The structure of matter flows in semi-detached binaries after the termination of mass transfer

We present the results of three-dimensional gas-dynamical simulations of matter flows in semi-detached binaries after termination of the mass transfer between the components of the system. The structure of the residual accretion disk is studied. When the mass transfer has ended, the quasi-elliptical disk becomes circular and its structure changes: tidal interactions result in the formation of a second arm in the spiral shock wave. In addition, a condensation (blob) moving through the disk with variable velocity is formed. The blob is maintained by interactions with the arms of the spiral shock and exists essentially over the entire lifetime of the disk. We also show that, for a viscosity corresponding to α～0.01 (typical for observed accretion disks), the lifetime of the residual disk is about 50 orbital periods.     

Spectral types of four binaries based on photometric observations

We present results of photometric and spectroscopic observations of four close binaries with subdwarf B components: PG 0918+029, PG 1000+408, PG 1116+301, PG 0001+275. We discovered that PG 1000+408 is a close binary, with the most probable orbital period being P _orb = 1.041145 day. Based on a comparison of the observed light curves at selected orbital phases and theoretical predictions for their variations, all the systems are classified as doubly degenerate binaries with low-luminosity white-dwarf secondaries.     

A photometric study of the eclipsing dwarf nova GY Cnc in quiescence and during an outburst

The results of photometric observations of the dwarf nova GY Cnc in the Rc filter acquired in 2013–2015 (~3900 orbital cycles, 19 nights in total) are presented, including observations during its outburst in April 2014. The binary’s orbital elements have been refined. The orbital period has changed only insignificantly during the ~30 000P_orb since the earlier observations; no systematic O–C variations were detected, only fluctuations within 0.004^d on time scales of 1500–2000P_orb. A “combined” model is used to solve for the parameters of GY Cnc during two states of the system. The flux from the white dwarf is negligible due to the star’s small size. The temperature of the donor star, T₂ ~ 3667 K (Sp M0.2 V), varies between 3440 and 3900 K (Sp K8.8–M1.7 V). The semi-major axis of the disk is a ~ 0.22a₀, on average. In quiescence, a varies within ~40%. The disk has a considerable eccentricity (e ~ 0.2?0.3) for a < 0.2a₀. The disk shape becomes more circular (e < 0.1) with increasing a. The outburst of GY Cnc was associated with increased luminosity of the disk due to the parameter α_g (related to the viscosity of the disk material) decreasing to 0.1–0.2 and the temperature in the inner parts of the disk increasing twofold, to T_in ~ 95 000 K. These changes were apparently due to the infall of matter onto the surface of the white dwarf as the outburst developed. All parameters of the accretion disk in quiescence display considerable variations about their mean values.     

Formation and evolution of inclined accretion disks in intermediate polars

The results of 3D modeling of the formation of the accretion disks of intermediate polars are presented. A model with misaligned rotation axes of accretor and the orbit is onsidered, in which it is assumed that the white dwarf has a dipolar magnetic field with its symmetry axis inclined to the whitedwarf rotation and orbital axes. The computations show that, in the early stages of formation of the disk, the action of magnetic field is able to create the initial (seed) inclination of the disk. This inclination is then supported mainly by the dynamical pressure of the flow from the inner Lagrangian point L₁. As themass of the disk increases, the inclination disappears. Under certain conditions, the disk inclination does not arise in systems with misaligned white-dwarf rotation and orbital axes. The influence of the magnetic field and asynchronous rotation of the accretor may result in the formation of spiral waves in the disk with amplitudes sufficient to be detected observationally.     

Synthetic Doppler tomograms of gas flows in the binary system IP Peg

We have synthesized Doppler tomograms of gas flows in the binary system IP Peg using the results of three-dimensional gas-dynamical computations. Gas-dynamical modeling in combination with Doppler tomography enables identification of the key elements of flows in Doppler maps without solution of an ill-posed inverse problem. A comparison of the synthetic tomograms with observations shows that, in the quiescent state of the system, the most luminous components are (1) the shock wave induced by interaction between the circumbinary envelope and the stream from the Lagrange point L ₁ (the “hot line”) and (2) the gas condensation at the apogee of the quasi-elliptical disk. Both the single spiral shock wave arm in the gas-dynamical solution and the stream from L ₁ contribute little to the luminosity. In the active state of the system, when the stream from L ₁ does not play an appreciable role and the disk dominates, both areas of enhanced luminosity in the observational tomograms are associated with the two arms of the spiral shock wave in the disk.     

