The evolutionary status of ultraluminous X-ray sources

We analyze models for quasi-stationary, ultraluminous X-ray sources (ULXs) with luminosities 10³⁸–10⁴⁰ erg/s exceeding the Eddington limit for a ～1.4M_⊙ neutron star. With the exception of relatively rare stationary ULXs that are associated with supernova remnants or background quasars, most ULXs are close binary systems containing a massive stellar black hole (BH) that accretes matter donated by a stellar companion. To explain the observed luminosities of ～10⁴⁰ erg/s, the mass of the BH must be ～40M_⊙ if the accreted matter is helium and ～60M_⊙ if the accreted matter has the solar chemical composition. We consider donors in the form of main-sequence stars, red giants, red supergiants, degenerate helium dwarfs, heavy disks that are the remnants of disrupted degenerate dwarfs, helium nondegenerate stars, and Wolf-Rayet stars. The most common ULXs in galaxies with active star formation are BHs with Roche-lobe-filling main-sequence companions with masses ～7M_⊙ or close Wolf-Rayet companions, which support the required mass-exchange rate via their strong stellar winds. The most probable candidate ULXs in old galaxies are BHs surrounded by massive disks and close binaries containing a BH and degenerate helium-dwarf, red-giant, or red-supergiant donor.     

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.     

Variations in the orbital periods of the Algol-type eclipsing binaries RZ Cas and Z Dra

A detailed study of variations of the orbital periods of the Algol-type eclipsing binary systems RZ Cas and Z Dra is presented. The fairly complex variations of the periods of both systems can be represented as a superposition of a secular increase of the period, slow periodic fluctuations, and quasiperiodic oscillations with a small amplitude occurring on timescales of decades. The secular increase of the period can be explained by the steady mass transfer from the less massive to the more massive component with conservation of the total angular momentum. The mass-transfer rate is 5.7 × 10^?9M_⊙/yr for RZ Cas and 3.0×10^?8M_⊙/yr for Z Dra. To explain the long-period cyclic variations of the orbital periods of RZCas and Z Dra, it must be assumed that the eclipsing binaries move in long-period orbits. RZ Cas moves with a period of 133 yr around a third body withmass M₃ > 0.55M_⊙, while Z Dra moves with a period of 60 yr around a third body with mass M₃ > 0.7M_⊙. The residual fluctuations of the periods may be due to a superposition of variations due to magnetic cycles and non-stationary ejections of matter.     

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 _⊙.     

New dwarf galaxy candidates in the Leo-I Group

We have carried out a search for low-surface-brightness dwarf galaxies in the region of the Leo-I Group (M96) in images of the second Palomar Sky Survey. We found a total of 36 likely dwarf members of the group with typical magnitudes B _t ～18^m–19^m in an area of sky covering 120 square degrees. Half of these galaxies are absent from known catalogs and lists of galaxies. The radial-velocity dispersion calculated for 19 galaxies is 130 km/s. The Leo-I Group has a mean distance from the Sun of 10.4 Mpc, a mean projected radius of 352 kpc, an integrated luminosity of 6.7 × 10¹⁰L_⊙, a virial mass-to-luminosity ratio of 107 M_⊙/L_⊙, and a mean crossing time of 2.7 Gyr. The group shows evidence for a radial segregation of the galaxies according to morphological type and luminosity, suggesting that the group is in a state of dynamical relaxation. The subsystem of bright galaxies in the Leo-I Group is smaller in size (250 kpc) and has a lower velocity dispersion (92 km/s), resulting in a lower virial mass-to-luminosity ratio (34 M_⊙/L_⊙), as is typical of the Local Group and other nearby groups of galaxies.     

Galactic orbits of selected companions of the Milky Way

High-accuracy absolute proper motions, radial velocities, and distances have now been measured for a number of dwarf-galaxy companions of the Milky Way, making it possible to study their 3D dynamics. Galactic orbits for 11 such galaxies (Fornax, Sagittarius, Ursa Minor, LMC, SMC, Sculptor, Sextans, Carina, Draco, Leo I, Leo II) have been derived using two previously refined models for the Galactic potential with the Navarro–Frenk–White and Allen–Santillán expressions for the potential of the dark-matter halo, and two different masses for the Galaxy within 200 kpc—0.75 × 10¹² M _⊙ and 1.45 × 10¹² M _⊙. The character of the orbits of most of these galaxies indicates that they are tightly gravitationally bound to the Milky Way, even with the lower-mass model for the gravitational potential. One exception is the most distant galaxy in the list, Leo I, whose orbit demonstrates that it is only weakly gravitationally bound, even using the higher-mass model of the gravitational potential.     

Radial pulsations of helium stars and a model for BX CIR

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.     

