Radial pulsations of Wolf-Rayet stars and the problem of mass loss in them

In order to study the problem of mass loss by Wolf-Rayet stars, we carried out numerical simulations of non-linear pulsations of these objects. Although our computations do not show direct dynamical mass loss, qualitative estimates show that certain as yet unobserved pulsations could in principle, create conditions facilitating mass outflows from Wolf-Rayet stars.     

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.     

Identification of gamma-ray sources with Wolf-Rayet stars

An analysis of unidentified discrete sources of gamma-rays with energies E>100 MeV demonstrates that the spatial characteristics of this group of gamma-ray sources coincides with those of Wolf-Rayet stars. It is concluded that Wolf-Rayet stars are potential steady sources of high-energy gamma rays with mean luminosities L(>100 MeV)≈10³⁵ erg/s.     

Thermal instability in the envelopes of Wolf-Rayet stars

Astronomy Reports - We briefly consider thermal instabilities developing in the expanding envelopes of Wolf-Rayet stars and their possible implications. Due to the specific physical conditions in...     

Dynamical evolution of gaseous clouds in the atmospheres of Wolf-Rayet stars

We have computed the dynamical evolution of homogeneous, spherical gaseous condensations in the atmosphere of a Wolf-Rayet star. The physical conditions in the condensations vary substantially in the course of their motion in the stellar wind, which should result in variations in the observed spectrum of the star. The condensations also move at velocities of up to 1000 km/s relative to the surrounding stellar wind. Variations of the physical conditions in these condensations should be taken into account in models of the stellar winds of Wolf-Rayet stars.     

Modeling of rapid variability in the spectral line profiles of Wolf-Rayet stars

Profiles of variable emission lines in the spectra of Wolf-Rayet stars are calculated using a stochastic cloud model for the inhomogeneous atmospheres of early-type stars. The model assumes that most of the line flux is formed in cold, dense condensations (clouds) that move through a rarified inter-cloud medium whose density monotonically decreases outwards. The formation of clouds is taken to be stochastic. Wavelet analysis is used to estimate the parameters of cloud ensembles. The model can reproduce the general pattern of line-profile variability observed in the spectra of Wolf-Rayet 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.     

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_⊙.     

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.     

Evolution of Wolf-Rayet stars in binary systems: An analysis of the mass and orbital-eccentricity distributions

We have undertaken a statistical study of the component mass ratios and the orbital eccentricities of WR + O close binary, detached main-sequence (DMS), contact early-type (CE), and semidetached (SD) systems. A comparison of the characteristics of WR + O systems and of DMS, CE, and SD systems has enabled us to draw certain conclusions about the evolutionary paths of WR + O binaries and to demonstrate that up to 90% of all known WR + O binaries formed as a result of mass transfer in massive close O + O binary systems. Since there is a clear correlation between the component masses in SD systems with subgiants, the absence of an anticorrelation between the masses of the WR stars and O stars in WR + O binaries cannot be considered evidence against the formation of WR + O binaries via mass transfer. The spectroscopic transitional orbital period P _tr ^sp corresponding to the transition from nearly circular orbits (e _sp<0.1) to elliptical orbits (e _sp≥0.1) is ～14^d for WR + O systems and ～2^d–3^d for OB + OB systems. The period range in which all WR + O orbits are circular \((1\mathop d\limits_. 6 \leqslant P \leqslant 14^d )\) is close to the range for SD systems with subgiants, \(0\mathop d\limits_. 7 \leqslant P \leqslant 15^d \). The large difference between the P _tr ^sp values for WR + O and OB + OB systems suggests that a mechanism of orbit circularization additional to that for OB + OB systems at the DMS stage (tidal dissipation of the orbital energy due to radiative damping of the dynamical tides) acts in WR + O binaries. It is natural to suggest mass transfer in the parent O + O binaries as this supplementary orbit-circularization mechanism. Since the transitional period between circular and elliptical orbits for close binaries with convective envelopes and ages of 5×10⁹ years is \(P_{tr} = 12\mathop d\limits_. 4\), the orbits of most known SD systems with subgiants had enough time to circularize during the DMS stage, prior to the mass transfer. Thus, for most SD systems, mass transfer plays a secondary role in circularization of their orbits.In many cases, the initial orbital eccentricities of the O + O binary progenitors of WR + O systems are preserved, due to the low viscosity of the O-star envelopes and the short timescale for their nuclear evolution until the primary O star fills its Roche lobe and the mass transfer begins. The mass transfer in the parent O + O systems is short-lived, and the number of orbital cycles during the early mass-transfer stage is relatively low (lower than for the progenitors of SD systems by three or four orders of magnitude). The continued transfer of mass from the less massive to the more massive star after the component masses have become equal leads to the formation of a WR + O system, and the orbit's residual eccentricity increases to the observed value. The increase of the orbital eccentricity is also facilitated by variable radial mass loss via the wind from the WR star in the WR + O system during its motion in the elliptical orbit. The result is that WR + O binaries can have considerable orbital eccentricities, despite their intense mass transfer. For this reason, the presence of appreciable eccentricities among WR + O binaries with large orbital periods cannot be considered firm evidence against mass transfer in the parent O + O binary systems. Only for the WR + O binaries with the longest orbital periods (4 of 35 known systems, or 11 %) can the evolution of the parent O + O binaries occur without filling of the Roche lobe by the primary O star, being governed by radial outflow in the form of the stellar wind and possibly by the LBV phenomenon, as in the case of HD 5980.     

