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.     

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.     

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.     

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.     

Estimation of the accuracy of methods for determining component masses for low-mass X-ray binary systems

Modern modeling of the population of low-mass X-ray binary systems containing black holes applying standard assumptions leads to a lack of agreement between the modeled and observed mass distributions for the optical components, with the observed masses being lower. This makes the task of estimating the systematic errors in the derived component masses due to imperfect models relevant. To estimate the influence of systematic errors in the derived masses of stars in X-ray binary systems, we considered two approximations for the tidally deformed star in a Roche model. Approximating the star as a sphere with a volume equal to that of the Roche lobe leads to slight overestimation of the equatorial rotational velocity V _rot sin i, and hence to slight underestimation of the mass ratio q = M _x /M _v . Approximating the star as a flat, circular disk with constant local line profiles and a linear limb-darkening law (a classical rotational broadeningmodel) is an appreciably cruder approach, and leads to overestimation of V _rot sin i by about 20%. In the case of high values of q = M _x /M _v , this approximation leads to substantial underestimation of the mass ratio q, which can reach several tens of percent. The mass of the optical star is overestimated by a factor of 1.5 in this case, while the mass of the black hole is changed only slightly. Since most estimates of component mass ratios for X-ray binary systems are carried out using a classical rotational broadening model for the lines, this leads to the need for appreciable corrections to (reductions of) previously published masses for the optical stars, which enhances the contradiction with the standard evolutionary scenario for low-mass X-ray binaries containing black holes.     

Radial-velocity curves and theoretical spectral-line profiles of the components of low-mass close X-ray binary systems

We present the results of calculations of theoretical absorption-line profiles and radial-velocity curves for optical components in X-ray binary systems. Tidal distortion of the optical star and X-ray heating by incident radiation from the relativistic object are taken into account. An emission component forms whose intensity varies with orbital phase in the absorption-line profile in the presence of significant X-ray heating. As a result, the width of the line decreases rather than increases at quadrature. The line profiles and equivalent widths and the radial-velocity curves depend substantially on the parameters of the binary systems. This provides the possibility of directly determining component masses and orbital inclinations from high-resolution spectroscopic observations of X-ray binary systems.     

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.     

The quiescent X-ray emission of X-ray novae and the coronal emission of late-type stars

The X-ray luminosities and spectra of F-M stars of luminosity classes IV–V are analyzed. In dwarfs with rotational velocities of about 100 km/s, such as the optical components of low-mass X-ray novae with black holes, hot plasma can be confined in coronal loops even in the presence of fairly weak magnetic fields. Thus, the soft X-ray emission of such systems in their quiescent state (to 10³¹ erg/s) could be associated with the coronal emission of the optical component/dwarf. Two systems studied with subgiants (V1033 Sco and V404 Cyg) have X-ray luminosities 2×10³²–2×10³³ erg/s. The X-ray emission of a solar-type corona cannot provide such luminosities. However, a transition to a non-solar corona is possible in rapidly rotating subgiants—a dynamical corona whose X-ray emission can be one to two orders of magnitude higher than observed for more slowly rotating late-type subgiants in the solar neighborhood. This suggests that the quiescent X-ray emission of these two systems is provided by emission from the corona of the subgiant optical component.     

The decay of triple systems

Numerical simulations have been carried out in the general three-body problem with equal masses with zero initial velocities, to investigate the distribution of the decay times T based on a representative sample of initial conditions. The distribution has a power-law character on long time scales, f(T) ∝ T ^?α , with α = 1.74. Over small times T < 30T _cr (T _cr is the mean crossing time for a component of the triple system), a series of local maxima separated by about 1.0T _cr is observed in the decay-time distribution. These local peaks correspond to zones of decay after one or a few triple encounters. Figures showing the arrangement of these zones in the domain of the initial conditions are presented.     

Trajectories of bodies in triple systems with moderate lifetimes

The general three-body problem with equal masses and zero initial velocities is considered. Sets of initial conditions for which the triple systems decay over comparatively short times, 10T _cr < T < 20T _cr, are distinguished (T _cr is the mean crossing time for a component of the system). These sets form distinct families of structures in the domain of the initial conditions. The properties of trajectories of the bodies within some of these structures are described. It is shown that the set of families is no more than countable. A new classification for families of trajectories in decaying triple systems is proposed. Some problems in classifying trajectories in the three-body problem that must be addressed in the future are formulated.     

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.     

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.     

