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.”     

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.     

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.     

Merging of components in close binaries: Type Ia supernovae,massive white dwarfs,and Ap stars

The “Scenario Machine” (a computer code designed for studies of the evolution of close binaries) was used to carry out a population synthesis for a wide range of merging astrophysical objects: main-sequence stars with main-sequence stars; white dwarfs with white dwarfs, neutron stars, and black holes; neutron stars with neutron stars and black holes; and black holes with black holes. We calculate the rates of such events, and plot the mass distributions for merging white dwarfs and main-sequence stars. It is shown that Type Ia supernovae can be used as standard candles only after approximately one billion years of evolution of galaxies. In the course of this evolution, the average energy of Type Ia supernovae should decrease by roughly 10%; the maximum and minimum energies of Type Ia supernovae may differ by no less than by a factor of 1.5. This circumstance must be taken into account at estimating the parameters of the Universe expansion acceleration. According to theoretical estimates, the most massive—as a rule, magnetic—white dwarfs probably originate from mergers of white dwarfs of lower mass. At least some magnetic Ap and Bp stars may form in mergers of low-mass main-sequence stars (M ? 1.5 M _⊙) with convective envelopes.     

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.     

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 origin of the rotational and spatial velocities of radio pulsars

We analyze possible origins of the observed high rotational and spatial velocities of radio pulsars. In particular, these can be understood if all radio pulsars originate in close binary systems with orbital periods of 0.1–100 days, with the neutron star being formed by a type Ib,c supernova. The high spatial velocities of pulsars (v _p up to 1000 km/s) reflect the high Keplerian velocities of the components of these binaries, while their short periods of rotation (P _p < 4 s) are due to the rapid rotation of the presupernova helium-star components with masses of 2.5–10 M_⊙, which is synchronous with their orbital rotation. Single massive stars or components in wide binaries are likely to produce only slowly rotating (P _p > 4 s) neutron stars or black holes, which cannot be radio pulsars. As a result, the rate of formation of radio pulsars should be a factor of a few lower than the rate of type II and type Ib,c supernovae estimated from observations. This scenario for the formation of radio pulsars is supported by (i) the bimodal spatial velocity distribution of radio pulsars; (ii) the coincidence of the observed spatial velocities of radio pulsars with the orbital velocities of the components of close binaries with nondegenerate helium presupernovae; (iii) the correlation between the orbital and rotational periods for 22 observed radio pulsars in binaries with elliptical orbits; and (iv) the similarity of the observed rate of formation of radio pulsars and the rate of type Ib,c supernovae.     

A model for the population of helium stars in the Galaxy: Low-mass stars

We model the Galactic ensemble of helium stars using population synthesis techniques, assuming that all helium stars are formed in binaries. In this picture, single helium stars are produced by mergers of helium remnants of the components of close binaries (mainly, the merging of helium white dwarfs) or in the disruption of binaries with helium components during supernova explosions. The estimated total birthrate of helium stars in the Galaxy is 0.043 yr^?1; the total number is 4 × 10⁶; and the binarity rate is 76%. We construct a subsample of low-mass (M_He ? 2M_⊙) helium stars defined by observational selection effects: the limiting magnitude (V_He ≤ 16), ratio of the magnitudes of the components in binaries (V_He ≤ V_comp), and lower limit for the semiamplitude of the radial velocity required for detecting binarity (K_min = 30 km s^?1). The parameters of this subsample are in satisfactory agreement with observations of helium subdwarfs. In particular, the binarity rate in the selection-limited sample is 58%. We analyze the relations between the orbital periods and masses of helium subdwarfs and their companions in systems with various combinations of components. We predict that the overwhelming majority (～97%) of unobserved companions to helium stars will be white dwarfs, predominantly, carbon-oxygen white dwarfs.     