Evolution of the velocity ellipsoids in the thin disk of the Galaxy and the radial migration of stars

Data from the revised Geneva-Copenhagen catalog are used to study the influence of radial migration of stars on the age dependences of parameters of the velocity ellipsoids for nearby stars in the thin disk of the Galaxy, assuming that the mean radii of the stellar orbits remain constant. It is demonstrated that precisely the radial migration of stars, together with the negative metallicity gradient in the thin disk, are responsible for the observed negative correlation between the metallicities and angular momenta of nearby stars, while the angular momenta of stars that were born at the same Galactocentric distances do not depend on either age or metallicity. The velocity components of the Sun relative to the Local Standard of Rest derived using data for stars born at the solar Galactocentric distance are (U _⊙, V _⊙, W _⊙) _LSR = (5.1 ± 0.4, 7.9 ± 0.5, 7.7 ± 0.2) km/s. The two coordinates of the apex of the solar motion remain equal to 〈l _⊙〉 = 70° ± 7° and 〈b _⊙〉 = 41° ± 2°, within the errors. The indices for the power-law age dependences of them ajor, middle, and minor semi-axes become 0.26±0.04, 0.32±0.03, and 0.07±0.03, respectively. As a result, with age, the velocity ellipsoid for thin-disk stars born at the solar Galactocentric distance increases only in the plane of the disk, remaining virtually constant in the perpendicular direction. Its shape remains far from equilibrium, and the direction of the major axis does not change with age: the ellipsoid vertex deviation remains constant and equal to zero within the errors (〈L〉 = 0.7° ± 0.6°, 〈B〉 = 1.9° ± 1.1°). Such a small increase in the velocity dispersion perpendicular to the Galactic plane with age can probably be explained by “heating” of the stellar system purely by spiral density waves, without a contribution from giant molecular clouds.     

Nonlinear radial consolidation of vertical drains under a general time‐variable loading

By incorporating the nonlinear variation of a soil's compressibility and permeability during the process of consolidation, an analytical solution for the radial consolidation of vertical drains has been developed for a general time‐variable loading. The general solution was verified for the cases of instantaneous loading and ramp loading. Detailed solutions were further derived for two special loading schemes: multistage loading and preloading–unloading–reloading. The nonlinear consolidation behavior of a vertical drain subjected to these two types of loading schemes was then investigated by a parametric study. The results show that the loading rate, the ratio of the compressibility index to the permeability index (C_c/C_k), and the initial stress state have a significant influence on the consolidation rate. A smaller value of C_c/C_k, a larger initial stress, or a fast loading rate always leads to a rapid consolidation rate. During the unloading period, a negative excess pore water pressure may occur, and a slower unloading rate may reduce this negative value. Copyright © 2014 John Wiley & Sons, Ltd.     

Spectral and photometric studies of the Wolf-Rayet star WR 134 = HD 191765

The results of spectral and photometric observations of the Wolf-Rayet star WR 134 = HD 191765 performed at the N. Tusi Shamakha Astrophysical Observatory (ShAO) of the National Academy of Sciences of Azerbaijan in 2006?C2010 are presented. The spectral observations were carried out at the ShAO Zeiss-2000 telescope with an echelle spectrometer. Thirty-four echelle spectrograms of WR 134 were obtained. Profiles of the five strongest emission lines were analyzed: HeII 4859, HeII 5411, CIV 5808, HeI 5875, and (HeII+H??) 6560. Various parameters of these emission lines are determined: their equivalent widths, radial velocities, central intensities, and half-widths. Only the radial velocity was found to be variable. Variability of the shapes of all emission-line profiles was found, but the largest changes are observed for the (HeII+H??) 6560 emission band. Photometric observations were carried out at the ShAO Zeiss-600 telescope using an Alta U-47 CCD array (1024 × 1024 pixels) in the V filter of the photometric UBV system. Photometric observations were carried out on 18 nights, with from 100 to 300 measurements made during each night. The mean V magnitudes of WR 134 and a control star were determined for each night. Variability of WR 134 was detected, both within a night and during the entire observation period. The exposure time varied from 1 to 6 s on different nights. A statistical analysis of the mean magnitudes indicated that this series contains a peak at a frequency of ?? = 0.530 day^?1, corresponding to the period P = 1.887^d. This period is interpreted as the manifestation binarity for this star. It is suggested that the secondary component of the system may be a low-mass optical K-M star.     

