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.     

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.     

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.     

Formation and evolution of Ae and Be stars

Several scenarios for the formation of accretion and decretion disks in single and binary Ae and Be stars are proposed. It is shown that, in order for a rapidly rotating main-sequence Be star to lose mass via a disk, the star’s rotation must be quasi-rigid-body. Estimates show that such rotation can be maintained by the star’s magnetic field, which is probably a relict field. The evolution of single Be main-sequence stars is numerically simulated allowing for mass loss via the stellar wind and rotational mass loss assuming rigid-body rotation. The stellar wind is the factor that determines the maximum mass of Be stars, which is close to 30M _⊙. The evolution of Be stars in close binaries is analyzed in the approximation adopted in our scenario. Long gamma-ray bursts can be obtained as a result of the collapse of rapidly rotating oxygen—neon degenerate dwarfs—the accreting companions of Be stars—into neutron stars.     

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.     

The stellar epoch in the evolution of the Galaxy

We consider the astrophysical evolution of the Galaxy over large time scales, from early stages (an age of ～10⁸ yrs) to the end of traditional stellar evolution (～10¹¹ yrs). Despite the fact that the basic parameters of our stellar system (such as its size, mass, and general structure) have varied little over this time, variations in the characteristics of stars (their total luminosity, color, mass function, and chemical composition) are rather substantial. The interaction of the Galaxy with other stellar systems becomes an important factor in its evolution 100–1000 Gyr after its origin; however, we take the Galaxy to be isolated. In the model considered, the basic stages of Galactic evolution are as follows. The Galaxy forms as the result of the contraction (collapse) of a protogalactic cloud. The beginning of the Milky Way’s life—the relaxation period, which lasts about 1–2 Gyr—is characterized by active star formation and final structurization. The luminosity and colors of the Galaxy are correlated to the star formation rate (SFR). The young Galaxy intensely radiates high-energy photons, which are mostly absorbed by dust and re-emitted at IR wavelengths. In the subsequent period of steady-state evolution, the gas content in the Galactic disk gradually decreases; accordingly, the SFR decreases, reaching 3–5M _⊙/yr at the present epoch and decreasing to 0.03M _⊙/yr by an age of 100 Gyr. Essentially all other basic parameters of the Galaxy vary little. Later, the decrease in the SFR accelerates, since the evolution of stars with masses exceeding 0.4M _⊙ (i.e., those able to lose matter and renew the supply of interstellar gas) comes to an end. The Galaxy enters a period of “dying”, and becomes fainter and redder. The variation of its chemical composition is manifested most appreciably in a dramatic enrichment of the interstellar gas in iron. The final “stellar epoch” in the life of the Galaxy is completed ～10¹³ yrs after its formation, when the evolution of the least massive stars comes to an end. By this time, the supplies of interstellar and intergalactic gas are exhausted, the remaining stars become dark, compact remnants, there is no further formation of new stars, and the Galactic disk no longer radiates. Eventually, infrequent outbursts originating from collisions of stellar remnants in the densest central regions of the Galaxy will remain the only source of emission.     

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.     

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.”     

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 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.     

Stellar sources of the short-lived radionuclides in the early solar system

We discuss the possible stellar sources of short-lived radionuclides (SLRs) known to have been present in the early solar system (²⁶Al, ³⁶Cl, ⁴¹Ca, ⁵³Mn, ⁶⁰Fe, ¹⁰⁷Pd, ¹²⁹I, ¹⁸²Hf, ²⁴⁴Pu). SLRs produced primarily by irradiation (⁷Be, ¹⁰Be) are not discussed in this paper. We evaluate the role of the galactic background in explaining the inventory of SLRs in the early solar system. We review the nucleosynthetic processes that produce the different SLRs and place the processes in the context of stellar evolution of stars from 1 to 120 M_⊙. The ejection of newly synthesized SLRs from these stars is also discussed. We then examine the extent to which each stellar source can, by itself, explain the relative abundances of the different SLRs in the early solar system, and the probability that each source would have been in the right place at the right time to provide the SLRs. We conclude that intermediate-mass AGB stars and massive stars in the range from ∼20 to ∼60 M_⊙ are the most plausible sources. Low-mass AGB stars fail to produce enough ⁶⁰Fe. Core-collapse Type II supernovae from stars with initial masses of <20 M_⊙ produce too much ⁶⁰Fe and ⁵³Mn. Sources such as novae, Type Ia supernovae, and core-collapse supernovae of O-Ne-Mg white dwarfs do not appear to provide the SLRs in the correct proportions. However, intermediate-mass AGB stars cannot provide ⁵³Mn or the r-process elements, so if an AGB star provided the ⁴¹Ca, ³⁶Cl, ²⁶Al, ⁶⁰Fe, and ¹⁰⁷Pd, and if a late stellar source is required for ⁵³Mn and the r-process elements, then two types of sources would be required. A separate discussion of the production of r-process elements highlights the difficulties in modeling their production. There appear to be two sources of r-process elements, one that produces the heavy r-process elements, including the actinides, and one that produces the elements from N to Ge and the elements ∼110 < A < ∼130. These can be assigned to SNII explosions of stars of ?11 M_⊙ and stars of 12-25 M_⊙, respectively. More-massive stars, which leave black holes as supernova remnants, apparently do not produce r-process elements.     

