Neutron stars in globular clusters: Formation and observational manifestations

Population synthesis is used to model the number of neutron stars in globular clusters that are observed as low-mass X-ray sources and millisecond radio pulsars. The dynamical interactions between binary and single stars in a cluster are assumed to take place only with a continuously replenished “background” of single stars whose properties keep track of the variations in parameters of the cluster as a whole and the evolution of single stars. We use the hypothesis that the neutron stars forming in binary systems from components with initial masses of ～8–12 M _⊙ during the collapse of degenerate O-Ne-Mg cores through electron captures do not acquire a high space velocity. The remaining neutron stars (from single stars with masses >8 M _⊙ or from binary components with masses >12 M _⊙) are assumed to be born with high space velocities. According to this hypothesis, a sizeable fraction of the forming neutron stars remain in globular clusters (about 1000 stars in a cluster with a mass of 5 × 10⁵ M _⊙). The number of millisecond radio pulsars forming in such a cluster in the case of accretion-driven spinup in binary systems is found to be ～10, in agreement with observations. Our modeling also reproduces the observed shape of the X-ray luminosity function for accreting neutron stars in binary systems with normal and degenerate components and the distribution of spin periods for millisecond pulsars.     

Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics.

1. The formation and the evolution of very massive stars (with masses >120 M_⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed, but with a maximum mass ≈70 M_⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability supernovae or for the formation of intermediate-mass black holes with a mass of several 100 M_⊙.
2. Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario), or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.

     

The masses of sdB and sdO stars

Mass is a fundamental parameter, but the masses are not well known for most hot subdwarfs. We propose a method of determining the masses of hot subdwarfs. Using this method, we studied the masses of hot subdwarfs from the ESO supernova Ia progenitor survey and the Hamburg quasar survey. The study shows that most of the subdwarf B stars have masses between 0.42 and 0.54 M _⊙, whilst most sdO stars are in the range 0.40～0.55 M _⊙. Comparing our study to the theoretical mass distributions of Han et al. (Mon. Not. R. Astron. Soc. 341:669, 2003), we found that sdO stars with mass less than ～0.5 M _⊙ may evolve from sdB stars, whilst most high-mass (>0.5 M _⊙) sdO stars result from mergers directly.     

Very massive close binaries and the puzzling temporal evolution of 14N in the Solar Neighbourhood

Low metallicity very massive stars with an initial mass between 140M_⊙ and 260M_⊙ can be subdivided into two groups: those between 140M_⊙ and 200M_⊙ which produce a relatively small amount of Fe, and those with a mass between 200M_⊙ and 260M_⊙ where the Fe-yield ejected during the supernova explosion is enormous. We first demonstrate that the inclusion of the second group into a chemical evolutionary model for the Solar Neighbourhood predicts an early temporal evolution of Fe, which is at variance with observations whereas it cannot be excluded that the first group could have been present. We then show that a low metallicity binary with very massive components (with a mass corresponding to the first group) can be an efficient site of primary ¹⁴N production through the explosion of a binary component that has been polluted by the pair instability supernova ejecta of its companion. When we implement these massive binary ¹⁴N yields in a chemical evolution model, we conclude that very massive close binaries may be important sites of ¹⁴N enrichment during the early evolution of the Galaxy.     

Very massive stars: Evolution with mass loss

The evolution of mass-losing very massive stars in the 500–10000M _⊙ range has been investigated for two different initial compositions, (X, Z)=(0.8,0.0) and (X, Z)=(1.0,0.0). The evolutionary tracks are governed by two opposing factors which are the increase in the mean molecular weight in the convective core and the effect of mass loss. Conservative evolution of stars with massM?10000M _⊙ is similar to that of massive stars (20–100M _⊙), always moving to lower effective temperatures. For low values of the standard mass loss parameterN (50?N?200) the two opposing factors are almost in balance and the star is forced to move in a series of loops. For higher mass loss rates the loops disappear. In the 10000M _⊙ case no loops are observed and the tracks always move to higher effective temperatures. For a given mass loss rate the transition between right and left moving tracks occurs at higher masses the lower is the mass loss rate.     