Neutron stars in close binaries with elliptical component orbits

We consider the evolution of close binaries in which the initial secondary component is a nondegenerate helium star with mass M_He = 0.4–60 M_⊙, while the initially more massive primary has evolved into a black hole, neutron star, or degenerate dwarf. The neutron star is assumed to originate as a result of the evolution of a helium star with a mass of 2.5 M_⊙ ≤ M_He ≤ 10 M_⊙ after the explosion of a type Ib,c supernova. If the axial rotation of the helium star before the explosion is rigid-body and synchronized with the orbital rotation, for P_orb ≤ 0.16 day, the rotational energy of the young neutron star will exceed the energy of an ordinary supernova. If the magnetic field of the neutron star is sufficiently strong, the necessary conditions for a magnetic-rotational supernova are provided. The initial rotational period of a young neutron star originating in a system with an orbital period shorter than ～50 days is shorter than ～4 s, which, according to observations, is required for the appearance of a radio pulsar. A helium star whose mass exceeds ～10 M_⊙ in a close binary with an orbital period shorter than one day and with the axial rotation of the helium presupernova synchronous with the orbital rotation evolves into a Kerr black hole, whose formation is likely to be accompanied by a gamma-ray burst with a duration longer than two seconds. In particular, we consider close binaries in which the second supernova results in the formation of a neutron star that remains in the binary. The theoretical distribution of orbital periods and eccentricities for such systems is consistent with that observed for radio pulsars in the Galactic disk in binaries with compact components and orbital eccentricities exceeding ～0.09, providing an explanation for the observed correlation between the orbital eccentricities and orbital periods for these systems.     

Three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr with an accretor wind

We present three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr taking into account explicitly radiative cooling and the stellar wind of the accretor. Our computations show that flow forces wind out from the orbital plane, where an accretion disk with a radius of 0.4–0.5 and a height of about 0.15–0.17 (in units of orbital separation) is formed. Gas motions directed upward from the orbital plane are initiated in the region of interaction of the flow from L₁ and the accretor wind (x = 0.91, y = ?0.17); i.e., a jetlike structure forms. This structure has the shape of a gas pillar above the orbital plane, where gas moves with the velocity of stellar wind. The number density of the gas in this structure is about 10¹⁴ cm^?3, and its temperature is 20 000–45 000 K. At heights of about 0.15–0.20 above the orbital plane, in the region between the jetlike structure and the disk, two spiral shocks form. It is possible that the emission lines observed in the spectrum of β Lyr binary originate in this region.     

Light-curve syntheses for close binary systems: Modeling spiral waves in an elliptical disk around a white dwarf

We present an algorithm for synthesizing the light curve of a close binary consisting of a normal star (a red dwarf that fills its Roche lobe) and a spherical star (a white dwarf). The spherical component is surrounded by an elliptical accretion disk with a complex shape: it is geometrically thin near the spherical star and geometrically thick at the edge of the disk. An additional complication is presented by the presence of a one-or two-armed spiral pattern at the inner surface of the disk. The maximum height of the spiral arm above the disk surface is located at ～9 R _d , and the height decreases exponentially as the arm approaches the inner regions of the disk. Shielding of the inner hot parts of the disk by the crests of the spirals results in the formation of “steps” in out-of-eclipse parts of the orbital light curves. The algorithm takes into account the presence of a “hot line” by the lateral surface of the disk, making it possible to model binary systems in both quiescence and outburst. In the latter case, the hot line degenerates into a small bulge at the outer lateral surface of the disk, which can be considered an analog of a hot spot. The algorithm was applied to the orbital light curve of the cataclysmic binary IP Peg during its October 30, 2000, outburst. To explain the variations of the out-of-eclipse brightness of the system during the outburst, it is necessary to include the presence of a one-armed spiral wave at the inner surface of the disk, close to the periastron of the elliptical disk. We have obtained the parameters of IP Peg during the outburst for various models of the system.     

Three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr

We present a three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr taking radiative cooling into account explicitly. The assumed mass-transfer rate through the first Lagrangian point L₁ is 3.0 × 10^?5 M _⊙/yr. A flow with a radius of 0.14–0.16 (in units of orbital separation) is formed in the vicinity of L₁. This flow forms an accretion disk with a radius close to 23 R _⊙ and a thickness of about 10 R _⊙. The accretion disk is surrounded by an outer envelope that extends beyond the computational domain. A spiral shock forms at the outer boundary of the disk at orbital phase 0.25. Geometrically, the disk is toruslike, while the outer envelope is cylinder-like. In this model, which has low temperatures inside the computational domain, no jetlike structures form in the disk. It is possible that the jetlike structure in β Lyr arises due to the interaction of radiative wind from the accretor with the flow from L₁. In the model considered, a hot region exists over the poles of the accretor at a height of about 0.21. The amount of matter lost by the system is close to 10% of the mass flowing through L₁; i.e., the mass transfer in the system is almost conservative. For a mass-transfer rate of 3.0 × 10^?5 M _⊙/yr, the orbital period varies by 40.4 s/yr. This means that the observed variation of the orbital period of 19 s/yr should correspond to a mass-transfer rate close to 1.0 × 10^?5 M _⊙/yr.     

