The mass spectrum of black holes in close binary systems

We present the results of population syntheses obtained using our “scenario machine.” The mass spectra of black holes in X-ray binary systems before and after the stage of accretion from an optical companion are obtained for various evolutionary scenarios. The results of the model computations are compared to observational data. The observational data are used to estimate the fraction of a presupernova’s mass that collapses into a black hole. This model can explain the formation of low-mass (2–4M_⊙) black holes in binary systems with optical companions. We show that the number of low-mass black holes in the Galaxy is sufficiently high for them to be detected. The population-synthesis results suggest that the vast majority of low-mass black holes are formed via the accretion-induced collapse of neutron stars. The percentage of low-mass black holes in binary systems that form due to accretion-induced collapse is 2–15% of the total number of black holes in binaries, depending on the evolutionary scenario.     

The evolution of close binary systems with intermediate-mass black holes and ultra-luminous X-ray sources

The results of numerical studies of the evolution of a close binary system containing a black hole with a mass of ～3000M_⊙ are presented. Such a black hole could form in the center of a sufficiently rich and massive globular cluster. The secondary could be a main-sequence star, giant, or degenerate dwarf that fills or nearly fills its Roche lobe. The numerical simulations of the evolution of such a system take into account the magnetic wind of the donor together with the wind induced by X-ray irradiation from the primary, the radiation of gravitational waves by the system, and the nuclear evolution of the donor. Mass transfer between the components is possible when the donor fills its Roche lobe, and also via the black hole’s capture of some material from the induced stellar wind. The computations show that the evolution of systems with solar-mass donors depends only weakly on the mass of the accretor. We conclude that the observed ultra-luminous X-ray sources (L _X ? 10³⁸ erg/s) in nearby galaxies could include accreting black holes with masses of 10²?10⁴M_⊙. Three scenarios for the formation of black holes with such masses in the cores of globular clusters are considered: the collapse of superstars with the corresponding masses, the accretion of gas by a black hole with a stellar initial mass (<100M_⊙), and the tidal accumulation of stellar black holes. We conclude that the tidal accumulation of stellar-mass black holes is the main scenario for the formation of intermediate-mass black holes (10²?10⁴M_⊙) in the cores of globular clusters.     

Formation of supermassive black holes due to the tidal deceleration of stellar black holes, globular clusters, and galaxies

The formation and evolution of supermassive (10²?10¹⁰ M _⊙) black holes (SMBHs) in the dense cores of globular clusters and galaxies is investigated. The raw material for the construction of the SMBHs is stellar black holes produced during the evolution of massive (25?150M _⊙) stars. The first SMBHs, with masses of ～1000M _⊙, arise in the centers of the densest and most massive globular clusters. Current scenarios for the formation of SMBHs in the cores of globular clusters are analyzed. The dynamical deceleration of the most massive and slowly moving stellar-mass (< 100M _⊙) black holes, accompanied by the radiation of gravitational waves in late stages, is a probable scenario for the formation of SMBHs in the most massive and densest globular clusters. The dynamical friction of the most massive globular clusters close to the dense cores of their galaxies, with the formation of close binary black holes due to the radiation of gravitational waves, leads to the formation of SMBHs with masses ? 10³ M _⊙ in these regions. The stars of these galaxies form galactic bulges, providing a possible explanation for the correlation between the masses of the bulge and of the central SMBHs. The deceleration of the most massive galaxies in the central regions of the most massive and dense clusters of galaxies could lead to the appearance of the most massive (to 10¹⁰ M _⊙) SMBHs in the cores of cD galaxies. A side product of this cascade scenario for the formation of massive galaxies with SMBHs in their cores is the appearance of stars with high spatial velocities (> 300 km/s). The velocities of neutron stars and stellar-mass black holes can reach ～10⁵ km/s.     

Black holes in close binary systems and galactic nuclei

After 50 years of observational studies of black holes, great progress has been achieved in this branch of astrophysics. Several dozen stellar-mass black holes have been discovered in X-ray binaries, and several hundred supermassive black holes in galactic nuclei. The remarkable recent discovery of gravitational waves from merging black holes in a binary system by LIGO marks the beginning of a new stage in black-hole research. It is quite possible that gravitational-wave studies will provide definitive evidence for the existence of event horizons in black holes in the near future. On the other hand, the development of methods for space and ground-based radio-interferometry observations provides hope that it will be possible to obtain images of “shadows” of supermassive black holes in galactic nuclei, and to observe directly processes occurring in the vicinities of the event horizons of supermassive black holes. This is important for tests of general relativity in extremely strong gravitational fields.     

