Close binaries containing Supermassive Black Holes

We consider the evolution of binary systems formed by a Supermassive Black Hole (SMBH) residing in the center of a galaxy or a globular cluster and a star in its immediate vicinity. The star is assumed to fill its Roche lobe, and the SMBH accretes primarily the matter of this star. The evolution of such a system is mainly determined by the same processes as for an ordinary binary. The main differences are that the donor star is irradiated by hard radiation emitted during accretion onto the SMBH; in a detached system, nearly all the donor wind is captured by the black hole, which strongly affects the evolution of the semi-major axis; it is not possible for companions of the most massive SMBHs to fill their Roche lobes, since the corresponding orbital separations are smaller than the radius of the last stable orbit in the gravitational field of the SMBH. Moreover, there may not be efficient exchange between the orbital angular momentum and the angular momentum of the overflowing matter in such systems. Our computations assumed that, if the characteristic timescale for mass transfer is smaller than the thermal timescale of the star, no momentum exchange occurs. Absorption of incident external radiation in the stellar envelope was treated using the same formalism that was used when computing the radiative transfer in the stellar atmosphere. Numerical simulations show that Roche-lobe overflow is possible for a broad range of initial system parameters. The evolution of semi-detached systems containing a star and a SMBH nearly always ends with the dynamical disruption of the star. Stars with masses close to the solar mass are destroyed immediately after they fill their Roche lobes. During the accretion of matter of disrupted stars, the SMBH can achieve quasar luminosities. If the SMBH accretes ambient gas as well as gas stripped from stars, the star is subject to additional radiation in the detached phase of its evolution, strengthening its stellar wind. This leads to an increase of the semi-major axis and subsequent decrease of the probability of Roche-lobe overflow during the subsequent evolution of the system.     

The evolution of stars paired with supermassive black holes

A star located in the close vicinity of a supermassive black hole (SMBH) in a galactic nucleus or a globular-cluster core could form a close binary with the SMBH, with the star possibly filling its Roche lobe. The evolution of such binary systems is studied assuming that the SMBH mainly accretes matter from the companion star and that the presence of gas in the vicinity of the SMBH does not appreciably influence variations in the star’s orbit. The evolution of the star–SMBH system is mainly determined by the same processes as those determining the evolution of ordinary binaries. The main differences are that the star is subject to an incident flux of hard radiation arising during the accretion of matter by the SMBH, and, in detached systems, the SMBH captures virtually all the wind emitted by its stellar companion, which appreciably influences the evolution of the major axis of the orbit. Moreover, the exchange between the orbital angular momentum and the angular momentum of the overflowing matter may not be entirely standard in such systems. The computations assume that there will be no such exchange of angular momentum if the characteristic timescale for mass transfer is shorter than the thermal time scale of the star. The absorption of external radiation in the stellar envelope was computed using the same formalism applied when computing the opacity of the stellar matter. The numerical simulations show that, with the adopted assumptions, three types of evolution are possible for such a binary system, depending on the masses and the initial separation of the SMBH and star. Type I evolution leads to the complete destruction of the star. Only this type of evolution is realized for low-mass main-sequence (MS) stars, even those with large initial separations from their SMBHs. Massive MS stars will also be destroyed if the initial separation is sufficiently small. However, two other types of evolution are possible for massive stars, with a determining role in the time variations of the parameters of the star–SMBH system being played by the possible growth of the massive star into a red giant during the time it is located in the close vicinity of the SMBH. Type II evolution can be realized for massive MS stars that are initially farther from the SMBH than in the case of disruption. In this case, the massive star fills its Roche lobe during its expansion, but is not fully destroyed; the star retreats inside its Roche lobe after a period of intense mass loss. This type of evolution is characterized by an increase in the orbital period of the system with time. As a result, the remnant of the star (its former core) is preserved as a white dwarf, and can end up at a fairly large distance from the SMBH. Type III evolution can be realized formassiveMSstars that are initially located still farther from their SMBHs, and also for massive stars that are already evolved at the initial time. In these cases, the star moves away from the SMBH without filling its Roche lobe, due to its intense stellar wind. The remnants of such stars can also end up at a fairly large distances from their SMBHs.     

