Spin-down of millisecond pulsars owing to gravitational wave emission

The gravitational radiation from millisecond pulsars owing to glitches in their angular velocity is examined. It is assumed that the energy transferred from interior superfluid regions to the crust of a neutron star is converted into gravitational wave energy by damping oscillations of the matter in the star. The gravitational wave intensity and amplitude are calculated for fourteen millisecond pulsars. Gravitational radiation can explain the observed spin-down of millisecond pulsars and an estimate is given for the magnetic field at which the proposed mechanism predominates in the spin-down of these pulsars. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 479–486 (August 2008).     

Gravitational Radiation from Fluctuations in Rotating Neutron Stars

Undamped quasiradial fluctuations of rotating neutron stars and the gravitation radiation generated by them are discussed. Two possible sources of energy for maintaining these fluctuations are mentioned: the energy of deformation of the decelerating neutron star (spin down) and the energy released during a jump in the star's angular velocity (glitch). Expressions are derived for the intensity of the gravitational radiation and the amplitude of a plane gravitational wave for an earthbound observer. Estimates of these quantities are obtained for the Vela and Crab pulsars, for which the secular variation in the angular velocity is most often accompanied by irregular variations. It is shown that gravitational waves from these pulsars could be detected by the new generation of detectors.     

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).     

Influence of the r-mode instability on hypercritically accreting neutron stars

We have investigated the influence of the r-mode instability on hypercritically accreting neutron stars in close binary systems during their common envelope phases, based on the scenario proposed by Brown et al. On the one hand, neutron stars are heated by the accreted matter at the stellar surface, but on the other hand they are also cooled down by the neutrino radiation. At the same time, the accreted matter transports its angular momentum and mass to the star. We have studied the evolution of the stellar mass, temperature and rotational frequency.
The gravitational-wave-driven instability of the r-mode oscillation strongly suppresses spinning up of the star, the final rotational frequency of which is well below the mass-shedding limit, in fact typically as low as 10 per cent of that of the mass-shedding state. On a very short time-scale the rotational frequency tends to approach a certain constant value and saturates there, as long as the amount of accreted mass does not exceed a certain limit to collapse to a black hole. This implies that a similar mechanism of gravitational radiation to that in the so-called 'Wagoner star' may work in this process. The star is spun up by accretion until the angular momentum loss by gravitational radiation balances the accretion torque. The time-integrated dimensionless strain of the radiated gravitational wave may be large enough to be detectable by gravitational wave detectors such as LIGO II.     

Gravitational radiation from approaching neutron stars and the rotational explosion mechanism for collapsing supernovae

We consider the evolution of a neutron star binary system under the effect of two factors: gravitational radiation and mass transfer between the components. Gravitational radiation is specified under the justified assumption of a circular orbit and point masses and in the approximation of a weak gravitational field at nonrelativistic velocities of the binary components. During the first evolutionary phase determined only by gravitational radiation, the neutron stars approach each other according to a simple analytical solution. The second evolutionary phase begins at the time of Roche-lobe filling by the low-mass component, when the second factor, mass transfer as a result of mass loss by the latter, also begins to affect the evolution. Under the simplest assumptions of conservative mass transfer and exact equality between the Roche-lobe radius and the radius of the low-mass neutron star, it is still possible to extend the analytical solution of the problem of evolution to its second phase. We present this complete solution at both phases and, in particular, give theoretical light curves of gravitational radiation that depend only on two dimensionless parameters (m _t and δ ₀). Based on the solution found, we analyze the theoretical gravitational signals from SN 1987A; this analysis includes the hypothesis about the rotational explosion mechanism for collapsing supernovae.     

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.     

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.     

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.     

The effects of mass on the radiation of a relativistically rotating neutron star

We investigate the effect of mass on the radiation of a relativistically rotating neutron star. The method of Haxton and Ruffini is used to find the radiation flux from a relativistically rotating neutron star. By extending the idea of a point charge orbiting a black hole, a pulsar is modeled by simulating a relativistically rotating magnetic dipole embedded within a neutron star. The resulting equations retain the mass of the neutron star, thereby introducing effects of general relativity on the radiation from the dipole. We present exact solutions to the modeling equation as well as plots of energy spectra at different rotational velocities and inclination angles. We also present plots of total energy versus mass and two tables containing a comparison of energy ratios. These demonstrate that, for realistic neutron star masses, the high speed enhancement of the radiation is always more than compensated by the frame dragging effect, leading to a net reduction of radiation from the star. It is found that the inclusion of mass not only reduced the special relativistic enhancement, but negates it entirely as the mass of the neutron star approaches the mass limit.     