Absolute parameters of eclipsing binaries in Southern Hemisphere sky – II: QY Tel

This paper presents the first analysis of spectroscopic and photometric observations of the neglected southern eclipsing binary star, QY Tel. Spectroscopic observations were carried out at the South African Astronomical Observatory in 2013. New radial velocity curves from this study and V light curves from the All Sky Automated Survey were solved simultaneously using modern light and radial velocity curve synthesis methods. The final model describes QY Tel as a detached binary star where both component stars fill at least half of their Roche limiting lobes. The masses and radii were found to be 1.32 (± 0.06) M_⊙, 1.74 (± 0.15) R_⊙ and 1.44 (± 0.09) M_⊙, 2.70 (± 0.16) R_⊙ for the primary and secondary components of the system, respectively. The distance to QY Tel was calculated as 365 (± 40) pc, taking into account interstellar extinction. The evolution case of QY Tel is also examined. Both components of the system are evolved main-sequence stars with an age of approximately 3.2  Gy, when compared to Geneva theoretical evolution models.     

A rare reflection effect eclipsing sdB+dM binary: 2M 1533+3759

In this paper, we report a rare reflection effect eclipsing sdB+dM binary, 2M?1533+3759. It is the seventh eclipsing sdB+dM binary that has been discovered to date. This system has an orbital period of 0.16177042 day and a velocity semi-amplitude of 71.1 km?s^?1. Using a grid of zero-metallicity NLTE model atmospheres, we derived T _eff=29250 K, log?g=5.58 and [He/H]=?2.37 from spectra taken near the reflection effection minimum. Lightcurve modeling resulted in a system mass ratio of 0.301 and an orbital inclination angle of 86.6°. The derived primary mass for 2M?1533+3759, 0.376±0.055 M _⊙, is significantly lower than the canonical mass (0.48 M _⊙) found for most previously investigated sdB stars. This implies an initial progenitor mass >1.8 M _⊙, at least a main sequence A star and perhaps even one massive enough to undergo non-degenerate helium ignition.     

Properties of Wolf-Rayet stars in eclipsing binary systems

The results of investigations of a number of eclipsing Wolf-Rayet binaries are presented. The ‘core’ radiuses, the ‘core’ temperatures and masses of WR stars in the eclipsing WR+OB binary systems V 444 Cyg, CX Cep, CQ Cep, and CV Ser are obtained (see Table I). The results obtained from the light curves analysis of the V 444 Cyg in the range λλ2460 Å-3.5μ give strong evidence for the Beals (1944) model of WR phenomenon. The chromospheric-coronal effects in the WN5 extended atmosphere are not observed up to a distance ofr?20R _⊙. In the Hertzsprung—Russell diagram all the WR stars lie on the left side from the main sequence between the main sequence and the sequence of uniform helium stars (see Figure 9). Their locations are close to those of the helium remnants formed as a result of mass exchange in massive close binary systems. The period variations in the systems V 444 Cyg and CQ Cep have been discovered and a reliable value of the mass loss rateM=10^?5 M _⊙yr^?1 is obtained, for the two WR stars. The results of the photometric and spectroscopic investigations of the WR stars with low mass companions (post X-ray binary stage?) are presented too (see Table II). The masses of the companions are (1–2)M _⊙, their optical luminosity is ～10³⁶, erg s^?1 which implies that these companions cannot be the normal stars. It is possible that these companions are neutron stars accreting from the stellar wind of the WR stars. Low values of the X-ray luminosities of such WR stars with low mass companions imply that the accretion of matter in such systems is distinct from the accretion process in classical X-ray binary systems. It is noted also that the parameters of low massive companions coupled with WR stars are close to those of helium stars.     

Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

Composite spectra: XVII. 12 Comae,a member of the Coma open cluster

The components of binary stars offer the potential to examine the predictions of stellar‐evolution theory with particularly tight constraints. Those constraints are further tightened when the binary belongs to a cluster whose properties have been well determined independently. 12 Comae presents both advantages, belonging as it does to the Coma Cluster, Melotte 111. The orbit of 12 Comae has an eccentricity of nearly 0.6 and a period of 13 months. By a process of subtraction we separate the spectra of the component stars, derive a precise double‐lined orbit solution, and by modelling the photometry we extract the individual stellar photometric and physical properties, ages and rotation. By fitting theoretical evolutionary tracks to the positions of the stars in the H‐R diagram we confirm their individual masses, and derive a ZAMS of ∼0.65 Gyr, which accords well with measurements published for the cluster itself. We show that the primary of 12 Comae is an evolving giant of spectral type ∼G7 and mass 2.6 M_⊙, while its secondary (whose spectrum could be isolated particularly cleanly) is an A3 dwarf which has a mass of 2.05 M_⊙ and has commenced its evolution away from the main sequence. There is evidence that both stars are slightly metal‐weak (–0.25 < [Fe/H] < 0.0), well in keeping with analyses of other members of this cluster (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Supernovae in close binaries

The impact of a supernova shell onto 2.82M _⊙ and 20.0M _⊙ main-sequence stars is investigated for various initial orbital separations, and various supernova shell masses and velocities. The inelastic collision between the star and the supernova shell, the shock propagation into the companion star, and other forms of momentum transfer such as the rocket effect are considered. The total momentum transfer due to the supernova is insufficient to eject the companion from the binary as long as the companion retains most of its mass, regardless of the initial orbital separation. Ejection of the companion may occur if the companion is nearly destroyed. Even in contact binaries destruction does not necessarily occur, and if the orbital separation exceeds 10¹² cm, destruction of the companion becomes quite unlikely.     

Mass—luminosity relation and pulsational properties of Wolf—Rayet stars

The evolution of Population I stars with initial masses 70M _⊙ ≤ M _ZAMS ≤ 130M _⊙ is considered. The computations were performed under various assumptions about the mass loss rate and were terminated at the phase of gravitational contraction after core helium exhaustion. The mass loss rate at the helium burning phase, ?_3α , is shown to be the main parameter that determines the coefficients of the mass—luminosity relation for Wolf—Rayet stars. Several more accurate mass—luminosity relations for mass loss rates ? = f _3α ?_3α , where 0.5 ≤ f _3α ≤ 3, are suggested, along with the mass—luminosity relation that combines all of the evolutionary sequences considered. The results of the stellar evolution computations were used as initial conditions in solving the hydrodynamic equations describing the spherically symmetric motions of a self-gravitating gas. The outer layers of massive Population I stars are unstable against radial oscillations throughout the helium burning phase. The oscillation amplitude is largest at enhanced carbon and oxygen abundances in the outer stellar layers, i.e., at a lower initial stellar mass M _ZAMS or a lower mass loss rate during the entire preceding evolution. In the course of evolution, the radial oscillation amplitude decreases and the small nonlinearity of the oscillations at M < 10M _⊙ allow the integral of mechanical work W done by an elementary spherical layer of gas in a closed thermodynamic cycle to be calculated with the necessary accuracy. The maximum of the radial dependence of W is shown to be located in layers with a gas temperature T ～ 2 × 10⁵ K, where the oscillations are excited by the iron Z-bump κ-mechanism. Comparison of the radial dependences of the integral of mechanical work W and the amplitude of the radiative flux variations suggests that the nonlinear radial oscillations of more massive Wolf—Rayet stars are also excited by the κ-mechanism.     

Evolution of magnetic fields in stars across the upper main sequence: II. Observed distribution of the magnetic field geometry