Sub-parsec structure of binary supermassive black holes in active galactic nuclei

Long-term, multi-frequency monitoring of the radio fluxes of the four BL Lac objects 3C 120, OJ 287, 1308+326, and BL Lac is considered. Harmonic components of the flux variability on scales from one year to decades are determined. The observational data used were obtained at the Radio Astronomy Laboratory of the Crimean Astrophysical Observatory (Ukraine) and the University of Michigan Radio Astronomy Observatory (USA). These data are used to construct kinematic models for active galactic nuclei using values for the orbital and precessional periods of binary systems consisting of supermassive black holes. The derived speeds of the companions in their orbits lie in the narrow range 3000–4000 km/s. The orbital radii for the binary supermassive black holes also lie in a narrow range, 10¹⁷–10¹⁸ cm, providing evidence that observed prominent examples of active galactic nuclei are fairly close binary systems. The parameters of the mediumin which the components of the binary systems are moving are estimated, as well as the rates at which the systems are losing orbital angular momentum and their lifetimes to coalescence.     

Wolf-Rayet stars,black holes,and gamma-ray bursters in close binaries

We consider the evolutionary status of observed close binary systems containing black holes and Wolf-Rayet (WR) stars. When the component masses and the orbital period of a system are known, the reason for the formation of a WR star in an initial massive system of two main-sequence stars can be established. Such WR stars can form due to the action of the stellar wind from a massive OB star (M_OB≥50M_⊙), conservative mass transfer between components with close initial masses, or the loss of the common envelope in a system with a large (up to ～25) initial component mass ratio. The strong impact of observational selection effects on the creation of samples of close binaries with black holes and WR stars is demonstrated. We estimate theoretical mass-loss rates for WR stars, which are essential for our understanding the observed ratio of the numbers of carbon and nitrogen WR stars in the Galaxy \(\dot M_{WR} (M_ \odot yr^{ - 1} ) = 5 \times 10^{ - 7} (M_{WR} /M_ \odot )^{1.3} \). We also estimate the minimum initial masses of the components in close binaries producing black holes and WR stars to be ～25M_⊙. The spatial velocities of systems with black holes indicate that, during the formation of a black hole from a WR star, the mass loss reaches at least several solar masses. The rate of formation of rapidly rotating Kerr black holes in close binaries in the Galaxy is ～3×10^?6 yr^?1. Their formation may be accompanied by a burst of gamma radiation, possibly providing clues to the nature of gamma-ray bursts. The initial distribution of the component mass ratios for close binaries is dN～dq=dM₂/M₁ in the interval 0.04?q₀≤1, suggesting a single mechanism for their formation.     

Evolution of close stellar binaries with black holes under the action of gravitational radiation and magnetic and induced stellar winds of the donor

We show that semi-detached close binary systems with massive (4–25M_⊙) black holes are formed in the evolution of massive stellar binaries in which the initial mass of the primary exceeds ～25M_⊙. The mass exchange in such systems is maintained by the nuclear evolution of the donor and by its magnetic and induced stellar winds. The donor in such systems can be a main-sequence star, subgiant, non-degenerate helium star, or white dwarf. The evolution of corresponding systems with black-hole masses of 10M_⊙ is investigated.     

Formation of low-mass X-ray novae with black holes from triple systems

We apply a population synthesis technique to study the formation and evolution of low-mass X-ray binaries with black holes, observed as X-ray novae, from hierarchical triple systems. A scenario is suggested in which an inner close binary system evolves into an X-ray system with a large mass ratio. The high rate of accretion onto the neutron star leads to a common envelope stage, which may result in the formation of a Thorne-Zytkow (TZ) object. During its evolution, the envelope of the TZ object expands, encompassing the third star. The recurrent common-envelope stage decreases the size of the orbit of the third star, leading to the formation of a lowmass X-ray nova with a black hole. The dynamical stability of triple systems automatically ensures that only lowmass X-ray novae form. We also consider the possible formation of an X-ray nova from a binary in the case of asymmetrical core collapse during a supernova explosion.     

Supermassive black holes: Relation to dark halos

Estimates of the masses of supermassive black holes (M _bh ) in the nuclei of disk galaxies with known rotation curves are compared with estimates of the rotational velocities V _m and the “indicative” masses of the galaxies M _i . Although there is a correlation between M _bh and V _m or M _i , it is appreciably weaker than the correlation with the central velocity dispersion. The values of M _bh for early-type galaxies (S0-Sab), which have more massive bulges, are, on average, higher than the values for late-type galaxies with the same rotational velocities. We conclude that the black-hole masses are determined primarily by the properties of the bulge and not the rotational velocity or the mass of the galaxy.     

The evolution of close binary stars

A review of our current understanding of the physics and evolution of close binary stars with various masses under the influence of the nuclear evolution of their components and their magnetic stellar winds is presented. The role of gravitational-wave radiation by close binaries on their evolution and the loss of their orbital angular momentum is also considered. The final stages in the evolution of close binary systems are described. The review also notes the main remaining tasks related to studies of the physics and evolution of various classes of close binaries, including analyses of collisions of close binaries and supermassive black holes in galactic nuclei. Such a collision could lead to the capture of one of the components by the black hole and the acceleration of the remaining component to relativistic speeds.     