Evolution of Stars Paired with Intermediate-Mass Black Holes

Under certain conditions, stars close to intermediate-mass black holes (IMBHs) can form close binary systems with these objects, in which the Roche lobe can be filled by the star and intense accretion of the star’s matter onto the IMBH is possible. Recently, accreting IMBHs have been associated with hyperluminous X-ray sources (HLXs), whose X-ray luminosities can exceed 10⁴¹ erg/s. In this paper, the evolution of star—IMBH binary systems is investigated assuming that the IMBH mainly accretes the matter of its companion star, and that the presence of gas in the vicinity of the IMBH does not appreciably affect changes in the orbit of the star. The computations take into account all processes determining the evolution of ordinary binary systems, as well as the irradiation of a star by hard radiation during the accretion of its matter onto the IMBH. The absorption of external radiation in the stellar envelope was calculated applying the same formalism that is used to calculate the opacity of the stellar matter. The computations also assumed that, if the characteristic time for the mass transfer is less than the thermal time scale of the star, there is no exchange betwween the orbital angular momentum of the system and the angular momentum of the matter flowing onto the IMBH.

Numerical simulations have shown that, under these assumptions, three types of evolution are possible for such a binary system, depending on the mass of the IMBH and the star, as well as on the star’s initial distance from the IMBH. The first type ends with the destruction of the star. For low-mass main sequence (MS) stars, only this option is realized, even in the case of large initial distances from IMBH. For massive MS stars, the star is also destroyed if the mass of the IMBH is high and the initial distance of the star from the IMBH is sufficiently small.

The second type of evolution can occur for massive MS stars, which are initially located farther from the IMBH than in the first type of evolution. In this case, the massive star fills its Roche lobe during its evolutionary expansion, after which a stage of intense mass transfer begins. It is in this phase of the evolution that the star- IMBH system can manifest itself as a HLX, when its X-ray luminosity L_X exceeds 10⁴¹ erg/s for a fairly long time. Numerical simulations show that the initial mass of the donor star in systems with M_BH = (10³?10⁵)M_⊙ must be close to ～10 M_⊙ in this case. The characteristic duration of the HLX stage is 30 000–70 000 years. For smaller initial donor masses close to ～5M_⊙, L_X does not reach 10⁴¹ erg/s in the stage of intense mass transfer, but can exceed 10⁴⁰ erg/s. The duration of this stage of evolution is 300 000–800 000 years. A characteristic feature of this second type of evolution is an increase in the orbital period of the system over time. As a result, after a period of intense mass loss, the star “retreats” inside the Roche lobe. A remnant of the star in the form of a white dwarf is left behind, and can end up fairly far from the IMBH.

The third type of evolution can occur for massive MS stars that are initially even farther from the IMBH, as well as for massive stars that are already evolved at the initial time. In this case, conservative mass exchange in the presence of intense stellar wind leads to the star moving away from the IMBH, without filling its Roche lobe at all. For massive stars with sufficiently strong stellar winds (for example, stars with masses ～50M_⊙), the accretion rate of matter onto the IMBH in this case can reach values that are characteristic of HLXs. As in the case of the second type of evolution, the stellar remnant can remain at a fairly large distance from the IMBH.