The equilibrium configuration of rapid rotating compact stars and some gravitational effects

In this paper, the equilibrium configurations of rapid rotating compact stars and some gravitational effects are studied within the general relativity by use of the Harrison-Wheeler equation of state and by the self-consistent field method. Numerical calculations show that the equilibrium configuration of a rotating star is a spheroid. For large spin velocities, say, ω > 3.0 × 10² sec⁻¹ the eccentricity and mass increase very rapidly as the angular velocity increases, for the critical angular velocity of the rotating star, the eccentricity is about 0.7, the increase in mass is about 10–35%. The difference of the gravitational redshifts at the surface of the star caused by rotation, and the difference of the light bending when the beam moves in the direction of rotation or in the opposite direction are obvious.     

Modeling the luminosity function of galactic low-mass X-ray binaries

The evolution of the family of binaries with a low-mass star and a compact neutron star companion (low-mass X-ray binaries (LMXBs) with neutron stars) ismodeled by the method of population synthesis. Continuous Roche-lobe filling by the optical star in LMXBs is assumed to be maintained by the removal of orbital angular momentum from the binary by a magnetic stellar wind from the optical star and the radiation of gravitational waves by the binary. The developed model of LMXB evolution has the following significant distinctions: (1) allowance for the effect of the rotational evolution of a magnetized compact remnant on themass transfer scenario in the binary, (2) amore accurate allowance for the response of the donor star to mass loss at the Roche-lobe filling stage. The results of theoretical calculations are shown to be in good agreement with the observed orbital period-X-ray luminosity diagrams for persistent Galactic LMXBs and their X-ray luminosity function. This suggests that the main elements of binary evolution, on the whole, are correctly reflected in the developed code. It is shown that most of the Galactic bulge LMXBs at luminosities L _x > 10³⁷ erg s^?1 should have a post-main-sequence Roche-lobe-filling secondary component (low-mass giants). Almost all of the models considered predict a deficit of LMXBs at X-ray luminosities near ～10^36.5 erg s^?1 due to the transition of the binary from the regime of angular momentum removal by a magnetic stellar wind to the regime of gravitational waves (analogous to the widely known period gap in cataclysmic variables, accreting white dwarfs). At low luminosities, the shape of the model luminosity function for LMXBs is affected significantly by their transient behavior-the accretion rate onto the compact companion is not always equal to the mass transfer rate due to instabilities in the accretion disk around the compact object. The best agreement with observed binaries is achieved in the models suggesting that heavy neutron stars with masses 1.4–1.9M _⊙ can be born.     

Dark Matter Objects: Possible New Source of Gravitational Waves

Gravitational waves from mergers of black holes and neutron stars are now being detected by LIGO. Here we look at a new source of gravitational waves, i.e., a class of dark matter objects whose properties were earlier elaborated. We show that the frequency of gravitational waves and strains on the detectors from such objects (including their mergers) could be within the sensitivity range of LIGO. The gravitational waves from the possible mergers of these dark matter objects will be different from those produced by neutron star mergers in the sense that they will not be accompanied by electromagnetic radiation since dark matter does not couple with radiation.

     

Radial diffusion rate of planetesimals due to gravitational encounters

We study the rate of radial diffusion of planetesimals due to mutual gravitational encounters under Hill’s approximations in the three-body problem. Planetesimals orbiting a central star radially migrate inward and outward as a result of mutual gravitational encounters and transfer angular momentum. We calculate the viscosity in a disk of equal-sized planetesimals due to their mutual gravitational encounters using three-body orbital integrations, and obtain a semianalytic expression that reproduces the numerical results. We find that the viscosity is independent of the velocity dispersion of planetesimals when the velocity dispersion is so small that Kepler shear dominates planetesimals’ relative velocities. On the other hand, in high-velocity cases where random velocities dominate the relative velocities, the viscosity is a decreasing function of the velocity dispersion, and is found to agree with previous estimates under the two-body approximation neglecting the solar gravity. We also calculate the rate of radial diffusion of planetesimals due to gravitational scattering by a massive protoplanet. Using these results, we discuss a condition for formation of nonuniform radial surface density distribution of planetesimals by gravitational perturbation of an embedded protoplanet.     

Generation of a toroidal magnetic field in rotating neutron stars

The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).     

