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.     

Gas–Dynamical Features of the Envelopes of Contact Binary Stars

The results of three-dimensional numerical simulations of the gaseous envelope of a contact binary star with parameters similar to those of SV Cen are presented. The outflow of matter from the vicinity of the Lagrange point L₂ leads to the formation of a disk-like common envelope with a radius of order three times the component separation. The characteristics of this envelope and its structure and dynamics are discussed, as well as possible observational manifestations of such an envelope.     

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.     

Observational manifestations of the common envelope in a close binary

Three-dimensional (3D) numerical models of close binaries are used to study the structure and dynamics of common envelopes formed due to periodic ejections of matter from the accretion disk through the vicinity of the Lagrange point L₃. The results are used to estimate the physical parameters of the envelope, including its 3D matter distribution, and the matter-flow configuration and dynamics. Possible observational manifestations of such envelopes are estimated. We present the envelope’s radialvelocity distributions at various phases and times, as well as model light curves taking into account extinction in the envelope. The envelope becomes optically thick for systems with high mass-exchange rates, ? > 10^?8 M _⊙/year, and has a significant influence on the binary’s observed features. The uneven phase distributions of the matter and density variations due to periodic injections of matter into the envelope are important for interpretations of observations of close binary stars.     

Three-dimensional hydrodynamical modeling of the two-component wind and accretion disk in the close binary β Lyrae

This paper continues a series of studies on three-dimensional hydrodynamical modeling of mass transfer in the binary system β Lyr. The model takes into account the stellar wind from the donor star, which outflows at a rate of , as demonstrated by radio observations. This stellar wind should appreciably influence the formation of the envelope in the binary. Computations have shown that the interaction of the matter flow from the Lagrangian point L₁ and the accretor wind leads to the formation of an optically and geometrically thick gaseous envelope around the accretor. The matter flow meets the accretor wind, spreads out, accumulates over the outer edge of the wind, and forms a geometrically thick envelope (disk). The wind flows freely at the center of the disk, over the accretor poles. Jet-like structures arise beyond the wind-propagation region, above the thick accretion disk. The matter flowing from the outer edge of the disk interacts with the donor wind, leading to the formation of a standing shock between L₁ and the outer edge of the disk, in the direction corresponding to orbital phase 0.25. This shock is able to explain the origin of the X-ray radiation from the binary β Lyr.     

Types of gaseous envelopes of “hot Jupiter” exoplanets

As a rule, the orbital velocities of “hot Jupiters,” i.e., exoplanets with masses comparable to the mass of Jupiter and orbital semi-major axes less than 0.1 AU, are supersonic relative to the stellar wind, resulting in the formation of a bow shock. Gas-dynamical modeling shows that the gaseous envelopes around hot Jupiters can belong to two classes, depending on the position of the collision point. if the collision point is inside the Roche lobe of the planet, the envelopes have the almost spherical shapes of classical atmospheres, slightly distorted by the influence of the star and interactions with the stellar-wind gas; if the collision point is located outside the Roche lobe, outflows from the vicinity of the Lagrangian points L₁ and L₂ arise, and the envelope becomes substantially asymmetrical. The latter class of objects can also be divided into two types. If the dynamical pressure of the stellar-wind gas is high enough to stop the most powerful outflow from the vicinity of the inner Lagrangian point L₁, a closed quasi-spherical envelope with a complex shape forms in the system. If the wind is unable to stop the outflow from L₁, an open aspherical envelope forms. The possible existence of atmospheres of these three types is confirmed by 3D numerical modeling. Using the typical hot Jupiter HD 209458b as an example, it is shown that all three types of atmospheres could exist within the range of estimated parameters of this planet. Since different types of envelopes have different observational manifestations, determining the type of envelope in HD 209458b could apply additional constrains on the parameters of this exoplanet.     

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.     

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.     

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.     

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.     

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 matter-flow structure in the SS Cyg system in its quiescent state from comparisons of observational and synthetic Doppler tomograms

Doppler tomograms are constructed for the quiescent state of the SS Cyg system based on Hβ and Hγ spectral-line observations carried out in August 2006 with the 2-m telescope at Terskol Peak. Gasdynamical simulations combined with the Doppler tomograms enable identification of the main features of the flow. Comparisons of synthetic tomograms with observations indicate that an accretion disk is present in the quiescent system. In the tomograms, the luminosity is maximum at the arms of the spiral tidal shock at the shock front due to the interaction between the gas of the circum-binary envelope and material in the stream issuing from the Lagrangian point L₁ (the “hot line”), and in the region behind the bow shock due to the motion of the accretor and disk in the gas of the envelope. The contribution of this last element results in appreciable asymmetry of the tomograms.     

