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.     

Partial mixing in early-type main-sequence B stars

Partial mixing of material in the radiative envelopes and convective cores of rotating main sequence stars with masses of 8 and 16 M _⊙ is considered as a function of the inital angular momentum of the stars. Losses of rotational kinetic energy to the generation of shear turbulence in the radiative envelope and the subsequent mixing of material in the envelope are taken into account. With an initial equatorial rotational velocity of 100 km/s, partial mixing develops in the upper part of the layer with variable chemical composition and the lower part of the chemically homogeneous radiative envelope. When the initial equatorial rotational velocity is 150–250 km/s, the joint action of shear turbulence and semi-convection leads to partial mixing in the radiative envelope and central parts of the star. The surface abundance of helium is enhanced, with this effect increasing with the angular momentum of the star. With an initial equatorial rotational velocity of 250 km/s, the ratio of the surface abundances of helium and hydrogen grows by ~30% and ~70% toward the end of the main-sequence evolution of an 8 M _⊙ and 16 M _⊙ star, respectively. The transformation of rotational kinetic energy into the energy of partial mixing increases with the angular momentum of the star, but does not exceed ~2%?3% in the cases considered.     

Enhancement of surface helium abundance in intermediate-mass main-sequence stars

The evolution of rapidly rotating 8, 4, and 2 M _⊙ main-sequence stars is considered together with hydrodynamical transfer in their interiors. The conditions under which turbulent erosion, semiconvection, and shear turbulence lead to partial mixing of the matter in the radiative envelope and central regions of the stars are determined. The enhancement of the surface helium abundance with time depends on both the intensity of partial mixing in their interiors and mass loss by the stellar wind. The ratio of the number densities of helium and hydrogen at the surface can rise by the end of main-sequence stage by ～30% for a 8 M _⊙ star and ～10?20% for a 4 M _⊙ star, depending on the mass-loss rate. Partial mixing of the matter in the radiative envelope and in the central region of the star can provide an explanation for the observed enhancement of the atmospheric helium abundances of early B stars toward the end of their main-sequence evolution. The enhancement of the surface helium abundance in a 2 M _⊙ star is so small that it cannot be detected, and is appreciably lower than the enhancement beneath the surface.     

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.     

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.     

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.

     

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.     

Rotational mass loss by Be stars

We have carried out a numerical study of rotational mass loss by rapidly rotating Be stars assuming preservation of rigid-body rotation during their main-sequence evolution. Evolutionary models are computed for stars with solar chemical composition and initial masses of 3, 10 and M_⊙. As a result of their rapid initial rotation, these stars can lose one to four percent of their initial mass during the main-sequence stage. The amount of mass lost increases with the initial mass of the star. The matter lost by Be stars can form gas-dust disks with masses comparable to the masses of planets, which, in principle, makes possible the formation of planetary systems around such stars.     

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.     

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.     

Wolf-Rayet stars and relativistic objects: Distinctions between the mass distributions in close binary systems

The observed properties of Wolf-Rayet stars and relativistic objects in close binary systems are analyzed. The final masses M _CO ^f for the carbon-oxygen cores of WR stars in WR + O binaries are calculated taking into account the radial loss of matter via stellar wind, which depends on the mass of the star. The analysis includes new data on the clumpy structure of WR winds, which appreciably decreases the required mass-loss rates $\dot M_{WR}$ for the WR stars. The masses M _CO ^f lie in the range (1–2)M _⊙–(20–44)M _⊙ and have a continuous distribution. The masses of the relativistic objects M _x are 1–20M _⊙ and have a bimodal distribution: the mean masses for neutron stars and black holes are 1.35 ± 0.15M _⊙ and 8–10M _⊙, respectively, with a gap from 2–4M _⊙ in which no neutron stars or black holes are observed in close binaries. The mean final CO-core mass is $\overline M _{CO}^f = 7.4 - 10.3M_ \odot$ , close to the mean mass for the black holes. This suggests that it is not only the mass of the progenitor that determines the nature of the relativistic object, but other parameters as well-rotation, magnetic field, etc. One SB1R Wolf-Rayet binary and 11 suspected WR + C binaries that may have low-mass companions (main-sequence or subgiant M-A stars) are identified; these could be the progenitors of low-mass X-ray binaries with neutron stars and black holes.     

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.     