We re‐discuss the evolutionary state of upper main sequence magnetic stars using a sample of Ap and Bp stars with accurate Hipparcos parallaxes and definitely determined longitudinal magnetic fields. We confirm our previous results obtained from the study of Ap and Bp stars with accurate measurements of the mean magnetic field modulus and mean quadratic magnetic fields that magnetic stars of mass M < 3 M_⊙ are concentrated towards the centre of the main‐sequence band. In contrast, stars with masses M > 3 M_⊙ seem to be concentrated closer to the ZAMS. The study of a few known members of nearby open clusters with accurate Hipparcos parallaxes confirms these conclusions. Stronger magnetic fields tend to be found in hotter, younger and more massive stars, as well as in stars with shorter rotation periods. The longest rotation periods are found only in stars which spent already more than 40% of their main sequence life, in the mass domain between 1.8 and 3 M_⊙ and with log g values ranging from 3.80 to 4.13. No evidence is found for any loss of angular momentum during the main‐sequence life. The magnetic flux remains constant over the stellar life time on the main sequence. An excess of stars with large obliquities β is detected in both higher and lower mass stars. It is quite possible that the angle β becomes close to 0. in slower rotating stars of mass M > 3 M_⊙ too, analog to the behaviour of angles β in slowly rotating stars of M < 3 M_⊙. The obliquity angle distribution as inferred from the distribution of r ‐values appears random at the time magnetic stars become observable on the H‐R diagram. After quite a short time spent on the main sequence, the obliquity angle β tends to reach values close to either 90. or 0. for M < 3 M_⊙. The evolution of the obliquity angle β seems to be somewhat different for low and high mass stars. While we find a strong hint for an increase of β with the elapsed time on the main sequence for stars with M > 3 M_⊙, no similar trend is found for stars with M < 3 M_⊙. However, the predominance of high values of β at advanced ages in these stars is notable. As the physics governing the processes taking place in magnetised atmospheres remains poorly understood, magnetic field properties have to be considered in the framework of dynamo or fossil field theories. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pulsations of intermediate–mass stars on the asymptotic giant branch

Evolutionary tracks from the zero age main sequence to the asymptotic giant branch were computed for stars with initial masses 2 M _⊙ ≤ M _ZAMS ≤ 5 M _⊙ and metallicity Z = 0.02. Some models of evolutionary sequences were used as initial conditions for equations of radiation hydrodynamics and turbulent convection describing radial stellar pulsations. The early asymptotic giant branch stars are shown to pulsate in the fundamental mode with periods 30 day ? Π ? 400day. The rate of period change gradually increases as the star evolves but is too small to be detected (Π?/Π < 10^?5 yr^?1). Pulsation properties of thermally pulsing AGB stars are investigated on time intervals comprising 17 thermal pulses for evolutionary sequences with initial masses M _ZAMS = 2 M _⊙ and 3 M _⊙ and 6 thermal pulses for M _ZAMS = 4 M _⊙ and 5 M _⊙. Stars with initial masses M _ZAMS ≤ 3 M _⊙ pulsate either in the fundamental mode or in the first overtone, whereas more massive red giants (M _ZAMS ≥ 4 M _⊙) pulsate in the fundamental mode with periods Π ? 10³ day. Most rapid pulsation period change with rate ?0.02 yr^?1 ? Π?/Π ? ?0.01 yr^?1 occurs during decrease of the surface luminosity after the maximum of the luminosity in the helium shell source. The rate of subsequent increase of the period is Π?/Π ? 5 × 10^?3 yr^?1.     

A Model of the Mira–Type Star T UMi

Stellar evolution calculations were carried out from the main sequence to the final stage of the asymptotic giant branch for stars with initial masses 1 M_⊙ ≤ M_ZAMS ≤ 2 M_⊙ and metallicity Z = 0.01. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar pulsations. The study was aimed to construct the hydrodynamic models of Mira–type stars that show the secular decrease in the pulsation period Π commenced in 1970th at Π = 315 day. We show that such a condition for the period change is satisfied with evolutionary sequences 1 M_⊙ ≤ M_ZAMS ≤ 1.2 M_⊙ and the best agreement with observations is obtained for M_ZAMS = 1.2 M_⊙. The pulsation period reduction is due to both the stellar radius decrease during the thermal pulse of the helium burning shell and mode switch from the fundamental mode to the first overtone. Theoretical estimates of the fundament parameters of the star at the onset of pulsation period reduction are as follows: the mass is M = 0.93 M_⊙, the luminosity is L = 4080 L_⊙, and the radius is R = 220 R_⊙. The mode switch occurs 35 years after the onset of period reduction.     