Formation of a radiative wind and accretion disk in microquasars. Generation of flare activity in the disk due to an increase in the supply of material to the Lagrange point L<Subscript>1</Subscript>. The system LMC X-3

Three-dimensional numerical hydrodynamical modeling of a radiative wind and accretion disk in a close binary system with a compact object is carried out, using the massive X-ray binary LMC X-3 as an example. This system contains a precessing disk, and may have relativistic jets. These computations show that an accretion disk with a radius of about 0.20 (in units of the component separation) forms from the radiative wind from the donor when the action of the wind on the central source is taken into account, when the accretion rate is equal to the observed value (about 3.0 × 10^?8 M _⊙/year, which corresponds to the case when the donor overflows its Roche lobe by nearly 1%). It is assumed that the speed of the donor wind at infinity is about 2200 km/s. The disk that forms is geometrically thick and nearly cylindrical in shape, with a low-density tunnel at its center extending from the accretor through the disk along the rotational axis. We have also modeled a flare in the disk due to short-term variations in the supply of material through the Lagrange point L₁, whose brightnesses and durations are able to explain flares in cataclysmic variables and X-ray binaries. The accretion disk is not formed when the donor underfills its Roche lobe by 0.5%, which corresponds to an accretion rate onto the compact object of 2.0 × 10^?9 M _⊙/year. In place of a disk, an accretion envelope with a radius of about 0.03 forms, within which gas moves along very steep spiral trajectories before falling onto the compact object. As in the accretion-disk case, a tunnel forms along the rotational axis of the accretion envelope; a shock forms behind the accretor, where flares occur in a compact region a small distance from the accretor at a rate of about six flares per orbital period, with amplitudes of about 10 ^m or more. The flare durations are two to four minutes, and the energies of individual particles at the flare maximum are about 100–150 keV. These flares appear to be analogous to the flares observed in gamma-ray and X-ray burst sources. We accordingly propose a model in which these phenomena are associated with massive, close X-ray binary systems with component-mass ratios exceeding unity, in which the donor does not fill its Roche lobe. Although no accretion disk forms around the compact object, an accretion region develops near the accretor, where the gamma-ray and X-ray flares occur.     

The mechanism of circumbinary envelope formation in close binaries

We consider the structure and formation of the circumbinary envelopes in semi-detached binary systems. Three-dimensional numerical simulations of the gas dynamics are used to study the flow pattern in a binary system after it has reached the steady-state accretion regime. The outer parts of the circumbinary envelope are replenished by periodic ejections from the accretion disk and circum-disk halo through the vicinity of the Lagrange point L₃. In this mechanism, the shape and position of a substantial part of the disk is specified by a precessional density wave. On timescales comparable to the orbital period, the precessional wave (and hence an appreciable fraction of the disk) will be virtually stationary in the observer’s frame, whereas the positions of other elements of the flow will vary due to the orbital rotation. The periodic variations of the positions of the disk and the bow shock formed when the inner parts of the circumbinary envelope flow around the disk result in variations in both the rate of angular-momentum transfer to the disk and the flow structure near L₃. All these factors lead to a periodic increase of the matter flow into the outer layers of the circumbinary envelope through the vicinity of L₃. The total duration of the ejection is approximately half the orbital period.     

Three-dimensional hydrodynamical modeling of accretion-disk formation in microquasars. Cen X-3

We have carried out three-dimensional hydrodynamical modeling of the formation of an accretion disk around a compact object due to radiative wind of a massive donor in a close binary system. The massive X-ray binary Cen X-3, which has a precessing accretion disk and may possess relativistic jets, is considered as an example. The computations show that, when the action of the central compact object on the formation of the wind is taken into account, the radiative wind forms an accretion disk with a radius of 0.16 (in units of the orbital separation), which accretes at a rate close to 1 × 10^?8 M _⊙/yr. In this model, the disk is spherically symmetrical and geometrically thick, with a tunnel going from the accretor to the upper layers of the disk along the accretor’s rotational axis at the disk center. The number density of the gas in the tunnel is five orders of magnitude lower than in the disk. The wind-disk interaction at the outer boundary of the disk produces a strong shock (wind-disk shock) directed toward the donor. The black-body emission of the disk and tunnel is nonstationary, and resembles the outbursts observed in Cen X-3. An analysis of the location of the region of nonstationary emission suggests that the outbursts occur in the wind-disk shock.     