Neutron stars in close binaries with elliptical component orbits

We consider the evolution of close binaries in which the initial secondary component is a nondegenerate helium star with mass M_He = 0.4–60 M_⊙, while the initially more massive primary has evolved into a black hole, neutron star, or degenerate dwarf. The neutron star is assumed to originate as a result of the evolution of a helium star with a mass of 2.5 M_⊙ ≤ M_He ≤ 10 M_⊙ after the explosion of a type Ib,c supernova. If the axial rotation of the helium star before the explosion is rigid-body and synchronized with the orbital rotation, for P_orb ≤ 0.16 day, the rotational energy of the young neutron star will exceed the energy of an ordinary supernova. If the magnetic field of the neutron star is sufficiently strong, the necessary conditions for a magnetic-rotational supernova are provided. The initial rotational period of a young neutron star originating in a system with an orbital period shorter than ～50 days is shorter than ～4 s, which, according to observations, is required for the appearance of a radio pulsar. A helium star whose mass exceeds ～10 M_⊙ in a close binary with an orbital period shorter than one day and with the axial rotation of the helium presupernova synchronous with the orbital rotation evolves into a Kerr black hole, whose formation is likely to be accompanied by a gamma-ray burst with a duration longer than two seconds. In particular, we consider close binaries in which the second supernova results in the formation of a neutron star that remains in the binary. The theoretical distribution of orbital periods and eccentricities for such systems is consistent with that observed for radio pulsars in the Galactic disk in binaries with compact components and orbital eccentricities exceeding ～0.09, providing an explanation for the observed correlation between the orbital eccentricities and orbital periods for these systems.     

The probability of forming hyperveloicty stars in the Galaxy

The probability of forming a Galactic hypervelocity star is estimated for the scenario of Hills, which describes the dynamical capture of one component of a binary star by the gravitational field of the supermassive black hole in the Galactic center, leading to the ejection of the other component. Ten thousand initial orientations of the binary orbits were considered, and the semi-major axes of the binary orbits were varied in a wide range from 11.3 R _⊙ to 425 R _⊙. Two series of computations were carried out, in which the mass of the supermassive black hole was taken to be 10⁶ M _⊙ and 3.4 × 10⁶ M _⊙. Numerical simulations of encounters of the binary and black hole in the framework of the three-body and N-body problems are used to localize regions favorable for the formation of hypervelocity stars. The motion of the ejected star in the regular field of the Galaxy is calculated, and the conditions under which the star escapes the Galaxy defined. The probability of escaping the Galaxy is caluclated as a function of various parameters the initial separation of the binary components and the distance of the binary from the black hole. On average, the probability of forming a hypervelocity star is higher for closer encounters and more tightly bound binary pairs.

     

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_⊙.     

Subsystems of RR Lyrae variable stars in our Galaxy

We have used published, high-accuracy, ground-based and satellite proper-motion measurements, a compilation of radial velocities, and photometric distances to compute the spatial velocities and Galactic orbital elements for 174 RR Lyrae (ab) variable stars in the solar neighborhood. The computed orbital elements and published heavy-element abundances are used to study relationships between the chemical, spatial, and kinematic characteristics of nearby RR Lyrae variables. We observe abrupt changes of the spatial and kinematic characteristics at the metallicity [Fe/H]≈?0.95 and also when the residual spatial velocities relative to the LSR cross the critical value V _res≈290 km/s. This provides evidence that the general population of RR Lyrae stars is not uniform and includes at least three subsystems occupying different volumes in the Galaxy. Based on the agreement between typical parameters for corresponding subsystems of RR Lyrae stars and globular clusters, we conclude that metal-rich stars and globular clusters belong to a rapidly rotating and fairly flat, thick-disk subsystem with a large negative vertical metallicity gradient. Objects with larger metal deficiencies can, in turn, be subdivided into two populations, but using different criteria for stars and clusters. We suggest that field stars with velocities below the critical value and clusters with extremely blue horizontal branches form a spherical, slowly rotating subsystem of the protodisk halo, which has a common origin with the thick disk; this subsystem has small but nonzero radial and vertical metallicity gradients. The dimensions of this subsystem, estimated from the apogalactic radii of orbits of field stars, are approximately the same. Field stars displaying more rapid motion and clusters with redder horizontal branches constitute the spheroidal subsystem of the accreted outer halo, which is approximately a factor of three larger in size than the first two subsystems. It has no metallicity gradients; most of its stars have eccentric orbits, many display retrograde motion in the Galaxy, and their ages are comparatively low, supporting the hypothesis that the objects in this subsystem had an extragalactic origin.     

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.     

The relation between the observed mass distribution for compact stars and the mechanism for supernova explosions

The observed mass distribution for the compact remnants of massive stars (neutron stars and black holes) and its relationship to the possible mechanism of ejection of the envelopes of type II and Ib/c supernovae are analyzed. The observed lack of compact remnants with masses 1.5–3 M _⊙ suggests a magneto-rotational mechanism for the supernovae, and a soft equation of state for neutron stars with limiting masses near 1.5 M _⊙. The observational consequences of this hypothesis are discussed.     

Evolution of the masses of neutron stars in binary systems

We study the growth of the masses of neutron stars in binary systems due to the accumulation of mass from the optical donors accreted onto the neutron-star surface. Possible scenarios for this accretion are considered. The masses and magnetic-field strengths of radio pulsars derived using population-synthesis methods are compared to the observational data. The population-synthesis analysis indicates that a neutron star can increase its mass from the standard value of m _x ? 1.35M_⊙ to the Oppenheimer-Volkoff limit, m _x ? 2.5M_⊙, via accretion from a companion.