Galaxies and stars

The distribution of galaxies in the vicinity of stars brighter than V=7.25^m is analyzed. The number density of galaxies is slightly decreased in such regions. This result is statistically significant and cannot be explained as a direct effect of the extended photographic images of these stars. The result is apparently associated with the presence of clouds near the stars, which absorb or scatter light.     

The activity of late-type stars: the Sun among stars with cyclic activity

The coronal and chromospheric emission of several hundred late-type stars whose activity was recently detected are analyzed. This confirms the previous conclusion for stars of HK project that there exist three groups of objects: active red M dwarfs, G-K stars with cyclic activity, and stars exhibiting high but irregular activity. The X-ray fluxes, EUV-spectra, and X-ray cycles can be used to study the main property of stellar coronas—the gradual increase in the number of high-temperature (T ≥ 10 MK) regions in the transition from the Sun to cyclically active K dwarfs and more rapidly rotating F and G stars with irregular activity. The level of X-ray emission is closely related to the spottedness of the stellar surface. The correlation between the chromospheric and coronal emission is weak when the cycles are well-defined, but becomes strong when the activity is less regular. Unexpectedly, stars whose chromospheric activity is even lower than that of the Sun are fairly numerous. Common and particular features of solar activity among the activity of other cyclically active stars are discussed. Our analysis suggests a new view of the problem of heating stellar coronas: the coronas of stars with pronounced cycles are probably heated by quasistationary processes in loops, while prolonged nonstationary coronal events are responsible for heating the coronas of F and G stars with high but irregular activity.     

Studies of classical barium stars

Using atmosphere models based on high-resolution spectra, we have derived the abundances of chemical elements in the atmospheres of seven classical barium stars and compared them with the elemental abundances of moderate barium stars and normal red giants. The behavior of elements up to the iron peak is the same in all three groups of giants, providing evidence that they have a common origin. The dependence of the anomalous abundances of s-process elements on stellar mass and metallicity is qualitatively similar for all three groups, probably indicating that a substantial role is played by the evolutionary phase of the stars. We conclude that the barium-star phenomenon and the overabundances of s-process elements in barium stars cannot be explained as a consequence of binarity alone. The extent to which the s-process elements are overabundant is affected by the mass, metallicity, and evolutionary phase of the given star, and any of these parameters may prove to be important in a specific object.     

Dynamical evolution of multiple stars

We have modeled the dynamical evolution of small groups of N=3–18 stars in the framework of the gravitational N-body problem, taking into account possible coalescences of stars and the ejection of single and binary stars from the system. The distribution of states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of the binaries and stable triple systems formed, as well as those of ejected single stars, are studied. In most cases, the evolution of the group results in the formation of a binary or stable triple system. The orbital eccentricities of the binaries formed are distributed according to the law f(e)=2e. As a rule, stable triple systems display pronounced hierarchy (the mean ratio of the semimajor axes of the outer and inner binaries is about 20:1). Stars are ejected with velocities from several km/s to several tens of km/s. The results of the modeling are compared with the parameters of observed wide binaries and triple systems.     

Geomagmatism, pulsations of the Earth, and Phanerozoic minerageny

Discontinuity and periodicity of tectonic processes, eustatic fluctuations of the ocean level, volcanic and metallogenic activity, and some other global processes in the Earth’s history are indicative of the pulsatory nature of the Earth’s evolution. Correlation of geomagnetic field variations with global geological processes shows the geomagnetic field polarity to be an indicator of pulsations. The phases of the Earth’s expansion correspond to normal (present-day) polarity, and the planet’s contraction to epochs of reversed polarity. In terms of the concept of geopulsations, the diversity of basic geodynamic regimes of continents is determined by the combination of three factors: the phases of the Earth’s evolution (contraction-expansion), the effects of deep fluid and heat flows (plumes), and the state of the asthenosphere (its depth, thickness, and degree of heating). The general evolution of Phanerozoic ore deposition and the specific metallogenic features of tectonomagmatic cycles may be considered in a new light in view of the Earth’s pulsatory history.     

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.