The formation of the first objects during the virialization of the dark-matter halos

The chemical and thermal evolution of the baryon component in the gravitational field of low-mass primordial dark-matter halos during their virialization is studied. We consider low-mass halos to be those for which the characteristic baryon cooling time can appreciably exceed the comoving Hubble time, so that the cooling process can continue to the current epoch (z～0). The virialization process is described in two scenarios: “quiet” virialization, in which the establishment of the virial state is assumed to be homogeneous over the entire volume considered, and “violent” virialization, in which the establishment of the virial state is assumed to be realized via the action of shock waves. In this second case, the efficiency of the formation of molecular hydrogen grows substantially, and can reach H₂/H～0.01 in some cases, which exceeds current estimates by at least an order of magnitude. This eases the condition for the birth of the first gravitationally bound objects with comparatively low masses (M ? 2 × 10⁵M_⊙), possibly leading to an appreciable increase in the fraction of the mass contained in Population III objects, and also to a shift in the onset of the formation of the first stars toward higher redshifts.     

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.     

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.     

The mass of the compact object in the X-ray binary 4U 1700-37

The results of a systematic analysis of master radial-velocity curves for the X-ray binary 4U 1700-37 are presented. The dependence of the mass of the X-ray component on the mass of the optical component is derived in a Roche model based on a fit of the master radial-velocity curve. The parameters of the optical star are used to estimate the mass of the compact object in three ways. The masses derived based on information about the surface gravity of the optical companion and various observational data are 2.25 _?0.24 ^+0.23 M_⊙ and 2.14 _?0.56 ^+0.50 M_⊙. The masses based on the radius of the optical star, 21.9R_⊙, are 1.76 _?0.21 ^+0.20 M_⊙ and 1.65 _?0.56 ^+0.78 M_⊙. The mass of the optical component derived from the mass-luminosity relation for X-ray binaries, 27.4M_⊙, yields masses for the compact object of 1.41 _?0.08 ⁺ M_⊙ and 1.35 _?0.18 ^+0.18 M_⊙.     

The evolution of GRS 1915+105—an X-ray binary with a black hole

A brief review of the observed parameters of binary systems with black holes is presented. We discuss in detail the evolutionary status of the X-ray binary GRS 1915+105, which contains a massive black hole. Numerical simulations of the evolution of GRS 1915+105 at the X-ray stage indicate that the most probable initial mass of the optical component (donor star) is (1.5–)M_⊙. Two possible scenarios are suggested for the evolution of the system prior to the formation of the black hole. If the initial mass of the optical component was (2.5–)M_⊙, the system underwent a common-envelope phase; in this case, the initial mass of the black hole progenitor did not exceed ～50M_⊙. If the initial mass of the donor was (1.5–2.5)M_⊙, a scenario without a common envelope is possible, with the initial mass of the black hole progenitor being smaller than ～50M_⊙. The lack of information about the initial mass-ratio distribution for binary components for small q and the uncertainty of the system parameters make it impossible to give preference to a particular scenario for the system's prior evolution.     

The probable quadruple systems FK Aql and FZ Del

Orbital-period variations of the eclipsing binaries FK Aql and FZ Del are analyzed. For each of the systems, a superposition of two cyclic variations of their orbital periods is found. FK Aql may be a quadruple system that contains two more bodies, besides the eclipsing binary, with masses M ₃ ? 1.75M _⊙ and M ₄ ? 1.47M _⊙, and the corresponding periods 15 and 82 yrs. This could also be a triple system with a third body of mass M ₃ ? 1.75M _⊙ and a period of the long-period orbit P ₃ = 15 yrs, or with a third body of mass M ₃ ? 1.30M _⊙ and a period of the long-period orbit P ₃ = 82 yrs. FZ Del may be a quadruple system with the additional componentmasses M ₃ ? 0.2M _⊙ and M ₄ ? 0.3M _⊙, with the periods 10.2 and 53.7 yrs. This could also be a triple system with a third-body mass M ₃ ? 0.2M _⊙ and a period of the long-period orbit P ₃ = 10.2 yrs. In both systems, the residual period variations could be due to magnetic cycles of the secondary. The period variations of the eclipsing binary FZ Del could also be due to apsidal motion, together with the influence of a third body or the effects of magnetic activity.     

The chemical evolution of globular clusters

The sequence of events determining the initial stages of star formation is analyzed in framework of the self-enrichment scenario. The computations are based on a single-zone chemo-dynamical model. It is shown that the first episode of star formation was characterized by an initial mass function shifted toward massive stars (M ≥ 8M_⊙). We argue that the transition to a star formation with a normal (Salpeter) initial mass function was due to more efficient radiative cooling of the proto-globular cluster gas after its enrichment to a metallicity of Z ～ 0.02 Z_⊙ in agreement with those observed in globular clusters.     