The eclipsing variable CM Dra: Surface activity and orbital elements

A long series of observations of the low-mass eclipsing system CM Dra (M ₁, M _⊙<0.25M _⊙, dM4.5e, V=12.9^m, P _orb=1.27^d) was obtained in 1996–1997 as part of the international TEP (Search for Transits of Extrasolar Planets) project. The observations were obtained on the 70-cm telescope of the Astronomical Observatory of Ural State University with an automatic two-star photometer. The total duration of the data series was 155 h. We construct and analyze a master light curve, including calculation of the photometric and absolute orbital elements. Evidence for surface activity was detected. The light curve of CM Dra outside eclipses shows low-amplitude (0.024^m) brightness variations, suggesting the presence of a starspot on one of the components. The amplitude of these variations stayed the same over 20 years, but the phase of the brightness maximum shifted by one-third of the orbital period, possibly reflecting changes in the longitude or asymmetry of a single large polar spot. We detected four flares whose energies were factors of several hundred higher than those of solar flares. The derived flare rate agrees with data for CM Dra in the literature but is much lower than is typical for Population I stars in our Galaxy.     

Phase transformations of enstatite in spherical shock waves

The analysis of available theoretical evaluations and experimental data reveals discrepancies and makes it possible to formulate the goals for the comprehensive study of the behavior of enstatite MgSiO₃ in shock isentropic waves of various scale and intensity. The paper presents the layout and results of an explosion experiment on the compression of an enstatite sphere with spherical shock waves and the subsequent recovery of the experimental material and its examination in discrete zones (along the sphere radius) that were produced by shock waves in the material. The latter were examined with the application of scanning electron microscopy, Raman spectroscopy, and X-ray diffraction analysis. The comparison of the systematic variations in the texture, chemistry, and phase composition of enstatite along the sphere radius with calculated pressure P(R, t) and temperature T(R, t) values led us to the following conclusions: enstatite starts melting on an isentrope upon pressure relief after shock wave compression at ?? _xx ?? 80 GPa and melts on the front of the spherically converging shock wave at ?? _xx ?? 160 GPa and T ?? 6300 K. Our laboratory experiments with shock waves were the world??s first in which enstatite was loaded with spherical converging shock isentropic waves and which provided evidence that shock wave-loaded MgSiO₃ shows certain morphological and mineralogical features never before detected in this mineral loaded with plane shock wave of smaller amplitude and duration. Goals are formulated for the further studying of shock wave-loaded materials, and the necessity is discussed for conducting an explosion experiment with a five to seven times greater spherical system in order to increase the duration of the shock wave loading impulse.     

PG 1316+678: A young pre-cataclysmic binary with weak reflection effects

The PG 1316+678 star is classified as a pre-cataclysmic binary, as is evidenced by its photometric and spectroscopic observations. Its orbital period is determined to be P _orb = 3.3803^d, which coincides with the photometric period. The intensities of the emission HI and HeI lines are shown to vary synchronously with the brightness of the object (Δm _V = 0.065 ^m , Δm _R = 0.08 ^m ). These variations arise as the UV radiation from the DAO white dwarf is reflected from the surface of the cold companion. The parameters of the binary are estimated and the time of its evolution after the common-envelope phase is determined to be t ≈ 240 000 years. Thus, PG 1316+678 is a young pre-cataclysmic NN Ser variable with the smallest known photometric reflection effect.     

The structure of the common envelope in a close binary system

As a result of the interaction between an elliptical accretion disk and gas flowing into it from the circumbinary envelope in a close binary in the course of its orbital motion, the matter of the disk and the circum-disk halo is periodically ejected from the vicinity of the Lagrange point L₃, and a common envelope is formed in the system. Three-dimensional numerical gas-dynamical modeling is used to study the structure and dynamics of the envelope and determine its basic parameters. The evolution of the envelope is followed on timescales of the order of several orbital periods. The matter flow ejected through the vicinity of L₃ displays a spiral shape. The maximum size of the forming spiral structure is restricted by the self-intersection point, and is of the order of four to five times the component separation. We consider the dynamics of the regions directly adjacent to the spiral structure: an inner, rarified and outer, fragmented region, which further makes a transition to an expanding diffuse ring.     

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.     

