Stochastic excitation of gravity modes in massive main-sequence stars

We investigate the possibility that gravity modes can be stochastically excited by turbulent convection in massive main-sequence (MS) stars. We build stellar models of MS stars with masses M=10?M _⊙,15?M _⊙, and 20?M _⊙. For each model, we then compute the power supplied to the modes by turbulent eddies in the convective core (CC) and the outer convective zones (OCZ). We found that, for asymptotic gravity modes, the major part of the driving occurs within the outer iron convective zone, while the excitation of low n order modes mainly occurs within the CC. We compute the mode lifetimes and deduce the expected mode amplitudes. We finally discuss the possibility of detecting such stochastically-excited gravity modes with the CoRoT space-based mission.     

Type Ia supernovae: An explosion in the regime of a convergent delayed detonation wave

The model of a presupernova’s carbon-oxygen (C-O) core with an initial mass of 1.33 M _⊙, an initial carbon abundance X _C ⁽⁰⁾ =0.27, and a mean rate of increase in mass of 5 × 10^?7 M _⊙ yr^?1 through accretion in a binary system evolved from the central density and temperature ρ_c=10⁹ g cm^?3 and T _c=2.05 × 10⁸K, respectively, by forming a convective core and its subsequent expansion to an explosive fuel ignition at the center. The evolution and explosion equations included only the carbon burning reaction ¹²C+¹²C with energy release corresponding to the complete conversion of carbon and oxygen (at the same rate as that of carbon) into ⁵⁶Ni. The ratio of mixing length to convection-zone size α_c was chosen as the parameter. Although the model assumptions were crude, we obtained an acceptable (for the theory of supernovae) pattern of explosion with a strong dependence of its duration on α_c. In our calculations with sufficiently large values of this parameter, α_c=4.0 × 10^?3 and 3.0×10^?3, fuel burned in the regime of prompt detonation. In the range 2.0×10^?3≥α_c≥3.0×10^?4, there was initially a deflagration with the generation of model pulsations whose amplitude gradually increased. Eventually, the detonation regime of burning arose, which was triggered from the model surface layers (with m ? 1.33 M _⊙) and propagated deep into the model up to the deflagration front. The generation of model pulsations and the formation of a detonation front are described in detail for α_c=1.0 × 10^?3.     

Early-type W UMa contact binary system: New data on V535 Ara

This paper presents the results of spectroscopic and photometric observations of the early-type W UMa system V535 Ara. New high-resolution spectra were taken at the Mt. John University Observatory in 2007. Radial velocities and spectroscopic orbital elements of the system were determined by applying KOREL spectral disentangling. The resulting orbital elements were: a₁sini = 0.0047 ± 0.0001 AU, a₂sini = 0.0146 ± 0.0001 AU, M₁sin³i = 1.85 ± 0.01 M_⊙, and M₂sin³i = 0.59 ± 0.01 M_⊙. The components were found to be in synchronous rotation following examination of their disentangled Hγ line profiles. Four photometric data-sets (1966 BV, 1967 BV, HIPPARCOS and ASAS) were modeled using the Wilson-Devinney method. The model describes V535 Ara as an A sub-type W UMa type eclipsing binary which has a fill out factor of 0.22 in marginal contact configuration. The simultaneous solution of light and radial velocity curves gave the following absolute parameters: M₁ = 1.94 ± 0.04 M_⊙, M₂ = 0.59 ± 0.02 M_⊙, R₁ = 2.09 ± 0.03 R_⊙, R₂ = 1.23 ± 0.02R_⊙, L₁ = 18 ± 3 L_⊙ and L₂ = 6 ± 1 L_⊙. The distance to V535 Ara was calculated as 123 ± 20 pc using distance modulus with correction for interstellar extinction.     

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.     

On the interaction between the URCA process and convection

The influence of the URCA process (β-decay, electron capture) on convective stability is investigated and a stability criterion is derived. The criterion contains the Schwarzschild criterion and the thermohaline convection. It is found that URCA may cause convective instability to an otherwise stable medium, but it cannot stabilize an unstable medium, only the growth rate is affected. A numerical example for the Na²³?Ne²³ URCA pair shows the regions in the ?-T plane where instability is caused (assuming given abundances of the isotopes). The evolution of C-O core of an evolved 3.5M _⊙–8M _⊙ star may be affected by formation of convective regions even prior to C¹² ignition.     

Smooth models of overshooting at the base of the solar convective zone

A set of smoothed temperature gradient profiles around overshooting layers at the solar convective zone bottom is considered. In classical local theories of convection the one point defined according to the Schwarzschild criterion is enough to describe a convective boundary. To get a sophisticated picture of the overshooting we use four points to compute the transition overshooting functions. Analyzing the transition gradient profiles we found that the overshooting convective flux may be either positive or negative. A negative overshooting flux appears in nonlocal convective theories and causes a steep temperature gradient profile. But we propose an evenly smoothed gradient which corresponds to a convective flux positive everywhere. To outline the effect of the temperature gradient on the solar oscillations the squared Brunt–Väisälä frequency N ² is calculated. In local convective theories the N ² profile shows the discontinuity of the first derivative at the convective boundary, while all smoothed profiles eliminate the break.     