     

Formation and evolution of Ae and Be stars

Several scenarios for the formation of accretion and decretion disks in single and binary Ae and Be stars are proposed. It is shown that, in order for a rapidly rotating main-sequence Be star to lose mass via a disk, the star’s rotation must be quasi-rigid-body. Estimates show that such rotation can be maintained by the star’s magnetic field, which is probably a relict field. The evolution of single Be main-sequence stars is numerically simulated allowing for mass loss via the stellar wind and rotational mass loss assuming rigid-body rotation. The stellar wind is the factor that determines the maximum mass of Be stars, which is close to 30M _⊙. The evolution of Be stars in close binaries is analyzed in the approximation adopted in our scenario. Long gamma-ray bursts can be obtained as a result of the collapse of rapidly rotating oxygen—neon degenerate dwarfs—the accreting companions of Be stars—into neutron stars.     

Enhancement of surface helium abundance in intermediate-mass main-sequence stars

The evolution of rapidly rotating 8, 4, and 2 M _⊙ main-sequence stars is considered together with hydrodynamical transfer in their interiors. The conditions under which turbulent erosion, semiconvection, and shear turbulence lead to partial mixing of the matter in the radiative envelope and central regions of the stars are determined. The enhancement of the surface helium abundance with time depends on both the intensity of partial mixing in their interiors and mass loss by the stellar wind. The ratio of the number densities of helium and hydrogen at the surface can rise by the end of main-sequence stage by ～30% for a 8 M _⊙ star and ～10?20% for a 4 M _⊙ star, depending on the mass-loss rate. Partial mixing of the matter in the radiative envelope and in the central region of the star can provide an explanation for the observed enhancement of the atmospheric helium abundances of early B stars toward the end of their main-sequence evolution. The enhancement of the surface helium abundance in a 2 M _⊙ star is so small that it cannot be detected, and is appreciably lower than the enhancement beneath the surface.     

The origin of intergalactic stars in galaxy clusters

The paper analyzes possible origins of stars located in intergalactic space that are not bound to specific galaxies, which comprise 15–50% of all stars in galaxy clusters. Some such stars can form in streams of intergalactic gas flowing around gas-rich disk galaxies moving in the cluster. Others may be the products of the decay of young, low-mass, spheroidal galaxies after the loss of their gaseous components during an initial burst of star formation. The decay of low-mass disk galaxies moving at high speeds after they have lost their gaseous components due to the pressure of the incident flow of dense intergalactic gas is possible in the cluster core. The largest fraction of intergalactic stars are probably produced by the partial disruption of galaxies as a result of close passages, collisions, or mergers. Collisions of low-mass, gas-rich galaxies are especially good suppliers of intergalactic stars. Both stars from decaying stellar components of galaxies and stars arising in the gaseous components of colliding galaxies can be supplied to the intergalactic medium. The merger of galaxies harboring supermassive black holes in their nuclei could lead to the partial or total disruption of these galaxies during the deceleration of the binary black hole that is formed during the merger. An enhanced density of intergalactic stars is observed in the cores of galaxy clusters, underscoring the role of galaxy collisions in the formation of the intergalactic stellar population, since the frequency of galaxy collisions grows with their density.     

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.     

Determining basic characteristics of stars from evolutionary computations

A technique for determining a star’s radius from its atmospheric characteristics (effective temperature, surface gravity, and metallicity) is realized based on modernmodel computations of the stellar internal structure and evolution. The atmospheric characteristics can also be used to find the mass and luminosity of the star. The star’s rate of evolution and the initial mass function are taken into account when determining the stellar characteristics, increasing the correctness of the results. Computations of stellar evolution of with and without the stellar rotation taken into account make it possible to remove ambiguity due to missing data on the star’s rotational velocity. The results are checked and uncertainties estimated using stars occupying two heavily populated regions in the Hertzsprung–Russell diagram that have been well studied using various methods: the main sequence and red giant branch. Good agreement with the observations is achieved; there are almost no systematic deviations of the derived point estimates of the fundamental characteristics. The metallicities of the individual components of eclipsing variable stars are estimated using observational data on for such stars displaying lines of both components in their spectra. These metallicities were determined as a function of the stellar masses in a way that eliminates systematic deviations in the derived fundamental characteristics.     