Structure of the accretion disk in the cataclysmic variable UX UMa in the transition to its quiescent state

Our analysis of BV RI light curves for the cataclysmic variable UX UMa obtained in intermediate activity states, in the transition between the active and quiescent states of the system on March 12, 1997 and May 3, 2000, shows that the shapes of these light curves cannot be adequately described using the standard hot-spot model. A model with a “hot line” near the edge of the disk and a two-armed spiral structure on the disk surface reproduces much better out-of-eclipse variations in the light curves. The presence of an extended hot line can explain the anomalous shape of the I light curve on March 12, 1997. The decrease in the observed luminosity of the system between March 12, 1997 and May 3, 2000 could be due to a decrease in the disk luminosity by a factor of 2–2.5; the higher disk luminosity on the earlier date is associated with appreciable deviations of the radial temperature distribution of the disk material from that for the standard model. The phases and depths of dips in the out-of-eclipse sections of the UX UMa light curves are due primarily to the parameters of the complex shape of the accretion disk, which has a spiral structure located mainly near its outer edge. The contribution of the spiral arms in the V filter reaches 20–50% of the total disk radiation. The crest of the first spiral wave in our model maintains its approximate position in azimuth; this structure could represent a bulge in a halo at the outer edge of the disk near orbital phases φ ～ 0.7, in the direction of the continuation of the extended shock in the disk itself. The position of the crest of the second spiral arm changes with time. This structure may represent a one-armed spiral wave near the apastron of the weakly elliptical disk. Finally, the observations testify to the presence of another spiral arm that is les clearly manifest in terms of both its luminosity and its height above the unperturbed disk surface. Thus, in an intermediate activity state of UX UMa, the surface of the accretion disk is distorted by the action of a two-armed spiral structure in the outer regions of the disk, which is asymmetric in both its luminosity and dimensions, and a bulge at the disk edge in the region of its interaction with the inflow to the disk.     

Changes in the parameters of the accretion disk around the dwarf nova SDSS J090350.73+330036.1 during an outburst

R-band photometric light curves of the eruptive eclipsing binary SDSS J090350.73+330036.1 obtained during a superoutburst in May 2010 (JD 2455341-2455347) are analyzed. Observations covering an interval near the outburst maximum and the post-maximum decrease by 0.7 ^m are presented. Oscillations (superhumps) whose period differs from the orbital period by several percent are observed in the light curve together with eclipses, suggesting that the studied system is a SU UMa dwarf nova. A ??spiral arm?? model is used to fit the light curves and determine the parameters of the accretion disk and other components of the binary system. Together with a hot line, this model takes into account, geometrical inhomogeneities on the surface of the accretion disk, namely, two thickenings at its outer edge that decrease exponentially in the vertical direction with approach toward the white dwarf. The increase in the R-band flux from the system during the superoutburst mainly results from the enhanced luminosity of the accretion disk due to the increase in its radius by up to ??0.44a ₀ at the outburst maximum (a ₀ is the component separation), as well as a shallower radial temperature decrease law than in the canonical case. As the superoutburst faded, the disk radius decreased smoothly at the end of our observation (to ??0.33a ₀), the thickness of its outer edge and temperature of its boundary layer decreased, and the parameter ?? _g approached its canonical value. Deviations from the mean brightness of the system as a function of the superhump period P _sh are analyzed for each out-of-eclipse set of observations. Various factors affecting the appearance and amplitudes of superhumps in the orbital light curves are considered.     

The probable quadruple systems FK Aql and FZ Del

Orbital-period variations of the eclipsing binaries FK Aql and FZ Del are analyzed. For each of the systems, a superposition of two cyclic variations of their orbital periods is found. FK Aql may be a quadruple system that contains two more bodies, besides the eclipsing binary, with masses M ₃ ? 1.75M _⊙ and M ₄ ? 1.47M _⊙, and the corresponding periods 15 and 82 yrs. This could also be a triple system with a third body of mass M ₃ ? 1.75M _⊙ and a period of the long-period orbit P ₃ = 15 yrs, or with a third body of mass M ₃ ? 1.30M _⊙ and a period of the long-period orbit P ₃ = 82 yrs. FZ Del may be a quadruple system with the additional componentmasses M ₃ ? 0.2M _⊙ and M ₄ ? 0.3M _⊙, with the periods 10.2 and 53.7 yrs. This could also be a triple system with a third-body mass M ₃ ? 0.2M _⊙ and a period of the long-period orbit P ₃ = 10.2 yrs. In both systems, the residual period variations could be due to magnetic cycles of the secondary. The period variations of the eclipsing binary FZ Del could also be due to apsidal motion, together with the influence of a third body or the effects of magnetic activity.