Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

Gravitational radiation of slowly rotating neutron stars

The gravitational rotation of slowly rotating neutron stars with rough surfaces is examined. The source of the gravitational waves is assumed to be the energy transferred to the crust of the star during irregular changes in its angular rotation velocity. It is shown that individual pulsars whose angular velocity regularly undergoes glitches will radiate a periodic gravitational signal that can be distinguished from noise by the latest generation of detectors. Simultaneous recording of a gravitational signal and of a glitch in the angular velocity of a pulsar will ensure reliable detection of gravitational radiation. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 221–229 (May 2006).     

A General Relativistic Calculation of Boundary Layer and Disc Luminosity for Accreting Non-magnetic Neutron Stars in Rapid Rotation

We calculate the disc and boundary layer luminosities for accreting rapidly rotating neutron stars with low magnetic fields in a fully general relativistic manner. Rotation increases the disc luminosity and decreases the boundary layer luminosity. A rapid rotation of the neutron star substantially modifies these quantities as compared with the static limit. For a neutron star rotating close to the centrifugal mass shed limit, the total luminosity has contribution only from the extended disc. For such maximal rotation rates, we find that well before the maximum stable gravitational mass configuration is reached, there exists a limiting central density, for which particles in the innermost stable orbit will be more tightly bound than those at the surface of the neutron star. We also calculate the angular velocity profiles of particles in Keplerian orbits around the rapidly rotating neutron star. The results are illustrated for a representative set of equation of state models of neutron star matter.     

Dynamical behaviour of the primitive asteroid belt

In this paper we consider the dynamical evolution and orbital stability of objects in the asteroid belt. A simple physical model, including full gravitational perturbations from both giant planets, is used to compute the dynamical evolution of 1000 test particles simulating the primitive asteroids. The criterion of planet crossing (or close approach in the case of resonant objects) is used to reject particles from the simulation. 44 per cent of the particles survived for the whole time-span covered by the numerical integration (∼10⁹ yr).
The 4:1, 3:1 and to a lesser extent the 2:1 Kirkwood gaps are formed in ∼10⁷ yr of evolution, representing direct numerical evidence about their gravitational origin.
We found that the rms eccentricity and inclination of the sample experience a fast increase during the first 10⁶ yr. The final rms eccentricity is 0.11, ∼60 per cent smaller than the present rms eccentricity (0.17). Nevertheless, the gravitational action of the giant planets suffices to prevent the formation of large objects, allowing catastrophic collisions and the subsequent depletion of material from this zone of the Solar system. The excited eccentricity by Jupiter and Saturn may favour mutual encounters and the further increase of the relative velocities up to their present values.     

General relativistic rotational properties of stellar models

In this paper we give general relativistic expressions for the angular momentum and rotational kinetic energy of slowly rotating stars. These expressions contain contributions from the presure, gravitational red shift, and Doppler shift, and the motion of inertial frames. These contributions are not negligible, e.g., there are stable neutron star models for which the angular velocity of inertial frames at the center is about 70% the angular velocity of the star. These expressions are useful in the study of pulsars if pulsars are rotating neutron stars.     

WASP-14b: 7.3 MJ transiting planet in an eccentric orbit

We report the discovery of a 7.3 M _J exoplanet WASP-14b, one of the most massive transiting exoplanets observed to date. The planet orbits the 10th-magnitude F5V star USNO-B1 11118−0262485 with a period of 2.243 752 d and orbital eccentricity   e = 0.09  . A simultaneous fit of the transit light curve and radial velocity measurements yields a planetary mass of 7.3 ± 0.5 M _J and a radius of 1.28 ± 0.08 R _J. This leads to a mean density of about 4.6 g cm⁻³ making it the densest transiting exoplanets yet found at an orbital period less than 3 d. We estimate this system to be at a distance of  160 ± 20  pc. Spectral analysis of the host star reveals a temperature of  6475 ± 100 K, log  g = 4.07  cm s⁻² and   v sin  i = 4.9 ± 1.0  km s⁻¹, and also a high lithium abundance,  log  N (Li) = 2.84 ± 0.05  . The stellar density, effective temperature and rotation rate suggest an age for the system of about 0.5–1.0 Gyr.     

Circinus X-1: survivor of a highly asymmetric supernova

We have analysed the kinematical parameters of Cir X-1 to constrain the nature of its companion star, the eccentricity of the binary and the pre-supernova parameter space. We argue that the companion is most likely to be a low-mass (≲2.0 M_⊙) unevolved star and that the eccentricity of the orbit is 0.94±0.04. We have evaluated the dynamical effects of the supernova explosion and we find it must have been asymmetric. On average , we find that a kick of ∼740 km s⁻¹ is needed to account for the recently measured radial velocity of +430 km s⁻¹ (Johnston, Fender & Wu) for this extreme system. The corresponding minimum kick velocity is ∼500 km s⁻¹. This is the largest kick needed to explain the motion of any observed binary system. If Cir X-1 is associated with the supernova remnant G321.9-0.3 then we find a limiting minimum age of this remnant of ∼60 000 yr. Furthermore, we predict that the companion star has lost ∼10 per cent of its mass as a result of stripping and ablation from the impact of the supernova shell shortly after the explosion.     