Evolution of close binaries and gamma-ray bursts

We analyze the late stages of evolution of massive (M ₀ ? 8 M _⊙) close binaries, from the point of view of possible mechanisms for the generation of gamma-ray bursts. It is assumed that a gamma-ray burst requires the formation of a massive (～1 M _⊙), compact (R ? 10 km) accretion disk around a Kerr black hole or neutron star. Such Kerr black holes are produced by core collapses of Wolf-Rayet stars in very close binaries, as well as by mergers of neutron stars and black holes or two neutron stars in binaries. The required accretion disks can also form around neutron stars that were formed via the collapse of ONeMg white dwarfs. We estimate the Galactic rate of events resulting in the formation of rapidly rotating relativistic objects. The computations were carried out using the “Scenario Machine.”     

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.     

Nonlinear radial pulsations of Wolf-Rayet stars

The evolution of Population I stars with initial masses 60 M _⊙ ≤ M _ZAMS ≤ 120 M _⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y _c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T _eff ～ 10⁵ K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T _eff ≈ 10⁵ K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M _⊙ to M = 6 M _⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 10⁵ K.     

Late stages of the evolution of close compact binaries: Type I supernovae,gamma-ray bursts,and supersoft X-ray sources

We consider the evolution of close binaries resulting in the most intensive explosive phenomena in the stellar Universe—Type Ia supernovae and gamma-ray bursts. For Type Ia supernovae, which represent thermonuclear explosions of carbon-oxygen dwarfs whose masses reach the Chandrasekhar limit during the accretion of matter from the donor star, we derive the conditions for the accumulation of the limiting mass by the degenerate dwarf in the close binary. Accretion onto the degenerate dwarf can be accompanied by supersoft X-ray radiation with luminosity 1–10⁴ L _⊙. Gamma-ray bursts are believe to accompany the formation and rapid evolution of compact accretion-decretion disks during the formation of relativistic objects—black holes and neutron stars. The rapid (～1 M _⊙/s) accretion of matter from these disks onto the central compact relativistic star results in an energy release of ～0.1 M _⊙ c ² ～ 10⁵³ erg in the form of gamma-rays and neutrinos over a time of 0.1–1000 s. Such disks can form via the collapse of the rapidly rotating cores of Type Ib, Ic supernovae, which are components in extremely close binaries, or alternately due to the collapse of accreting oxygen-neon degenerate dwarfs with the Chandrasekhar mass into neutron stars, or the merging of neutron stars with neutron stars or black holes in close binaries. We present numerical models of the evolution of some close binaries that result in Type Ia supernovae, and also estimate the rates of these supernovae (～0.003/year) and of gamma-ray bursts (～10^?4/year) in our Galaxy for various evolutionary scenarios. The collimation of the gamma-ray burst radiation within an opening angle of several degrees “matches” the latter estimate with the observed rate of these events, ～10^?7–10^?8/year calculated for a galaxy with the mass of our Galaxy.     

The mass of the black hole in the X-ray binary M33 X-7 and the evolutionary status of M33 X-7 and IC 10 X-1

We have analyzed the observed radial-velocity curve for the X-ray binary M33 X-7 in a Roche model. We have analyzed the dependence between the component masses and the degree of filling of the optical star’s Roche lobe to obtain the ratio of the masses of the optical star and compact object. For the most probable mass of the optical star, m _v = 70 M⊙, the mass of the compact object is m _x = 15.55 ± 3.20 M⊙. It has been shown that black holes with masses of mx = 15 M⊙ and even higher can form in binaries. We present characteristic evolutionary tracks for binary systems passing through an evolutionary stage with properties similar to M33 X-7-type objects. According to population-synthesis analyses, such binaries should be present in galaxies with masses of at least 10¹¹ M⊙. The present number of such systems in M33 should be of the order of unity. We have also studied the evolutionary status of the X-ray binary IC 10 X-1 with a Wolf-Rayet component, which may contain a massive black hole. The final stages of the evolution of the M33 X-7 and IC 10 X-1 systems should be accompanied by the radiation of gravitational waves.     

The mass of the compact object in the X-ray binary her X-1/HZ her

We have obtained the first estimates of the masses of the components of the Her X-1/HZ Her X-ray binary system taking into account non-LTE effects in the formation of the H _γ absorption line: m _x = 1.8 M _⊙ and m _v = 2.5 M _⊙. These mass estimates were made in a Roche model based on the observed radial-velocity curve of the optical star, HZ Her. The masses for the X-ray pulsar and optical star obtained for an LTE model lie are m _x = 0.85 ± 0.15 M _⊙ and m _v = 1.87 ± 0.13 M _⊙. These mass estimates for the components of Her X-1/HZ Her derived from the radial-velocity curve should be considered tentative. Further mass estimates from high-precision observations of the orbital variability of the absorption profiles in a non-LTE model for the atmosphere of the optical component should be made.