Evolutionary connection between low-mass detached binaries,contact W UMa systems,and blue stragglers

We analyze the distribution of close binary stars in the orbital semimajor axis—primary mass plane. The reduced spatial density of stars with semimajor axes below 10R_⊙ is confirmed. We identify the area in this plane occupied by precursors of W UMa stars, assuming that the driving force causing the components to approach each other is their magnetic stellar wind. This scenario enables us to estimate the rate of formation (0.02/year) and lifetime (10⁸ yr) of W UMa stars. We derive a theoretical estimate of the ratio of the number of blue stragglers, N _BS , and of horizontal-branch stars, N _HB , in globular clusters based on the hypothesis that all blue stragglers are the result of component mergers in W UMa contact binaries. This ratio is N _BS /N _HB =0.4, close to the observed value for 62 Galactic globular clusters. We discuss possible reasons for the considerable dispersion of the observed estimates of this ratio for different clusters in our Galaxy.     

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 _⊙.     

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.     

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 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.     

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.     

X Per and V725 Tau: infrared variations on timescales longer than fifteen years

The results of infrared observations of the two Be stars X Per and V725 Tau, which are the optical components of X-ray binary systems, obtained in 1994–2016 are presented. The observations cover Be-star phases as well as shell phases. The data analysis shows that the radiation observed from the binaries at 1.25, 3.5, and 5 μm can be explained as the combined radiation from the optical components and variable sources (shells/disks) that emit as blackbodies (BBs). Emission from a source with the color temperature T _c ~1000?1500 K was detected for X Per at λ ≥ 3.5 μm. The highest IR-brightness variation amplitudes for X Per were 0.9?1.2 ^m (JHK magnitudes) and ~1.45 ^m (LM magnitudes); for V725 Tau, they were 1.1?1.4 ^m and ~1.7 ^m (L magnitudes). The parameters of the optical components and interstellar extinction during the Be phases were estimated: the color excesswasE(B?V) = 0.65±0.08 ^m and 0.77 ± 0.03 ^m for X Per and V725 Tau, respectively. Light from the variable sources (disks/shells) was distinguished and their color temperatures, radii, and luminosities estimated for different observation epochs in a BB model. The variations of the binaries’ IR brightness and colors are shown to be due to changing parameters of the variable sources. The mean color temperature of the cool source (disk/shell) and the mean radius and mean luminosity of X Per are 9500± 2630 K, (35 ± 10) R_⊙, and (9100± 540) L_⊙. For V725 Tau, these parameters are 6200 ± 940 K, (27 ± 6) R_⊙, and (980 ± 420) L_⊙. The 1.25–5 μm radiation from X Per at different epochs can be represented as a sum of contributions from at least three sources: the optical component and two objects emitting as BBs. To reproduce the 1.25–3.5 μm radiation from V725 Tau, two components are sufficient: the optical component and a single variable BB object. For both binary systems, orbital variations of the IR brightness can be noted near the Be-star phase. The amplitudes of the J-band variations of X Per and V725 Tau are about 0.3 ^m and 0.1 ^m , respectively.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 25 Mon and HR 7389

An analysis of high-resolution CCD spectra of the giant 25 Mon, which shows signs of metallicity, and the normal giant HR 7389 is presented. The derived effective temperatures, gravitational accelerations, and microturbulence velocities are T_eff = 6700 K, log g = 3.24, and ξ _t = 3.1 km/s for 25 Mon and T_eff = 6630 K, log g = 3.71, and ξ _t = 2.6 km/s for HR 7389. The abundances (log ε) of nine elements are determined: carbon, nitrogen, oxygen, sodium, silicon, calcium, iron, nickel, and barium. The derived excess carbon abundances are 0.23 dex for 25 Mon and 0.16 dex for HR 7389. 25 Mon displays a modest (0.08 dex) oxygen excess, with the oxygen excess for HR 7389 being somewhat higher (0.15 dex). The nitrogen abundance is probably no lower than the solar value for both stars. The abundances of iron, sodium, calcium (for HR 7389), barium, and nickel exceed the solar values by 0.22–0.40 dex for both stars. The highest excess (0.62 dex) is exhibited by the calcium abundance for 25 Mon. Silicon displays a nearly solar abundance in both stars—small deficits of ?0.03 dex and ?0.07 dex for 25 Mon and HR 7389, respectively. No fundamental differences in the elemental abundances were found in the atmospheres of 25 Mon and HR 7389. Based on their T_eff and log g values, as well as theoretical calculations, A. Claret estimated the masses, radii, luminosities, and ages of 25 Mon (M/M_⊙ = 2.45, log(R/R_⊙) = 0.79, log(L/L_⊙) = 1.85, t = 5.3 × 10⁸ yr) and HR 7389 (M/M_⊙ = 2.36, log(R/R_⊙) = 0.50, log(L/L_⊙) = 1.24, t = 4.6 × 10⁸ yr), and also of the stars 20 Peg (M/M_⊙ = 2.36, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.79, t = 4.9 × 10⁸ yr) and 30 LMi (M/M_⊙ = 2.47, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.88, t = 4.8 × 10⁸ yr) studied by the author earlier.     

