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.     

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.

     

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.     

Stars with relativistic speeds in the Hills scenario

The dynamical capture of a binary system consisting of a supermassive black hole (SMBH) and an ordinary star in the gravitational field of a central (more massive) SMBH is considered in the three-body problem in the framework of a modified Hills scenario. The results of numerical simulations predict the existence of objects whose spatial speeds are comparable to the speed of light. The conditions for and constraints imposed on the ejection speeds realized in a classical scenario and the modified Hills scenario are analyzed. The star is modeled using an N-body approach, making it possible to treat it as a structured object, enabling estimation of the probability that the object survives when it is ejected with relativistic speed as a function of the mass of the star, the masses of both SMBHs, and the pericenter distance. It is possible that the modern kinematic classification for stars with anomalously high spatial velocities will be augmented with a new class—stars with relativistic speeds.     

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.     

Formation of planets during the evolution of single and binary stars

Current views of the origin and evolution of single and binary stars suggest that the planets can form aroundmain-sequence single and binary stars, degenerate dwarfs, neutron stars, and stellarmass black holes according to several scenarios. Planets can arise during the formation of a star mainly due to excess angular momentum leading to the formation of an accretion-decretion disk of gas and dust around a single star or the components of a binary. It is the evolution of such disks that gives rise to planetary systems. A disk can arise around a star during its evolution due to the accretion of matter from dense interstellar clouds of gas and dust onto the star, the accretion of mass froma companion in a binary system, and the loss of matter during the contraction of a rapidly rotating star, in particular, if the star rotates as a rigid body and the rotation accelerates with its evolution along the main sequence. The fraction of stars with planetary systems is theoretically estimated as 30–40%, which is close to the current observational estimate of ∼34%.     

An estimate of the probability of capture of a binary star by a supermassive black hole

A simple model for the dynamics of stars located in a sphere with a radius of one-tenth of the central parsec, designed to enable estimation of the probability of capture in the close vicinity (r < 10^?3 pc) of a supermassive black hole (SMBH) is presented. In the case of binary stars, such a capture with a high probability results in the formation of a hyper-velocity star. The population of stars in a sphere of radius <0.1 pc is calculated based on data for the Galactic rotation curve. To simulate the distortion of initially circular orbits of stars, these are subjected to a series of random shock encounters (“kicks”), whose net effect is to “push” these binary systems into the region of potential formation of hyper-velocity stars. The mean crossing time of the border of the close vicinity of the SMBH (r < 10^?3 pc) by the stellar orbit can be used to estimate the probability that a binary system is captured, followed by the possible ejection of a hyper-velocity star.     

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.     

Destruction of a Star during the Evolution of a Star + Supermassive Black Hole System

Astronomy Reports - Stars located closely to supermassive black holes (SMBHs) can, under certain conditions, form close binary systems with the SMBHs, in which the star may fill the Roche lobe and...     

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.     

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.     

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.     

Evolution of stars near bright quasars

We consider the evolution of stars that are located in the near vicinity of bright quasars and illuminated by their hard radiation. The absorption of the external radiation flux in the stellar envelope was calculated applying the formalism used to determine the opacity of the stellar material. The simulations show that the external irradiation heats the outer layers of the star, altering their structure and reducing the thickness of the convective envelope in low-mass stars, but leaves the inner layers essentially unaffected. In addition, the irradiation substantially increases the mass loss in the stars. This is important for our understanding of the evolution of quasar masses, since this increased mass loss by nearby stars can supply the quasar with additional accreting gas. The results can also be applied to detached binaries in which a low-mass star is irradiated by a very massive companion.     

Models for highly flattened, rapidly rotating cool stars in a Newtonian approximation

We investigate the physical characteristics of single, rapidly rotating white dwarfs, which could form as a result of a merger of two white dwarfs with different masses and filled Roche lobes, due to the radiation of gravitational waves. When the merging of the binary components occurs without loss of mass and angular momentum, the merger products are subject to secular instability, and the density in their cores does not exceed ～10⁸ g/cm³. Models are constructed for rapidly rotating neutron stars, which could form after the collapse of rotating iron cores of evolved massive stars. Dynamically unstable neutron-star models are characterized by a shift of the maximum density from the rotational axis. The total momentum of such neutron stars is about half the maximum possible momentum for the evolved cores of massive stars.     

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.     