The formation of millisecond radio pulsars in close binary systems

An analysis of the basic parameters of a sample of radio and X-ray pulsars that are members of close binary systems is used to separate them into several families according to the nature of the pulsar companions and the previous evolution of the systems. To quantitatively describe the main parameters of close binaries containing neutron stars, we have performed numerical modeling of their evolution. The main driving forces of the evolution of these systems are the nuclear evolution of the donor, the magnetically coupled and radiation-induced stellar winds of the donor, and gravitational-wave radiation. We have considered donors that are low-mass stars in various stages of their evolution, nondegenerate helium stars, and degenerate stars. The systems studied are either the products of the normal evolution of close binaries with large initial component-mass ratios or result from inelastic collisions of old neutron stars with single and binary low-mass, main-sequence stars in the dense cores of globular clusters. The formation of single millisecond pulsars requires either the dynamical disruption of a low-mass (?0.1M_⊙) donor or its complete evaporation under the action of the X-ray radiation of the millisecond pulsar. The observed properties of binary radio pulsars with eccentric orbits combined with the bimodal spatial-velocity distribution of single radio pulsars suggest that it may be possible to explain the observed rotational and spatial motions of all radio pulsars as a result of their formation in close binaries. In this case, neutron stars formed from massive single stars or the components of massive wide binaries probably cannot acquire the high spatial velocities or rapid rotation rates that are required for the birth of a radio pulsar.     

Evolution of the components of the close binary WR 20a

We have analyzed the evolution of the components of the unique massive binary system WR 20a, which consists of a Wolf-Rayet nitrogen star and an Of star with an extremely small separation. The estimated masses of the components are 83 and 82 M _⊙, which are among the highest stellar mass inferred. We have carried out numerical modeling of the evolution of the components, taking into account the mass loss due to the stellar wind inherent to massive stars. In a scenario in which the systemis detached from the time the components reach the main sequence until its present state, the initial component masses are inferred to be close to 110 M _⊙, if the initial masses of the stars were equal, or 120 and 100 M _⊙, if they were different. Currently, the components are evolved main-sequence stars, whose surfaces are relatively little enriched by helium. The further evolution of the system will result in one of the components filling its Roche lobe and evolution within a common envelope. As a result, the components may coalesce, leading to the formation of a single massive black hole the supernova explosion. Otherwise, depending on the masses of the resulting black holes, either a binary system with two black holes or two free black holes will be formed. In the latter case, gamma-ray bursts will be observed.     

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.     

Estimation of a star’s radius from its effective temperature and surface gravity taking into account stellar evolution

A method for determining the radius of a star based on its effective temperature and surface gravity together with computations of the star’s structure and evolution is proposed. Rotating and nonrotating stellar models are considered, making it possible to take into account uncertainties associated with the lack of data on the rotational velocities of the stars considered. Each point of an evolutionary track is assigned a weight in accordance with the rate of the stellar evolution and the initial mass function. This enables a more correct estimation of the stellar radius. The method is used to calculate the radius corresponding to the effective temperature and surface gravity obtained from theoretical spectra derived from model stellar atmospheres. This makes it possible to calculate not only the color indices, but also the brightness of the star, enabling estimation of the distance to the star based on photometric observations. The method has been tested and its accuracy estimated using more than a hundred binaries and two dozen well-studied bright stars. The derived radius estimates for stars near the main sequence display systematic deviations that do not exceed 0.03%, and standard deviations for the relative errors below 3.87%. Data on well studied bright stars have enabled verification of the applicability of the method for the red giant branch, and hence proved the possibility of applying it in this densely populated area of the Hertzsprung–Russell diagram.     