A possible manifestation of spiral shock waves in the accretion disks of cataclysmic variables

We present the results of three-dimensional numerical simulations of flow structures in binary systems with spiral shock waves. Variations of the mass-transfer rate perturb the equilibrium state of the accretion disk; consequently, a condensation (blob) behind the shock breaks away from the shock front and moves through the disk with variable speed. Our computations indicate that the blob is a long-lived formation, whose mean parameters do not vary substantially on timescales of several tens of orbital periods of the system. The presence of the spiral shocks maintains the compact blob in the disk: it prevents the blob from spreading due to the differential motion of matter in the disk, and dissipative spreading on this timescale is negligible. A number of cataclysmic variables display periodic or quasi-periodic photometric variations in their light curves with characteristic periods ～0.1–0.2P _orb, where P _orb is the orbital period. The blobs formed in systems with spiral shock waves are examined as a possible origin for these variations. The qualitative (and, in part, quantitative) agreement between our computations and observations of IP Peg and EX Dra provides evidence for the efficacy of the proposed model.     

Periodic Accretion in the T Tauri Binary UZ Tau E

Results of three-dimensional numerical simulations of the gas dynamics of the envelope of the young T Tauri binary star UZ Tau E are considered. The flow structure in the circumstellar envelope of the system is analyzed. It is shown that a regime with the impulsive accretion of matter from the circumstellar disk is realized in the binary system, in which there is a periodic transfer of matter to the accretion disk of the primary component through the accretion disk of the secondary.

     

Interaction of the stream from <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> with the outer edge of the accretion disk in a cataclysmic variable

Vertical oscillations of the gas at the outer edge of the accretion disk in a semi-detached binary due to interaction with the stream of matter from the inner Lagrangian point L ₁ are considered. Mixing of the matter from the stream from L ₁ with matter of the disk halo results in the formation of a system of two diverging shocks and a contact discontinuity, or so-called “hot line”. The passage of matter through the region of the hot line leads to an increase in its vertical velocity and a thickening of the disk at phases 0.7?0.8. Subsequently, the matter moving along the outer edge of the disk also experiences vertical oscillations, forming secondary maxima at phases 0.2?0.4. It is shown that, for systems with component mass ratios of 0.6, these oscillations will be amplified with each passage of the matter through the hotline zone, while the observations will be quenched in systems with component mass ratios ~0.07 and ~7. The most favorable conditions for the flow of matter from the stream through the edge of the disk arise for component mass ratios ~0.62. A theoretical relation between the phases of disk thickenings and the component mass ratio of the system is derived.     

Reduction of mass loss by the hot Jupiter WASP-12b due to its magnetic field

The influence of the dipolar magnetic field of a “hot Jupiter” with the parameters of the object WASP-12b on the mass-loss rate from its atmosphere is investigated. The results of three-dimensional gas-dynamical and magnetohydrodynamical computations show that the presence of a magnetic moment with a strength of ~0.1 the magnetic moment of Jupiter leads to appreciable variations of the matter flow structure. For example, in the case of the exoplanet WASP-12b with its specified set of atmospheric parameters, the stream from the vicinity of the Lagrange point L₁ is not stopped by the dynamical pressure of the stellar wind, and the envelope remains open. Including the effect of the magnetic field leads to a variation in this picture—the atmosphere becomes quasi-closed, with a characteristic size of order 14 planetary radii, which, in turn, substantially decreases the mass-loss rate by the exoplanet atmosphere (by~70%). This reduction of the mass-loss rate due to the influence of the magnetic fieldmakes it possible for exoplanets to form closed and quasi-closed envelopes in the presence of more strongly overflowing Roche lobes than is possible without a magnetic field.     

Two-dimensional hydrodynamical modeling of mass transfer in semidetached binaries with asynchronously rotating components

We have modeled the mass transfer in the three semidetached binaries U Cep, RZ Sct, and V373 Cas taking into account radiative cooling both implicitly and explicitly. The systems have asynchronously rotating components and high mass-transfer rates of the order of 10^?6M_⊙/yr; they are undergoing various stages of their evolution. An accreting star rotates asynchronously if added angular momentum is redistributed over the entire star over a time that exceeds the synchronization time. Calculations have indicated that, in the model considered, mass transfer through the point L₁ is unable to desynchronize the donor star. The formation of an accretion disk and outer envelope depends on the component-mass ratio of the binary. If this ratio is of the order of unity, the flow makes a direct impact with the atmosphere of the accreting star, resulting in the formation of a small accretion disk and a relatively dense outer envelope. This is true of the disks in U Cep and V373 Cas. When the component-mass ratio substantially exceeds unity (the case in RZ Sct), the flow forms a large, dense accretion disk and less dense outer envelope. Taking into account radiative cooling both implicitly and explicitly, we show that a series of shocks forms in the envelopes of these systems.     

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.     

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.     

A possible mechanism for the X-ray emission of Be/X stars

A new mechanism for the generation of X-ray emission in binary Be/X stars is proposed. It is shown that the mass-transfer rate through the point L₁ in a model in which the optical component of a Be/X star has an expanding envelope is sufficient to generate the observed X-ray luminosities of such stars. The results of computations indicate a dependence between the orbital periods and X-ray fluxes of these systems. The relationship between the orbital perod and the mass-transfer rate during flares obtained from modeling corresponds to the observed dependence of the maximum X-ray flux on the orbital period.