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.     

Activity observed by the Kepler space telescope: The M dwarf LHS 6351 (KIC 2164791)

Continuous 123.87-day observations with the “Kepler” space telescope are used to study the activity of the fully convective, low-mass M dwarf LHS 6351. The axial-rotation period of the star is 3.36 day. High-precision photometric observations of LHS 6351 enabled studies of its surfacetemperature inhomogeneities and their evolution. The difference in the longitudes of active regions increased from 120° at the beginning to 207° at the end of the observations, for i = 60° (and from 156° to 198° for i = 30°). This variation of the locations of the spots on the stellar surface provides evidence for differential rotation of the star. According to our estimates, the rate of displacement of the active regions is (0.006–0.014) ± 0.002 rad/day. Assuming i = 60°, the total area of spots S decreased, on average, from 1.2% to 0.92% of the total visible surface of the star; if i = 30°, this area decreased from 1.8% to 1.0%. We compared manifestations of the magnetic activity of LHS 6351 with the properties of the fully convective M dwarfs V374 Peg and GJ 1243, studied earlier. We derived the dependence of ΔΩ on the Rossby number for these M dwarfs, and identified two groups of stars with differing mass and differential rotation.     

Photometry and spectroscopy of the system V4641 sagittarii in quiescence

We present the results of our CCD photometric and moderate-dispersion spectroscopic observations of the binary system V4641 Sgr, which contains a black hole of mass ≈9.5M_⊙ and a normal B9III star. The photometric light curve reveals an ellipticity effect with very high amplitudes in V and R, 0.40^m and 0.37^m, and the color curve shows that the surface temperature is nonuniform. All this testifies to tidal distortion of the normal star's surface due to the massive companion and to a high inclination of the orbit to the line of sight. In June and July 2002, during quiescence, we obtained data during three flares with amplitudes up to 0.26^m. In particular, spectroscopic observations were acquired near the time of the black hole's inferior conjunction. One hour before conjunction, a depression by EW=0.5 Å was observed in the red wing of the Hα absorption line, interpreted as absorption by gas flowing in the direction from the observer toward the normal star. This flow is apparently associated with a rarefied gas disk around the black hole, and the conjunction grazes the stellar surface if the orbital inclination is close to 70.7°. The maximum velocity along a circular Keplerian orbit is 650 km/s at a distance of R=0.15–0.20a from the black hole (where a is the component separation). Thus, we find the mass of the black hole to be M _BH =7.1–9.5M_⊙, confirming the model of Orosz et al. (2001).     

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.     

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.     

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.     

Long-term variations in the spottedness of BY Dra M dwarfs

The results of a spottedness study for twelve red dwarf stars covering several decades and based on a vast amount of photometric observations are presented. The analysis makes use of multicolor (UBV RI) photometric monitoring of ten of these stars since 1991 at the Crimean Astrophysical Observatory, as well as data from the literature. The spottedness parameters for selected active BY Dra red dwarfs have been refined using an improved zonal model for the spotted stellar atmospheres to allow for the possible presence of two active longitudes on the stars. Time variations in the spot activity of these systems are analyzed in order to look for possible cycles. Three of the stars show a drift of their spots in the latitude towards the stellar poles; however, the magnitude of this latitude drift is a factor of two to three lower than the analogous value for sunspots. All the stars except for YZ CMi display relationships between the area of the spots and their latitude, with correlation coefficients R from 0.67 to 0.97. Evidence for the presence of activity cycles with durations from 25 to 40 years is found for six stars, which are characterized by synchronous variations in the areas and latitudes of their spots, as well as of the overall photometric brightness.     

Spectroscopic study of the envelopes of the novae V2467 Cyg and V2491 Cyg

Spectrophotometric observations are used to study the envelopes of the FeII nova V2467 Cyg and the HeN nova V2491 Cyg. The abundances of several elements in the nova envelopes and the envelope masses are estimated. The nitrogen mass abundance in the V2467 Cyg envelope is higher than the solar value by a factor of 186 and the oxygen abundance by the factor of 10. The nitrogen abundance in the envelope of V2491 Cyg exceeds the solar value by a factor of 56, the oxygen abundance by a factor of 12, and the neon abundance by a factor of 8. The masses of the envelopes were estimated to be 8.5×10^?5 M _⊙ for V2467 Cyg and 1.5×10^?5 M _⊙ for V2491 Cyg. These envelope elemental abundances and masses are in good agreement with those of low-mass CO white dwarfs (0.8 M _⊙) and ONe white dwarfs (1.15 M _⊙).     

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.