Disk wind in young binaries and its impact on the infrared excesses of young stars

We consider the effect of binarity of young stars on the spectral energy distribution of the IR radiation from circumstellar dust. The formation of a common dust envelope in a binary system with a low-mass secondary component is strongly affected by the disk wind from the secondary. The small velocities in peripheral areas of the wind are such that it can be partially or entirely captured by the primary, even when the distance between the components is up to several astronomical units. As a result, an envelope with a rather complex spatial and kinematic structure is formed. Its mass is many orders of magnitude smaller than that of the accretion disk around the binary. However, the thermal radiation emitted by dust particles of the envelope can be comparable to the total radiation of the accretion disk. This result is discussed in the context of the deficit at near-IR wavelengths (2–10µm) in current models for accretion disks around young stars.     

Molecular structure of brown-dwarf disks

We describe typical features of the chemical composition of proto-planetary disks around brown dwarfs. We model the chemical evolution in the disks around a low-mass T Tauri star and a cooler brown dwarf over a time span of 1 Myr using a model for the physical structure of an accretion disk with a vertical temperature gradient and an extensive set of gas-phase chemical reactions. We find that the disks of T Tauri stars are, in general, hotter and denser than the disks of lower-luminosity substellar objects. In addition, they have more pronounced vertical temperature gradients. The atmospheres of the disks around low-mass stars are more strongly ionized by UV and X-ray radiation, while less dense brown-dwarf disks have higher fractional ionizations in their midplanes. Nevertheless, in both cases, most molecules are concentrated in the so-called warm molecular layer between the ionized atmosphere and cold midplane, where grains with ice mantles are abundant.     

Analysis of the Na,Mg, Al,and Si abundances in the atmospheres of red giants of different spectral subgroups

We analyze the Na, Mg, Al, and Si abundances in the atmospheres of more than 40 stars, includingred giants of different spectral subgroups (normal red giants, mild and classical barium stars) and several supergiants. All these elements exhibit abundance excesses, with the overabundance increasing with the star’s luminosity. The dependence of the overabundances for each of these elements on the luminosity (or log g) is the same for all the spectral subgroups, testifying to a common origin: they are all products of hydrogen burning in the NeNa and MgAl cycles that have been dredged up from the stellar interiors to the outer atmospheric layers by convection that gradually develops during the star’s evolution from the main sequence to the red-giant stage. The sodium abundances derived for several stars are lower than for other stars with similar atmospheric parameters. The ages and kinematic characteristics of these two groups of stars suggest that they probably belong to different stellar generations.     

太阳系演化中的地球和月球起源(英文)

宇宙中恒星的演化始于巨星的形成 ,后者的质量是太阳系的数百倍 ,寿命估计为数百万年。重元素合成于巨星的内部。它们控制了巨星爆炸过程中 (超新星 )形成的气态云和盘状物的冷凝加速度。冷凝和旋转的加速导致后代恒星质量越来越小 ,寿命越来越长 ,直到形成像太阳这样的小星体 ,其质量为 1.989× 10 30 kg ,寿命已有几十亿年。这些小恒星的形成是冷凝过程中产生的水成冰氢星子不断聚集的结果。上一代巨星的原始星盘中的物质只有一小部分参与了冰氢星子的形成。这些星体形成于致密、高速旋转的原始恒星星盘中 ,周围环绕着巨行星和褐矮星。由于星体达到恒星状态 ,它们开始影响原恒星盘 ,结果导致星体相互分散 ,同时 ,最近的巨星发生表面去气作用。后者可以从巨星到恒星的质量衰减得到证实。UpsilonAndromedae、5 5Cancri和HD16 84 4 3等天体的巨行星记载了这样的事实。太阳系中的表面去气作用主要反映在近太阳巨星的流体外壳完全消失。由于流体外壳消失 ,铁硅酸盐熔融核暴露地表 ,形成小的类地行星。木星也经历过表面去气作用 ,依据是木星具有很高的平均密度 (1.3g cm3) ,几乎是土星密度 (0 .7g cm3)的两倍。因此 ,类地行星的形成经历了两个阶段 :原行星 (其父巨星具有重的熔融核 )和正常行星 (在其父行星     

Circumstellar nebulae of WR and OB stars with strong winds: Simultaneous excitation by stellar radiation and shocks