High-velocity stars as a result of encounters between stars and massive binary black holes in galactic nuclei

Numerical simulations of the motions of stars in the gravitational fields of binary black holes with various component mass ratios have been carried out. Two models are considered: (1) the two-body problem with two fixed centers; (2) the general three-body problem. The first model is applicable only over short times Δt ? T, where T is the period of the binary system. The second model is applicable at all times except for during close encounters of stars with one of the binary components, r ≤ 0.00002 pc, where r is the distance from the star to the nearer black hole. In very close passages, relativistic corrections must be taken into account. Estimates of the probability of formation of high-velocity stars as a result of such interactions are obtained. It is shown that this mechanism is not suitable for the nucleus of our Galaxy due to the probable absence of a second massive black hole in the central region of the Galaxy.     

Formation of a protoplanetary system through the merging of binary components that are contracting towards the main sequence

We have carried out three-dimensional hydrodynamical modeling of the formation of planets through the merging of a binary system comprised of low-mass (～0.5–1 M_⊙) stars in the stage of contracting towards the main sequence. Under certain conditions, the disruption of the more massive component results in the formation of an expanding disk and extended arm. The fragmentation of this arm leads to the formation of planetary-mass clouds (<5 M _J where M _J is the mass of Jupiter), whose orbits can have semimajor axes of 0.4 to 5 AU and substantial (～0.5) eccentricities.     

Elliptical motions of stars in close binary systems

The motion of stars in close binary systems with conservative mass transfer is considered. It is shown that the Paczynski-Huang model that is currently used to determine the variations of the semimajor axis of the relative orbit of the stars is not correct, and leads to large errors in the derived semi-major axis. A new model is proposed, suitable for elliptical stellar orbits. The reaction forces and gravitational forces between the stars and the stream of overflowing matter are taken into account. The possibility of mass transfer in the presence of an accretion disk is considered.     

Photoelectric lunar-occultation observations of several close binary stars

The results of photoelectric lunar-occultation observations for several stars are presented. Some of these are obvious close binary systems, while others are suspected close binaries or multiple systems, or show evidence for the presence of complex structure of some other kind. It is expected that new, efficient interferometric systems will enable detailed studies of the structure of many “ordinary” stars with an angular resolutions of 10^?4–10^?5 arcsec.     

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.     

Elliptical motion of a star in a close binary system

The motion of a rotating star in a close binary system with conservative mass exchange is considered. In contrast to the Paczyński-Huang model, the new model applied examines the relative motion of a star along an elliptical orbit in a close binary system, taking into account the mutual gravitation between the stars, reactive forces, the gravitation exered on the stars by the mass-transfer stream, and perturbations due to the rotation of the accreting star. The variations of the semi-major axis and eccentricity of the orbit and the orbital angular velocity of the accreting star as a function of the component-mass ratio q are determined. The results are applied to the BF Aurigae system.     

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.     

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.     

Early formation of galaxies induced by clusters of black holes

A model for the formation of supermassive black holes at the center of a cluster of primordial black holes is developed. It is assumed that ～10^?3 of the mass of the Universe consists of compact clusters of primordial black holes that arose as a result of phase transitions in the early Universe. These clusters also serve as centers for the condensation of dark matter. The formation of protogalaxies with masses of the order of 2 × 10⁸ M _⊙ at redshift z = 15 containing clusters of black holes is investigated. The nuclei of these protogalaxies contain central black holes with masses ～10⁵ M _⊙, and the protogalaxies themselves resemble dwarf spherical galaxies with their maximum density at their centers. Subsequent merging of these induced protogalaxies with ordinary halos of dark matter leads to the standard picture for the formation of the large-scale structure of the Universe. The merging of the primordial black holes leads to the formation of supermassive black holes in galactic nuclei and produces the observed correlation between the mass of the central black hole and the bulge velocity dispersion.     

Masses of stellar black holes and testing theories of gravitation

The paper analyzes the mass distribution of stellar black holes derived from the light and radial-velocity curves of optical stars in close binary systems using dynamical methods. The systematic errors inherent in this approach are discussed. These are associated primarily with uncertainties in models for the contribution from gaseous structures to the optical brightness of the systems under consideration. The mass distribution is nearly flat in the range 4–15M _⊙. This is compared with the mass distribution for black holes in massive close binaries, which can be manifest as ultrabright X-ray sources (L _x >10³⁹ erg/s) observed in other galaxies. If the X-ray luminosities of these objects correspond to the Eddington limit, the black-hole mass distribution should be described by a power law, which is incompatible with the flat shape derived dynamically from observations of close binaries in our Galaxy. One possible explanation of this discrepancy is the rapid evaporation of stellar-mass black holes predicted in recent multi-dimensional models of gravity. This hypothesis can be verified by refining the stellar black-hole mass spectrum or finding isolated or binary black holes with masses below ～3M _⊙.