Acceleration of spatial motions of stars by close-binary supermassive black holes in galactic nuclei

The conditions for the acceleration of the spatial motions of stars by close-binary supermassive black holes (SMBHs) in galactic nuclei are analyzed in order to derive the velocity distribution for stars ejected from galaxies by such black holes. A close binary system consisting of two SMBHs in circular orbits was subject to a spherically symmetrical “barrage” of solar-mass stars with various initial velocities. The SMBHs were treated as point objects with Newtonian gravitational fields. Models with binary component-mass ratios of 1, 0.1, 0.01, and 0.001 were studied. The results demonstrate the possibility of accelerating neutron stars, stellar-mass black holes, and degenerate dwarfs to velocities comparable to the relative orbital velocities of the binary-SMBH components. In the stage when the binary components are merging due to the action of gravitational-wave radiation, this velocity can approach the speed of light. The most massive binary black-holes (M ? 10⁹M_⊙) can also accelerate main-sequence stars with solar or subsolar masses to such velocities.     

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.     

The impact of reflection effects on the parameters of the old pre-cataclysmic variables MS Peg and LM Com

We have determined the main parameters of the old precataclysmic variable stars MS Peg and LM Com. The radial velocities of the components, reflection effects in the spectra, and light curves of the systems are studied based on model stellar atmospheres subject to external irradiation. Forty-seven moderate-resolution spectra for MS Peg and 57 for LM Com obtained with the 6-m telescope of the Special Astrophysical Observatory are used to derive the refined orbital periods of 0.1736660 days and 0.2586873 days, respectively; the orbital eccentricities do not exceed e=0.04. The mass (M _w =0.49e_⊙) and radius (e _w =0.015R_⊙) of the MS Peg primary calculated using the gravitational redshift correspond to those for a cooling carbon white dwarf with a thin hydrogen envelope. The parameters of the red dwarf (M _r =0.19M_⊙, T_eff=3560 K, R _r =0.18R_⊙) are close to those derived from evolutionary tracks for main-sequence M stars with solar chemical composition. The radius (R _r =0.22R_⊙) and temperature (T_eff=3650 K) of the LM Com secondary exceed theoretical estimates for main-sequence stars with masses of M _r =0.17M_⊙. The luminosity excess of the red dwarf in LM Com can be explained by a prolonged (T>5×10⁶ yrs) relaxation of the M star to its normal state after the binary leaves the common-envelope stage. For both systems, theoretical U, B, V, and R light curves and spectra calculated using the adopted sets of parameters are generally consistent with the observations. This confirms the radiative origin of the hot spots, the unimportance of horizontal radiative transport, and the absence of large-scale velocity fields with high values (V_trans>50 km/s) at the surfaces of the secondaries. Most of the emission lines in the spectra of these objects are formed under conditions close to thermalization, enabling modeling of their pro files in an LTE approximation. A strong λ3905 Å emission line has been identified as the 3s²3p4s 1P⁰-3s²3p² 1S SiI λ3905.52 Å line formed in the atmosphere of the hot spot. The observed intensity can be explained by non-LTE “superionization” of SiI atoms by soft UV radiation from the white dwarf. We suggest a technique for identifying binaries whose cool components are subject to UV irradiation based on observations of λ3905 Å emission in their spectra.