We use a two-phase model for the structure of the circumstellar nebulae of hot stars to analyze the radiative cooling of a dense, compact cloud behind the shock produced by the compression of the cloud by hot gas from the stellar wind, taking into account ionization and heating by radiation from the central star. We can distinguish three stages of the evolution of the cloud during its compression. In the first stage, relevant for the entire cloud before compression and the gas ahead of the shock front, the state of the gas is determined purely by ionization by the stellar radiation. The next stage is characterized by the simultaneous action of two gas excitation mechanisms—photoionization by the stellar radiation and shock heating. In this stage, the gas intensively radiates thermal energy received at the shock front. After radiative cooling, in the final stage, ionization and heating of the gas are again determined mainly by the star. To compute the spectrum of the cloud radiation, we solved for the propagation of a plane-parallel, homogeneous flux through the shock front in the radiation field of the hot star. The computations show that a combination of two excitation mechanisms considerably enriches the theoretical spectrum. The relative intensities of emission lines of a single cloud may resemble either those for an HII region or of a supernova remnant.     

Population synthesis of rapidly rotating main-sequence stars with companions

Usingthe “Scenario Machine” (a specialized numerical code formodeling the evolution of large ensembles of binary systems), we have studied the physical properties of rapidly rotating main-sequence binary stars (Be stars) with white-dwarf companions and their abundance in the Galaxy. The calculations are the first to take into account the cooling of the compact object and the effect of synchronization of the rotation on the evolution of Be stars in close binaries. The synchronization time scale can be shorter than the main-sequence lifetime of a Be star formed during the first mass transfer. This strongly influences the distribution of orbital periods for binary Be stars. In particular, it can explain the observed deficit of short-period Be binaries. According to our computations, the number of binary systems in the Galaxy containing a Be star and white dwarf is large: 70–80% of all Be stars in binaries should have degenerate dwarf companions. Based on our calculations, we conclude that the compact components in these systems have high surface temperatures. Despite their high surface temperatures, the detection of white dwarfs in such systems is hampered by the fact that the entire orbit of the white dwarf is embedded in the dense circumstellar envelope of the primary, and all the extreme-UV and soft X-ray emission of the compact object is absorbed by the Be star’s envelope. It may be possible to detect the white dwarfs via observations of helium emission lines of Be stars of not very early spectral types. The ultraviolet continuum energies of these stars are not sufficient to produce helium line emission. We also discuss numerical results for Be stars with other evolved companions, such as helium stars and neutron stars, and suggest an explanation for the absence of Be-black-hole binaries.     

WR + OB Binary Systems: Observational Evidence of Their Formation as a Result of Mass Exchange

An analysis of observational data shows that, in most cases,Wolf–Rayet (WR) stars in known WR+ OB binary systems were formed as a result of mass transfer in initial OB + OB systems, rather than through radial mass loss by the more massive OB star via its stellar wind.     

The evolutionary status of the most massive WNh stars in close binary systems. NGC 3603-A1

The evolution of the components of the unique, massive, close binary system NGC 3603-A1, which consists of stars of spectral types WN6ha and WN6h, is analyzed. The component masses are estimated to be 116 and 89M _⊙, close to the highest measured stellar masses. Numerical modeling of the evolution of the components has been carried out, taking into account mass loss via the stellar winds of the two massive stars. It is shown that the maximum possible initial component masses are close to 140 and 125M _⊙. The components are currently slightly evolved main-sequence stars, with a comparative low degree of helium enrichment at their surfaces. Further evolution of the system will lead to filling of the Roche lobe of the primary and subsequent evolution in a common envelope. This may lead to the merger of the components, with the evolution of the system ending in the formation of a singlemassive black hole after the second supernova explosion. Otherwise, depending on the masses of the resulting black holes, either a binary system of two black holes or two unbound black holes may form, accompanied by gamma-ray bursts.