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.     

Radial pulsation of less-massive yellow supergiants

Linear and nonlinear pulsation computations for the modelsM=0.8M _⊙,L=10000 and 20000L _⊙ were carried out in order to understand FG Sge's pulsation. The results may be summarized as follows:

1. In the modelsL=10000L _⊙, the fundamental blue edge is nearT _e =5700 K. The models show that instability of the third overtone extends to 7400 K and still has large positive growth rates. A nonlinear model of 7000 K shows a small amplitude ΔV=10 km s^?1, ΔM _bol=0.03 with a period of around 18 days, nearly equal to that of the third overtone.
2. In the linear models ofL=20000L _⊙, the fundamental blue edge is shifted to 7000 K but the damping of this mode is so small that it is marginally stable to 7700 K. The third overtone has large positive growth rates of this region. The nonlinear model at 7700 K, however, shows no indication of third overtone pulsation.

We also examine the possibility, suggested by Whitney (1978), that the mass of FG Sge is 0.4M _⊙.     

Graphite grain formation in the atmospheres of R coronae borealis stars

The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M _⊙,M _bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z _c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM _*≈10^?6 M _⊙yr^?1 forT _eff=5300 K toM _*≈10^?5 M _⊙ yr^?1 forT _eff=8300 K. As soon as the rate of mass loss exceedsM _* by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.     

A model of low-mass neutron stars with a quark core

We consider an equation of state that leads to a first-order phase transition from the nucleon state to the quark state with a transition parameter λ>3/2 (λ=ρ_Q/(ρ_N+P₀/c²)) in superdense nuclear matter. Our calculations of integrated parameters for superdense stars using this equation of state show that on the stable branch of the dependence of stellar mass on central pressure dM/dP_c>0) in the range of low masses, a new local maximum with M_max=0.082_⊙ and R=1251 km appears after the formation of a toothlike kink (M=0.08M_⊙, R=205 km) attributable to quark production. For such a star, the mass and radius of the quark core are M_core=0.005M_⊙ and R_core=1.73 km, respectively. In the model under consideration, mass accretion can result in two successive transitions to a quark-core neutron star with energy release similar to a supernova explosion: initially, a low-mass star with a quark core is formed; the subsequent accretion leads to configurations with a radius of ～1000 km; and, finally, the second catastrophic restructuring gives rise to a star with a radius of ～100 km.     

Theoretical rates of pulsation period change in the Galactic Cepheids

Theoretical estimates of the rates of radial pulsation period change in Galactic Cepheids with initial masses 5.5 M _⊙ ≤ M _ZAMS ≤ 13 M _⊙, chemical composition X = 0.7, Z = 0.02 and periods 1.5 day ≤ Π ≤ 100 day are obtained from consistent stellar evolution and nonlinear stellar pulsation computations. Pulsational instability was investigated for three crossings of the instability strip by the evolutionary track in the HR diagram. The first crossing occurs at the post-main sequence helium core gravitational contraction stage which proceeds in the Kelvin-Helmholtz timescale whereas the second and the third crossings take place at the evolutionary stage of thermonuclear core helium burning. During each crossing of the instability strip the period of radial pulsations is a quadratic function of the stellar evolution time. Theoretical rates of the pulsation period change agree with observations but the scatter of observational estimates of \(\dot \Pi\) noticeably exceeds the width of the band \(\left( {\delta \log \left| {\dot \Pi } \right| \leqslant 0.6} \right)\) confining evolutionary tracks in the period-period change rate diagram. One of the causes of the large scatter with very high values of \(\dot \Pi\) in Cepheids with increasing periods might be the stars that cross the instability strip for the first time. Their fraction ranges from 2% for M _ZAMS = 5.5 M _⊙ to 9% for M _ZAMS = 13 M _⊙ and variables α UMi and IX Cas seem to belong to such objects.     

A new well behaved class of charge analogue of Adler’s relativistic exact solution

The paper presents a new class of parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of electric field intensity. This solution gives us wide range of parameter, K (0.69≤K≤7.1), for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a superdense object is maximized with all degree of suitability by assuming the surface density of the star equal to the normal nuclear density ρ _nm=2.5×10¹⁷kg?m^?3. By this model we obtain the mass of the Crab pulsar M _Crab=1.401M _⊙ and the radius, R _Crab=12.98 km constraining the moment of inertia I _NS,38>1.61 for the conservative estimate of Crab nebula mass 2M _⊙ and M _Crab=2.0156M _⊙ with radius, R _Crab=14.07 km constraining the moment of inertia I _NS,38>3.04 for the newest estimate of Crab nebula mass 4.6M _⊙ which are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields the moments of inertia for PSR J0737-3039A and PSR J0737-3039B are I _A,38=1.4624 and I _B,38=1.2689 respectively. It has been observed that under well behaved conditions this class of parametric solution gives us the maximum gravitational mass of causal superdense object 2.8020M _⊙ with radius 14.49 km, surface redshift z _R =0.4319, charge Q=4.67×10²⁰ C, and central density ρ _c =2.68ρ _nm.     

