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.     

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.     

Masses of the visual components and black holes in X-ray novae: Effects of proximity of the components

It is shown that the approximation of the complex, tidally distorted shape of a star as a circular disc with local line profiles and a linear limb-darkening law, which is usually applied when deriving equatorial stellar rotation velocities from line profiles, leads to overestimation of the equatorial velocity V _rot sin i and underestimation of the component mass ratio q = M _x /M _v . A formula enabling correction of the effect of these simplifying assumptions on the shape of a star is used to re-determine the mass ratios q and the masses of the black holes M _x and visual components M _v in low-mass X-ray binary systems containing black holes. Taking into account the tidal–rotational distortion of the stellar shape can significantly increase the mass ratios q = M _x /M _v , reducing M _v , while M _x changes only slightly. The resulting distribution of M _v attains its maximum near M _v ? 0.35M _⊙, in disagreement with the results of population synthesis computations realizing standard models for Galactic X-ray novae with black holes. Possible ways to overcome this inconsistency are discussed. The derived distribution of M _x also differs strongly from the mass distribution for massive stars in the Galaxy.     

Supermassive black holes and galaxy kinematics

The statistical relation between the masses of supermassive black holes (SMBHs) in disk galaxies and the kinematic properties of their host galaxies is analyzed. Velocity estimates for several galaxies obtained earlier at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and the data for other galaxies taken from the literature are used. The SMBH masses correlate well with the rotational velocities at a distance of R ≈ 1 kpc, V ₁, which characterize the mean density of the central region of the galaxy. The SMBH masses correlate appreciably weaker with the asymptotic velocity at large distances from the center and the angular velocity at the optical radius R ₂₅. We have found for the first time a correlation between the SMBH mass and the total mass of the galaxy within the optical radius R ₂₅, M ₂₅, which includes both baryonic and “dark” mass. The masses of the nuclear star clusters in disk galaxies (based on the catalog of Seth et al.) are also related to the dynamical mass M ₂₅; the correlations with the luminosity and rotational velocity of the disk are appreciably weaker. For a given value of M ₂₅, the masses of the central cluster are, on average, an order of magnitude higher in S0-Sbc galaxies than in late-type galaxies, or than the SMBH masses. We suggest that the growth of the SMBH occurs in the forming “classical” bulge of the galaxy over a time < 10⁹ yr, during a monolithic collapse of gas in the central region of the protogalaxy. The central star clusters form on a different time scale, and their stellar masses continue to grow for a long time after the growth of the central black hole has ceased, if this process is not hindered by activity of the nucleus.     

Supermassive black holes in interacting galaxies

The possible influence of galactic interaction on the formation and growth of supermassive black holes in their nuclei and the dynamics of their circumnuclear regions are considered, based on new data from the updated Vorontsov-Velyaminov catalog of interacting galaxies and modern estimates of the masses of supermassive black holes. A sample of interacting galaxies with known black-hole masses is created, and the dependence of the masses of the central black holes on the absolute B magnitudes and central stellar velocity dispersions in the host galaxy derived for this sample. A statistical analysis of the sample shows that the black-hole masses in interacting galaxies satisfy the same mass-velocity dispersion relation as non-interacting galaxies. A higher mass dispersion is characteristic of merging pairs than for galaxies that interact in other ways. The maximum masses of the central black holes are observed in radio galaxies.     

Turning points in black holes astrophysics

Black hole astrophysics is expected to have a major breakthrough any day. Theoretical understanding is well advanced, so the breakthrough has to come from observers. Conclusive and direct evidence of event horizons, signatures of tidal deformation of gas clouds (and eventual disappearance of matter behind horizons) could be obtained in matter of months. At this juncture, we wish to summarize how the subject came to this stage and what is the state-of-the-art flow solution around a black hole. We touch upon the most crucial issue of (un)predictability of this subject. We believe that if viscosity is roughly what MRI simulations are pointing to us, we still require very detailed knowledge of properties of the companion, especially time dependent mass transfer from the companion to the black hole.     

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 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.     

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.     

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.     

A new method for determining the masses of black holes

Characteristic properties of the electromagnetic spectrum of a dipole freely falling radially toward a Schwartzschild black hole are determined. These properties can be used to determined the mass of the black hole, as well as some characteristics of the magnetosphere or accretion disk surrounding the black hole.     

I.S. Shklovskii,black holes and subsequent developments

The paper is dedicated to the evolution of the views of I.S. Shklovskii on black holes, his contribution to studies of astrophysical manifestations of black holes, and subsequent studies of these surprising objects.     

Polarimetric differences between Schwarzschild and Kerr black holes in active galactic nuclei

If the linear polarization of the optical emission of active galactic nuclei (AGNs) arises in magnetized accretion disk (the Milne problem), the degree of polarization should depend strongly on the spin of the central black hole. For the same black hole luminosities and masses, the polarization is substantially higher for rotating Kerr than for non-rotating Schwarzschild black holes. Statistically, this means that the majority of AGNs displaying appreciable linear polarization should have Kerr black holes. The spin dependence of the polarization is due to the fact that the radius of the innermost stable circular orbit r _isco depends on the spin—this radius is three gravitational radii for a Schwarzschild black hole, and a factor of six smaller for a rapidly rotating black hole. This means that the magnetic field in the region of emergence of the optical emission, which decreases with distance from r _isco , is higher for a non-rotating than for a rapidly rotating black hole. This higher magnetic field gives rise to strong Faraday depolarization, explaining the effect considered here.     

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.     

Formation of close binary black holes merging due to gravitational-wave radiation

The conditions for the formation of close-binary black-hole systems merging over the Hubble time due to gravitational-wave radiation are considered in the framework of current ideas about the evolution of massive close-binary systems. The original systems whose mergers were detected by LIGO consisted of main-sequence stars with masses of 30–100M _⊙. The preservation of the compactness of a binary black hole during the evolution of its components requires either the formation of a common envelope, probably also with a low initial abundance of metals, or the presence of a “kick”—a velocity obtained during a supernova explosion accompanied by the formation of a black hole. In principle, such a kick can explain the relatively low frequency of mergers of the components of close-binary stellar black holes, if the characteristic speed of the kick exceeds the orbital velocities of the system components during the supernova explosion. Another opportunity for the components of close-binary systems to approach each other is related to their possible motion in a dense molecular cloud.     

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.     

The collapse of matter and the formation of black holes. Conceptual aspects

We present a comparative study of the original metric of Schwarzschild and the metric introduced by Hilbert. The properties of these metrics, as well as the Tolman metric for collapsing dust, are analyzed.     

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.     

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.     

Early formation of (super)massive black holes and gravitational waves from their coalescence

Astronomical observations of last few years have presented a surprising evidence that the Universe at redshift of order 10 is densely populated by supermassive black holes (quasars), supernovae, and contains very large amount of dust. All these data are in conflict with the canonical theory of quasar and supernova formation. A model is discussed which in a simple and natural way solves all these problem. In addition it explains an existence of supermassive black holes in each large galaxy and even in small ones. An inverted picture of galaxy formation is suggested when primordial black holes serve as seeds of galaxy formation. Simultaneously the origin and properties of black hole binaries, sources of gravitational waves registered by LIGO are explained. As a by-product the model may lead to abundant cosmological antimatter even in the Galaxy.