Radiative transfer effects in rotationally distorted stars

A general expression for the gravity darkening of the tidally and non-uniformly rotating Roche components of close binary systems is used to calculate the uniform rotational effects on line profiles in an expanding atmosphere. We consider a non-local thermodynamic equilibrium (non-LTE) two-level atom approximation in an extended atmosphere, and use Von Zeipel's theorem for the incident radiation at the maximum optical depth  (τ=τ_max)  in the atmosphere. These calculations are performed with uniform rotational velocities of 1, 4 and 8 mtu (mean thermal units). It is found that rotation dilutes the radiation field which is similar to the expansion velocity.
We also study rotational aspects, which make the outer layers of the star distorted. The equation of line transfer is solved in the comoving frame of the expanding atmosphere of the primary using complete redistribution in the line. We use a linear law for the velocity of expansion such that the density varies as r ⁻³, where r is the radius of the star, satisfying the law of conservation of mass. It is found that rotation broadens the line profile, and P-Cygni-type line profiles are obtained.     

Dynamical evolution of two associated galactic bars

We study the dynamical interactions of mass systems in equilibrium under their own gravity that mutually exert and ex‐perience gravitational forces. The method we employ is to model the dynamical evolution of two isolated bars, hosted within the same galactic system, under their mutual gravitational interaction. In this study, we present an analytical treatment of the secular evolution of two bars that oscillate with respect to one another. Two cases of interaction, with and without geometrical deformation, are discussed. In the latter case, the bars are described as modified Jacobi ellipsoids. These triaxial systems are formed by a rotating fluid mass in gravitational equilibrium with its own rotational velocity and the gravitational field of the other bar. The governing equation for the variation of their relative angular separation is then numerically integrated, which also provides the time evolution of the geometrical parameters of the bodies. The case of rigid, non‐deformable, bars produces in some cases an oscillatory motion in the bodies similar to that of a harmonic oscillator. For the other case, a deformable rotating body that can be represented by a modified Jacobi ellipsoid under the influence of an exterior massive body will change its rotational velocity to escape from the attracting body, just as if the gravitational torque exerted by the exterior body were of opposite sign. Instead, the exchange of angular momentum will cause the Jacobian body to modify its geometry by enlarging its long axis, located in the plane of rotation, thus decreasing its axial ratios. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or the hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error ≲0.3 per cent, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses  ∼10¹⁵ M_⊙  , the effect of the gravitomagnetic term is ≲0.04 per cent on strong lensing estimates and ≲0.5 per cent in the weak-lensing analyses. The total kinematic effect on the mass estimate is then ≲1 per cent, which is negligible in current statistical studies. In the weak-lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow, in principle, a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current technological capabilities.     

Magnetized relativistic jets and long-duration GRBs from magnetar spin-down during core-collapse supernovae

We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spin-down of a newly formed millisecond,   B ∼ 10¹⁵ G  , magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) explosion. The mass, angular momentum and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron star's atmosphere and the wind's interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high spin-down powers  (∼10⁵¹–10⁵² erg s⁻¹)  , the magnetar wind is superfast at almost all latitudes, while for lower spin-down powers  (∼10⁵⁰ erg s⁻¹)  , the wind is subfast but still super-Alfvénic. In all cases, the rates at which the neutron star loses mass, angular momentum and energy are very similar to the corresponding free wind values (≲30 per cent differences), in spite of the causal contact between the neutron star and the stellar envelope. In addition, in all cases that we consider, the magnetar drives a collimated  (∼5–10°)  relativistic jet out along the rotation axis of the star. Nearly all of the spin-down power of the neutron star escapes via this polar jet, rather than being transferred to the more spherical SN explosion. The properties of this relativistic jet and its expected late-time evolution in the magnetar model are broadly consistent with observations of long duration gamma-ray bursts (GRBs) and their associated broad-lined Type Ic SN.     

Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

Global velocity field and bubbles in the blue compact dwarf galaxy Mrk 86

We have studied the velocity field of the blue compact dwarf galaxy Mrk 86 (NGC 2537) using data provided by 14 long-slit optical spectra obtained in 10 different orientations and positions. This kinematical information is complemented with narrow-band ([O  iii ]5007 Å and H α ) and broad-band ( B , V , Gunn r and K ) imaging. The analysis of the galaxy global velocity field suggests that the ionized gas could be distributed in a rotating inclined disc, with projected central angular velocity of Ω=34 km s⁻¹ kpc⁻¹. The comparison between the stellar, H  i and modelled dark matter density profile indicates that the total mass within its optical radius is dominated by the stellar component. Peculiarities observed in its velocity field can be explained by irregularities in the ionized gas distribution or local motions induced by star formation.
Kinematical evidences for two expanding bubbles, Mrk 86–B and Mrk 86–C, are given. They show expanding velocities of 34 and 17 km s⁻¹, H α luminosities of 3×10³⁸ and 1.7×10³⁹ erg s⁻¹, and physical radii of 374 and 120 pc, respectively. The change in the [S  ii ]/H α , [N  ii ]/H α , [O  ii ]/[O  iii ] and [O  iii ]/H β line ratios with the distance to the bubble precursor suggests a diminution in the ionization parameter and, in the case of Mrk 86–B, an enhancement of the shock-excited gas emission. The optical–near-infrared colours of the bubble precursors are characteristic of low‐metallicity star‐forming regions (∼0.2 Z_⊙) with burst strengths of about 1 per cent in mass.     

Models of rapidly rotating neutron stars: remnants of accretion-induced collapse

Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion-induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high-density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.     

The equilibrium structure of loaded rotating polytropes

The equilibrium structure of rotating polytropes with a compact core has been studied by means of Chandrasekhar's first-order perturbation theory. Several numerical solutions are given. The results show that the larger the core mass, the smaller the critical central angular velocity will be, and for the same angular velocity, the larger the core mass, the more oblate the rotation ellipsoid will be.     

Evolutionary status of the primary component of YZ Cassiopeiae

The models of non-rotating and rotating 2.31M _\ stars of Population I composition have been calculated, starting at the threshold of stability. A 2.31M _\ star was chosen to compare the results with the observational parameters of the primary component of the well-known detached binary YZ Cassiopeiae. The effects of rotation on the internal structure during the evolution of the star were studied by constructing sequences of axisymmetric rotating models under the assumption that angular momentum was conserved according to a predetermined angular velocity distribution depending on the structure of the star.The first section of this paper deals with effects of rotation on the evolutionary behaviours of the 2.31M _\ star through the pre-Main-Sequence evolution as well as the zero-age Main Sequence.In the second section of this paper, the evolutionary studies have been extended up to near-hydrogen exhaustion phase in order to obtain a theoretical model corresponding to the given mass and radius of the primary component of YZ Cassiopeiae. The theoretical models were found to be in a good agreement with observational parameters. The computed rotating models of the primary of YZ Cassiopeiae indicates that its evolutionary age is 6.01×10⁸ years; and the central hydrogen content 0.183 — which means that about 75% of its original value was depleted.     

Upper limit for the mass loss rate of rapidly rotating single main-sequence O9-B4 stars

An upper limit for the mass loss rate of rapidly rotating main-sequence O9-B4 stars has been determined. Themaximum mass loss rate of a rotating star is determined by the ability of radiation pressure in lines to remove matter from the gravitational potential well of the star. The maximum mass loss rate in the case of extremely rapid stellar rotation is a factor of 3–7 higher than that in the case of a nonrotating star. A simple formula for determining the ratio of the maximum mass loss rate of a rotating star to the maximum mass loss rate of a nonrotating star with the same mass, luminosity, and volume is suggested.     

Energy release on the surface of a rapidly rotating neutron star during disk accretion: A thermodynamic approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory, E=E(J, M) [in general relativity, the gravitational mass of a star as a function of its angular momentum J and rest mass m, M=M(J, m)], is used to determine the remaining parameters (angular velocity, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact equation of state at J=0.     

Magnetic field, dust and axisymmetrical mass loss on the asymptotic giant branch

I propose a mechanism for axisymmetrical mass loss on the asymptotic giant branch (AGB) that may account for the axially symmetric structure of elliptical planetary nebulae. The proposed model operates for slowly rotating AGB stars, having angular velocities in the range of 10⁻⁴ω _Kep  ω  10⁻² ω_Kep, where ω_Kep is the equatorial Keplerian angular velocity. Such angular velocities could be gained from a planet companion of mass  0.1  M _Jupiter, which deposits its orbital angular momentum to the envelope at late stages, or even from single stars that are fast rotators on the main sequence. The model assumes that dynamo magnetic activity results in the formation of cool spots, above which dust forms much more easily. The enhanced magnetic activity towards the equator results in a higher dust formation rate there, and hence higher mass-loss rate. As the star ascends the AGB, both the mass-loss rate and magnetic activity increase rapidly, and hence the mass loss becomes more asymmetrical, with higher mass-loss rate closer to the equatorial plane.     

On the determination of the earth''s rotation using the McDonald lunar laser ranging data of 1971.6 – 1979.0

Using 1658 normal points of the McDonald lunar ranging data in the period 1971.6–1979.0, I calculated the Earth's rotation curve, and found an offset of −330 × 10⁻¹⁰ for UT₁ – UTC. The difference between the UT₁ values given by the lunar data and BIH is 3.6 ms. This difference and the standard error of single determinations increase with increasing interval length used in the data reduction. This is shown to be due to the neglect of the secular term in UT₁-UTC. It appears that an interval length of 2 days is suitable when calculating the Earth's rotation.