The stochastic background of gravitational waves from neutron star formation at cosmological distances

We investigate the stochastic gravitational wave background that results from neutron star birth throughout the Universe. The neutron star birth rate, as a function of redshift, is calculated using an observation-based model for the evolving star formation rate, together with an estimate of the rate of core-collapse supernovae in the nearby Universe and an estimate of the neutron star/black hole branching ratio. Using three sample waveforms, based on numerical models of stellar core collapse by Zwerger & Müller, the spectral flux density, spectral strain, spectral energy density and duty cycle of the background have been computed. Our results show, contrary to recent claims, that the spectrum of the stochastic background clearly reflects the different physics in the core-collapse models. For a star formation model that is corrected for dust extinction, the neutron star formation rate throughout the Universe is high enough to result in a nearly continuous background of gravitational waves, with spectral features that can be related to emission mechanisms.     

A new representation of theH-functions of radiative transfer

The energetics involved in the formation of neutron stars in close binaries as a result of supernova explosions are considered. The gravitational binding energy of the neutron star must find proper outlets. The mass ejection and cosmic ray particles can carry away only a small fraction (up to a few per cent) of this energy. Most of the binding energy goes into rotational kinetic energy, gravitational radiation and neutrino emissions. A scenario is considered in which most of the gravitational binding energy goes into rotational kinetic energy and is, ultimately, radiated away as gravitational waves.     

Theory of relaxation of pulsar angular velocity within the framework of the general theory of relativity

The dynamics of the rotation of a two-component system in a neutron star is considered within the framework of the general theory of relativity. Equations for the angular velocities of the normal and superfluid components are obtained in the W approximation. It is shown that the solutions of these equations can describe the relaxation of pulsar angular velocity after a glitch. Translated from Astrofizika, Vol. 42, No. 1, pp. 89–100, January–March, 1999.     

Exotic bulk viscosity and its influence on neutron star r-modes

We investigate the effect of exotic matter in particular, hyperon matter on neutron star properties such as equation of state (EoS), mass-radius relationship and bulk viscosity. Here we construct equations of state within the framework of a relativistic field theoretical model. As hyperons are produced abundantly in dense matter, hyperon–hyperon interaction becomes important and is included in this model. Hyperon–hyperon interaction gives rise to a softer EoS which results in a smaller maximum mass neutron star compared with the case without the interaction. Next we compute the coefficient of bulk viscosity and the corresponding damping time scale due to the non-leptonic weak process including Λ hyperons. Further, we investigate the role of the bulk viscosity on gravitational radiation driven r-mode instability in a neutron star of given mass and temperature and find that the instability is effectively suppressed.      

The possible role of r-modes in post-glitch relaxation of the Crab pulsar

The loss of angular momentum through gravitational radiation, driven by the excitation of r-modes, is considered for neutron stars that have rotation frequencies lower than the associated critical frequency. We find that for reasonable values of the initial amplitudes of such pulsation modes of the star, being excited at the event of a glitch in a pulsar, the total post-glitch losses correspond to a negligible fraction of the initial rise of the spin frequency in the case of Vela and older pulsars. However, for the Crab pulsar the same effect would result, within a few months, in a decrease in its spin frequency by an amount larger than its glitch-induced frequency increase. This could provide an explanation for the peculiar behaviour observed in the post-glitch relaxations of the Crab pulsar.     

The spin evolution of nascent neutron stars

The loss of angular momentum owing to unstable r-modes in hot young neutron stars has been proposed as a mechanism for achieving the spin rates inferred for young pulsars. One factor that could have a significant effect on the action of the r-mode instability is fallback of supernova remnant material. The associated accretion torque could potentially counteract any gravitational-wave-induced spin-down, and accretion heating could affect the viscous damping rates and hence the instability. We discuss the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star. We find that the outcome depends strongly on the strength of the magnetic field of the star. Our model is capable of generating spin rates for young neutron stars that accord well with initial spin rates inferred from pulsar observations. The combined action of r-mode instability and fallback appears to cause the spin rates of neutron stars born with very different spin rates to converge, on a time-scale of approximately 1 year. The results suggest that stars with magnetic fields ≤10¹³ G could emit a detectable gravitational wave signal for perhaps several years after the supernova event. Stars with higher fields (magnetars) are unlikely to emit a detectable gravitational wave signal via the r-mode instability. The model also suggests that the r-mode instability could be extremely effective in preventing young neutron stars from going dynamically unstable to the bar-mode.