among all precataclysmic variables: the mass of the secondary exceeds the mass of the primary by more than a factor of 1.6. A full set of fundamental parameters for V664 Cas is determined based on modeling of the spectra and light curves, taking into account reflection effects in the system. Most of the emission lines are formed under conditions of appreciable deviations from local thermodynamic equilibrium. The possibility of carrying out correct modeling of the Balmer-line profiles assuming the stellar radiation is absorbed in a planetary nebula is demonstrated.     

A “tsunami” in the protoplanetary disk of SV Cep

The results of ~15 years of photometric observations of the UX Ori star SV Cep in the near-infrared (JHKL) are presented. They demonstrate the presence of a cyclic component with a period of ~7 years in the variations of the IR fluxes. This is clearly seen in all four IR bands, but is absent in the optical. The variation amplitude is highest in the K band: ΔK ≈ 0.68 ^m . The shape of the variations differs slightly in the transition from J to L. However, it is reproduced with good accuracy during two cycles, suggesting a periodic process is observed. If the periodic perturbations in the circumstellar disk of SV Cep are due to a companion’s orbitalmotion, the orbital semi-major axis should be ~5AU, foramass of SVCep of 2.6M _⊙. The absence of a seven-year period in the optical light curve of SV Cep means that the observed period cannot be due to variations in the circumstellar extinction. The IR brightness variations could be due to the companion’s motion along an eccentric orbit, resulting in a periodic modulation of the rate of accretion onto the star.     

Analysis of brightness variations in the massive close binary system UU Cassiopeia

We derive the parameters of the hot, massive close binary system UU Cas from earlier and recent photoelectric UBVR observations: M ₁ = 34.5M _⊙, M ₂ = 25.7M _⊙, A = 69R _⊙, and i=68°; the components' limb darkening coefficients are close to 1. Our fitting of the light curves provides evidence for a high degree of over-contact: the components fill their inner critical surfaces by 132% and 100%. It is possible that the appearance of the light curve is determined not only by the distorted shapes of the components and their eclipses but, to a considerable extent, by screening by a complex envelope and the envelope's contribution to the system's total luminosity.     

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.     

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.     

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_⊙).     

The eclipsing WN3(h)+O5V binary BAT99-129: Light curve analysis and parameters of its components

We have analyzed the broad-band light curve of the massive eclipsing binary BAT99-129, which is located in the Large Magellanic Cloud and consists of WN3(h) and O5V components. The light curve was obtained as part of the MACHO project. The dense extended atmosphere of the Wolf-Rayet (WR) star makes it impossible to apply a standard parametric model, such as that of Wilson and Devinney, to analyze the light curve. We reconstructed the distributions of the brightness and absorption across the disk of the WR component by directly solving the integral equations describing the eclipses in the system. Our analysis yields reliable estimates of the system’s orbital parameters and the parameters of its components. The orbital inclination is 78°, the size of the orbit 28.5 R _⊙, and the radius of the O component R _O = 7.1 R _⊙. The size of the WR core, which is opaque in the optical continuum, is R _WR = 3.4 R _⊙, and the brightness temperature at the center of the WR-component disk is T _br = 45 000 K. We discuss possible uncertainties in the parameters obtained. The derived information is used to draw conclusions about the system’s evolutionary status.     

The dwarf nova MN Dra: Periodic processes at various phases of the supercycle

We analyze photometry of the dwarf nova MN Dra carried out using various instruments at four observatories on 18 nights between May 20 and June 28, 2009. The observations cover a variety of activity states of the system: a superoutburst, three normal outbursts, and quiescence. Analysis of the system’s light curve during the superoutburst decline reveals positive superhumps that recur, on average, with a period of 0.105 days and are due to the direct apsidal precession of the accretion disk. These are observed until the end of the superoutburst, but their period decreases at a rate of −24.5 × 10⁻⁵ of the period per period. Both the positive-superhump period and its derivative are in good agreement with estimates made during previous superoutbursts. At the brightness minimum and in normal outbursts, MN Dra displays brightness variations with a period of 0.096 days, whose amplitude is much larger during the brightness minimum (0.8 ^m –1.5 ^m ) than during normal outbursts (0.1 ^m –0.2 ^m ). We suggest that these brightness variations could be negative superhumps due to nodal precession of the oblique accretion disk.     

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.     

X Per and V725 Tau: infrared variations on timescales longer than fifteen years

The results of infrared observations of the two Be stars X Per and V725 Tau, which are the optical components of X-ray binary systems, obtained in 1994–2016 are presented. The observations cover Be-star phases as well as shell phases. The data analysis shows that the radiation observed from the binaries at 1.25, 3.5, and 5 μm can be explained as the combined radiation from the optical components and variable sources (shells/disks) that emit as blackbodies (BBs). Emission from a source with the color temperature T _c ~1000?1500 K was detected for X Per at λ ≥ 3.5 μm. The highest IR-brightness variation amplitudes for X Per were 0.9?1.2 ^m (JHK magnitudes) and ~1.45 ^m (LM magnitudes); for V725 Tau, they were 1.1?1.4 ^m and ~1.7 ^m (L magnitudes). The parameters of the optical components and interstellar extinction during the Be phases were estimated: the color excesswasE(B?V) = 0.65±0.08 ^m and 0.77 ± 0.03 ^m for X Per and V725 Tau, respectively. Light from the variable sources (disks/shells) was distinguished and their color temperatures, radii, and luminosities estimated for different observation epochs in a BB model. The variations of the binaries’ IR brightness and colors are shown to be due to changing parameters of the variable sources. The mean color temperature of the cool source (disk/shell) and the mean radius and mean luminosity of X Per are 9500± 2630 K, (35 ± 10) R_⊙, and (9100± 540) L_⊙. For V725 Tau, these parameters are 6200 ± 940 K, (27 ± 6) R_⊙, and (980 ± 420) L_⊙. The 1.25–5 μm radiation from X Per at different epochs can be represented as a sum of contributions from at least three sources: the optical component and two objects emitting as BBs. To reproduce the 1.25–3.5 μm radiation from V725 Tau, two components are sufficient: the optical component and a single variable BB object. For both binary systems, orbital variations of the IR brightness can be noted near the Be-star phase. The amplitudes of the J-band variations of X Per and V725 Tau are about 0.3 ^m and 0.1 ^m , respectively.     

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.     

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_⊙.     

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.     

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_⊙.