Possible scenarios for the formation of Ap/Bp stars

Possible paths for the formation of Ap/Bp stars—massive main-sequence stars with strong magnetic fields—are analyzed based on modern theories for the evolution of single and binary stars. Assuming that the strong magnetic fields of these stars are the main reason for their comparatively slow axial rotation and the observed anomalies in the chemical compositions of their atmospheres, possible origins for these high magnetic fields are considered. Analysis of several possible scenarios for the formation of these stars leads to the conclusion that their surface magnetic fields are probably generated in the convective envelopes of the precursor stars. These precursors may be young, single stars with masses 1.5–3 M _⊙ that formed at the peripheries of forming star clusters and ended their accretion at the Hayashi boundary, or alternatively close binaries whose components have convective envelopes, whose merger leads to the formation of an Ap/Bp star. Arguments are presented supporting the view that the merger of close binaries is the main channel for the formation of Ap/Bp stars, and a detailed analysis of this scenario is presented. The initial major axes of the merging binary systems must be in the range 6–12 R _⊙, and the masses of their components in the range 0.7–1.5 M _⊙. When the merging components possess developed convective envelopes and fairly strong initial magnetic fields, these can generate powerful magnetic fields “inherited” by the products of the merger—Ap/Bp stars. The reason the components of the close binaries merge is a loss of angular momentum via the magnetic stellar winds of the components.     

The binary systems IC 10 X-1 and NGC 300 X-1: Accretion of matter from an intense Wolf–Rayet stellar wind onto a black hole

The current evolutionary stage of the binary systems IC 10 X-1 and NGC 300 X-1, which contain a massive black hole and a Wolf–Rayet star with a strong stellar wind that does not fill its Roche lobe, is considered. The high X-ray luminosity and X-ray properties testify to the presence of accretion disks in these systems. The consistency of the conditions for the existence of such a disk and the possibility of reproducing the observed X-ray luminosity in the framework of the Bondi–Hoyle–Littleton theory for a spherically symmetric stellar wind is analyzed. A brief review of information about the mass-loss rates of Wolf–Rayet stars and the speeds of their stellar winds is given. The evolution of these systems at the current stage is computed. Estimates made using the derived parameters show that it is not possible to achieve consistency, since the conditions for the existence of an accretion disk require that the speed of the Wolf–Rayetwind be appreciably lower than is required to reproduce the observedX-ray luminosity. Several explanations of this situation are possible: (1) the real pattern of the motion of the stellar-wind material in the binary is substantially more complex than is assumed in the Bondi–Hoyle–Littleton theory, changing the conditions for the formation of an accretion disk and influencing the accretion rate onto the black hole; (2) some of the accreting material leaves the accretor due to X-ray heating; (3) the accretion efficiency in these systems is nearly an order of magnitude lower than in the case of accretion through a thin disk onto a non-rotating black hole; (4) the intensity of the Wolf–Rayet wind is one to two orders of magnitude lower than has been suggested by modern studies.     

K-Corrections to radial-velocity curves of optical components in X-ray binaries. Massive systems with weak X-ray heating

The radial-velocity curves of optical components in X-ray binary systems can differ from the radial-velocity curves of their barycenters due to tidal distortion, gravitational darkening, X-ray heating, etc. This motivated us to investigate how the semi-amplitudes of the radial-velocity curves of these optical components can depend on the binary-system parameters in a Roche model. The K correction is taken to be the ratio of the radial velocity semi-amplitude for a star in the Roche model to the corresponding value for the stellar barycenter. K corrections are tabulated for the optical stars in the massive X-ray binaries Cen X-3, LMC X-4, SMC X-1, Vela X-1, and 4U 1538-52.     

Observations and optical light-curve analysis for the precataclysmic variable BE Ursae Majoris

We have acquired three-color observations of BE UMa, a precataclysmic eclipsing variable with a strong reflection effect. Using new photoelectric U BV data and archival photographic observations, we have refined the orbital period and demonstrated that the eclipse depth changes with wavelength. The photometric data are used to compute a model for the system. Computations show that the nuclear evolution time for the secondary is only slightly less than the time for the separation of the components to change due to the loss of orbital angular momentum. Therefore, the red dwarf in the BE UMa system will later fill its Roche lobe because of (1) the decrease in component separation due to the loss of energy and angular momentum via gravitational-wave radiation or the outflow of a magnetic stellar wind and (2) the increase in the red dwarf’s radius due to its nuclear evolution.