Unsteady mass outflow from Wolf-Rayet stars

We show that hydrostatically equilibrium models for the thin photospheres of helium stars based on new opacities κ_R (OPAL and OP) can be constructed only for masses M<5M _⊙. The parameter Г=κL/4πGMc, defined as the ratio of light pressure to gravity, exceeds a critical value of 1.0 for larger masses, which must result in mass outflow under light pressure. This mass limit matches the observed lower limit for the masses of Wolf-Rayet stars (M _WR>5M _⊙)), which is an additional argument that the Wolf-Rayet stellar cores are actually helium stars. By solving the equation of radiative transfer in extended atmospheres, we construct a semiempirical model for a WN5 star (M _WN5=10M _⊙)) with a helium core and an expanding envelope, whose physical and geometric parameters are known mainly from light-curve solution for the eclipsing binary V444 Cyg (WN5+06): outflow rate $\dot M \approx 1.0 \times 10^{ - 5} M_ \odot yr^{ - 1} $ , terminal velocity V _∞≈2000 km s^?1, and expanding-envelope optical depth τ_env≈25. The temperature at the outer boundary of the photosphere of a helium star surrounded by such an envelope is approximately 130 kK higher than that in the absence of an envelope, being T _ph≈240 kK. Because of the high temperatures, the absorption coefficients at the corresponding photospheric levels are smaller than those in models with no envelope; therefore, the photosphere turns out to be in hydrostatic equilibrium and stable against light pressure (Г_max≈0.9). As a way out of this conflicting situation (an expanding envelope together with a hydrostatically equilibrium photosphere), we propose a model of discrete mass outflow, which is also supported by the observed cloudy structure of the envelopes in this type of stars. To quantitatively estimate parameters of the nonuniform outflow model requires detailed gas-dynamical calculations.     

X-ray Observations of Eight Young Open Star Clusters: I. Membership and X-ray Luminosity

We present a detailed investigation of X-ray source contents of eight young open clusters with ages between 4 to 46 Myr using archival X-ray data from XMM-Newton. The probable cluster memberships of the X-ray sources have been established on the basis of multi-wavelength archival data, and samples of 152 pre-main sequence (PMS) low mass (<2M _⊙), 36 intermediate mass (2–10M _⊙) and 16 massive (>10M _⊙) stars have been generated. X-ray spectral analyses of high mass stars reveal the presence of high temperature plasma with temperature <2 keV, and mean L _X/L _bol of 10^???6.9. In the case of PMS low mass stars, the plasma temperatures have been found to be in the range of 0.2 keV to 3 keV with a median value of ~1.3 keV, with no significant difference in plasma temperatures during their evolution from 4 to 46 Myr. The X-ray luminosity distributions of the PMS low mass stars have been found to be similar in the young star clusters under study. This may suggest a nearly uniform X-ray activity in the PMS low mass stars of ages ~4–14 Myr. These observed values of L _X/L _bol are found to have a mean value of 10^??3.6±0.4, which is below the X-ray saturation level. The L _X/L _bol values for the PMS low mass stars are well correlated with their bolometric luminosities, that implies its dependence on the internal structure of the low mass stars. The difference between the X-ray luminosity distributions of the intermediate mass stars and the PMS low mass stars has not been found to be statistically significant. Their L _X/L _bol values, however have been found to be significantly different from each other with a confidence level greater than 99.999% and the strength of X-ray activity in the intermediate mass stars is found to be lower compared to the low mass stars. However, the possibility of X-ray emission from the intermediate mass stars due to a low mass star in close proximity of the intermediate mass star can not be ruled out.     

Evolution of massive close binaries

The further evolution of a massive X-ray binary consisting of a compact object and an OB supergiant is outlined. The supergiant exceeds its critical Roche lobe and a second stage of mass transfer starts. The remnant of the mass losing star — a pure helium star — develops a collapsing iron core and finally undergoes a supernova explosion. If the compact companion is a black hole the system remains bound; if the compact companion is a neutron star the system is disrupted unless an extra kick allowing an asymmetric explosion is given. Computations were performed for the massive binary 22.5M _⊙+2M _⊙. The possible final evolutionary products are: (1) a black hole and a compact object, in a binary system, (2) two run-away pulsars, (3) a binary pulsar. As final parameters for the described system the eccentricity and period for the recently discovered binary pulsar 1913+16 may be found. An orbital inclination ofi=40° may be derived. The probability for the generation of binary pulsars is very low; in most cases the system is disrupted during the supernova explosion.