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.     

Radial pulsations of helium stars with masses from 1 to 10 <Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We present the results of our hydrodynamic calculations of radial pulsations in helium stars with masses 1 M_⊙ ≤ M ≤ 10 M_⊙, luminosity-to-mass ratios 1 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for mass fractions of helium Y=0.98 and heavy elements Z=0.02. We show that the lower boundary of the pulsation-instability region corresponds to L/M ～ 10³L_⊙/M_⊙ and that the instability region for L/M ? 5 × 10³L_⊙/M_⊙ is bounded by effective temperatures T_eff ? 3 × 10⁴ K. As the luminosity rises, the instability boundary moves into the left part of the Hertzsprung-Russell diagram and radial pulsations can arise in stars with effective temperatures T_eff ? 10⁵ K at L/M ? 7 × 10³L_⊙/M_⊙. The velocity amplitude for the outer boundary of the hydrodynamic model increases with L/M and lies within the range 200 ? ΔU ? 700 km s^?1 for the models under consideration. The periodic shock waves that accompany radial pulsations cause a significant change of the gas-density distribution in the stellar atmosphere, which is described by a dynamic scale height comparable to the stellar radius. The dynamic instability boundary that corresponds to the separation of the outer stellar atmospheric layers at a superparabolic velocity is roughly determined by a luminosity-to-mass ratio L/M ～ 3 × 10⁴L_⊙/M_⊙.     

Supersonic steady accretion of a rotating cold “Iron Gas” onto a neutron star after gravitational collapse

We analytically generalize the well-known solution of steady supersonic spherically symmetric gas accretion onto a star (Bondi 1952) for an iron atmosphere with completely degenerate electrons with an arbitrary degree of relativity. This solution is used for typical physical conditions in the vicinity of protoneutron stars produced by gravitational collapse with masses M ₀=(1.4?1.8)M _⊙ and over a wide range of nonzero “iron gas” densities at infinity, ρ_∞=(10⁴?5×10⁶)g cm^?3. Under these conditions, we determine all accretion parameters, including the accretion rate, whose value is ～(10?50)M _⊙s^?1 at M ₀=1.8M _⊙ (it is a factor of 1.7 lower for M ₀=1.4M _⊙, because the accretion rate is exactly ∝M ₀ ² ). We take into account the effect of accreting-gas rotation in a quasi-one-dimensional approximation, which has generally proved to be marginal with respect to the accretion rate.     

Close binary system GO Cyg

In this study, we present long term photometric variations of the close binary system GO Cyg. Modelling of the system shows that the primary is filling Roche lobe and the secondary of the system is almost filling its Roche lobe. The physical parameters of the system are M₁ = 3.0 ± 0.2M_⊙, M₂ = 1.3 ± 0.1M_⊙, R₁ = 2.50 ± 0.12R_⊙, R₂ = 1.75 ± 0.09R_⊙, L₁ = 64 ± 9L_⊙, L₂ = 4.9 ± 0.7L_⊙, and a = 5.5 ± 0.3R_⊙. Our results show that GO Cyg is the most massive system near contact binary (NCB). Analysis of times of the minima shows a sinusoidal variation with a period of 92.3 ± 0.5 yr due to a third body whose mass is less than 2.3M_⊙. Finally a period variation rate of −1.4 × 10⁻⁹ d/yr has been determined using all available light curves.     

On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system

In this paper we explore the consequences of the recent determination of the mass m=(8.7±0.8)M _⊙ of Cygnus X-1, obtained from the Quasi-Periodic Oscillation (QPO)-photon index correlation scaling, on the orbital and physical properties of the binary system HDE 226868/Cygnus X-1. By using such a result and the latest spectroscopic optical data of the HDE 226868 supergiant star we get M=(24±5)M _⊙ for its mass. It turns out that deviations from the third Kepler law significant at more than 1-sigma level would occur if the inclination i of the system’s orbital plane to the plane of the sky falls outside the range ≈41–56 deg: such deviations cannot be due to the first post-Newtonian (1PN) correction to the orbital period because of its smallness; interpreted in the framework of the Newtonian theory of gravitation as due to the stellar quadrupole mass moment Q, they are unphysical because Q would take unreasonably large values. By conservatively assuming that the third Kepler law is an adequate model for the orbital period we obtain i=(48±7) deg which yields for the relative semimajor axis a=(42±9)R _⊙ (≈0.2 AU).     

On the interpretation of white dwarf spectra

Following the line of research outlined by Strittmatter and Wickramasinghe (1971) and recently by Shipman (1972), attention was drawn to the study of convective zones in white dwarfs for various masses and chemical compositions, in order to understand some observational features of their spectra. According to the results, convection strongly depends on the mass of the star, forM<0.5 M_⊙, and low hydrogen abundancesX?0.2) are sufficient to decrease the extension of the He-convection zones with respect to pure-He models. It is shown that the existence of DB white dwarfs seems not in agreement with the accretion rates predicted by Bondi (1952), and that DB's must evolve into H-lacking white dwarfs.