Kinematics of disk galaxies with known masses of their supermassive black holes. Observations

This is the first paper in a project aimed at analyzing relations between the masses of supermassive black holes or nuclear clusters in galaxies and the kinematic features of the host galaxies. We present long-slit spectroscopic observations of galaxies obtained on the 6-m telescope of the Special Astrophysical Observatory using the SCORPIO focal reducer. Radial profiles of the line-of-sight velocities and velocity dispersions of the stellar populations were obtained for seven galaxies with known masses of their supermassive black holes (Mkn 79, Mkn 279, NGC 2787, NGC 3245, NGC 3516, NGC 7457, and NGC 7469), and also for one galaxy with a nuclear cluster (NGC 428). Velocity profiles of the emitting gas were obtained for some of these galaxies as well. We present preliminary galactic rotation curves derived from these data.     

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 _⊙.     

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.     

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.     

Calibrating the Early Toarcian (Early Jurassic) with stratigraphic black holes (SBH)

Cyclostratigraphic analyses of Upper Pliensbachian and Lower Toarcian carbon-13 isotope (δ¹³C) data, together with radiometric dating, are used to calibrate biozones and magnetic chrons in the Astronomical Time Scale (ATS). In turn, the ATS is used to date sea-level and climate cycles in relation to the Early Toarcian carbon-isotope excursion (T-CIE) and the Karoo-Ferrar Large Igneous Provinces. The resulting chronology however is insufficiently accurate to determine if these global-scale events are causally related. In particular, cyclostratigraphic analyses typically underestimate the durations of biozones by failing to account for hiatuses in depositional discontinuities. To account for hiatuses this paper constructs a δ¹³C reference curve consisting of correlative segments from several localities and dates them with ammonite zones and subzones. By comparing the reference curve to those from numerous localities, four major discontinuity-prone intervals were identified and named ‘stratigraphic black holes’ (SBH). SBH 1 occurs in the Late Pliensbachian P. spinatum Zone. Early Toarcian SBH 2 occurs in a δ¹³C maximum interval in middle D. tenuicostatum Zone. The T-CIE is characterized by a decreasing δ¹³C trend (c. 0.4 myr falling limb) in D. semicelatum Subzone, a minimum δ¹³C interval (c. 0.4 myr valley) and an increasing δ¹³C trend (c. 0.4 myr rising limb) in the E. elegantulum Subzone. SBH 3 occurs at base T-CIE rising limb and SBH 4 near its top or above it in a c. 0.4 myr, post-T-CIE plateau in upper E. elegantulum Subzone. Comparisons to published floating chronologies resulted in an Early Toarcian timescale with ~1.0 myr for the D. tenuicostatum Zone, and ~1.6 myr for the H. serpentinum Zone. Initial volcanism in the Karoo Province correlates with the Pliensbachian/Toarcian boundary at ~183.6 Ma, while its second phase was coeval with the T-CIE. Volcanism in the Ferrar Province correlates with the T-CIE.     

The mass of the compact object in the low-mass X-ray binary 2S 0921-630

We interpret the observed radial-velocity curve of the optical star in the low-mass X-ray binary 2S 0921-630 using a Roche model, taking into account the X-ray heating of the optical star and screening of X-rays coming from the relativistic object by the accretion disk. Consequences of possible anisotropy of the X-ray radiation are considered. We obtain relations between the masses of the optical and compact (X-ray) components, m _v and m _x , for orbital inclinations i = 60°, 75°, and 90°. Including X-ray heating enabled us to reduce the compact object’s mass by ～0.5–1 M _⊙, compared to the case with no heating. Based on the K0III spectral type of the optical component (with a probable mass of m _v ? 2.9 M _⊙), we concluded that m _x ? 2.45?2.55 M _⊙ (for i = 75°?90°). If the K0III star has lost a substantial part of its mass as a result of mass exchange, as in the V404 Cyg and GRS 1905+105 systems, and its mass is m _v ? 0.65?0.75 M _⊙, the compact object’s mass is close to the standard mass of a neutron star, m _x ? 1.4 M _⊙ (for i = 75°?90°). Thus, it is probable that the X-ray source in the 2S 0921-630 binary is an accreting neutron star.     

Dark halos of wide triple systems of galaxies

A new class of metagalactic system—wide triple systems of galaxies with characteristic scale lengths of ～1 Mpc—are analyzed. Dynamical models of such systems are constructed, and the amount of dark mass contained in them is estimated. In principle, kinematic data for wide triplets allow two types of models: with individual galactic halos and with a common halo for the entire system. A choice between the two models can be made based on X-ray observations of these systems, which can determine whether clustering and hierarchical evolution continues on scales of ～1 Mpc or whether systems with such scale lengths are in a state of virial quasi-equilibrium.