Relaxation of the angular velocity of the vela pulsar within the framework of general relativity. Standard model of a neutron star

The dynamics of the rotation of a two-component system in the core of a neutron star is analyzed within the framework of the generai theory of relativity (GTR). A theory of the relaxation of the angular velocity of the Vela pulsar is developed with allowance for GTR corrections. From a comparison of the theory with observational data on the Vela pulsar, the relative moments and positions of the relaxation regions are found for one of the standard models of a neutron star. It is shown that the theory agrees with observations and supports this model neutron star as an acceptable pulsar model. Translated from Astrofizika, Vol. 43, No. 1, pp. 85-94, January–March, 2000.     

Relaxation of the Angular Velocity of the Vela Pulsar Following Its First Eight Glitches

The theory of the relaxation of pulsar angular velocity is compared with observational data for the first eight glitches of the Vela pulsar. Solutions of the inverse problem in relaxation theory are obtained in the regions of exponential and linear relaxation in the core of the neutron star. From these solutions, a distribution of vortices is found that results in the observed relaxation of the pulsar's angular velocity. It is shown that the pinning of neutron vortices plays the primary role in the region of exponential relaxation, while in the region of linear relaxation one must allow for the variation of the angular velocity of the superfluid component.     

Relaxation of the Vela pulsar’s angular velocity following its jumps

The dynamics of the vortex lattice in the inner crust of a neutron star is considered. A general equation of motion is obtained and solved under the assumption that there are regions of pinned and of free vortices. By comparing these solutions with observational data for the Vela pulsar, the relative moments of inertia of regions of relaxation with the corresponding characteristic times are calculated for two model stars with different equations of state. It is shown that the theory can be reconciled with observations of the relaxation of pulsar angular velocity only for model stars with extremely stiff equations of state. Translated from Astrofizika, Vol. 40, No. 1, pp. 67–76, January–March, 1997.     

Inverse Problem of the Theory of Relaxation of the Vela Pulsar's Angular Velocity after Glitches

A theory of the relaxation of pulsar angular velocity is compared with observational data for the first eight glitches of the Vela pulsar. The inverse problem of the theory of relaxation is considered and solutions of this problem in the regions of exponential and linear relaxation are found. General features in the distribution of neutron vortices in these regions immediately after a glitch are determined. It is shown that these properties may be related to the size of the glitch in pulsar angular velocity.     

Jumps in pulsar angular velocity and their relaxation with allowance for pinning and depinning of quantum vortex filaments

The dynamics of the rotating two-component system in the core of a neutron star is considered. Equations of motion are derived with allowance for the pinning and depinning of neutron vortices, and general solutions of these equations are found for relatively small changes in the star's angular velocity. It is shown that these solutions can describe both a jump in a pulsar's angular velocity and its subsequent relaxation. The characteristic pinning and depinning times are estimated qualitatively from observational data for jumps in the angular velocity of the Vela pulsar.Translated from Astrofizika, Vol. 39, No. 4, pp. 593–604, October–December, 1996.     

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.     

A model for the millisecond pulsar PSR 1937+214

We suggest a model for the millisecond pulsar 1937+214, according to which the immediate progenitor of the pulsar was a binary consisting of two neutron stars of unequal mass. The heavier neutron star was spun up by the transfer of angular momentum from the orbit, and the lighter neutron star was tidally disrupted, leaving behind a millisecond pulsar.     

Relaxation time of the superfluid core of a neutron star

The superconducting proton condensate in the “npe” phase of a neutron star is considered. It is shown to be a type II superconductor in the outer layer of the “npe” phase and a type I superconductor in the inner layer. Relaxation times are found for elastic scattering of normal relativistic electrons from the magnetic fields of proton vortex clusters in the case of a type II superconductor and elastic scattering from the magnetic field at the center of a neutron vortex in the case of a superconductor of the first kind. The dynamical relaxation times obtained for the angular velocity of the pulsar PSR 0833—45 vary, as a function of the density of the layers taking part in the relaxation process, within a fairly wide range: from several hours to l0⁹ years. This means that the characteristic times of variation of pulsar angular velocity may be observed to lie in the indicated time range. Translated from Astrofizika, Vol. 40, No. 4, op. 497–506, October–December, 1997.     

The formation of submillisecond pulsars and the possibility of detection

Pulsars have been recognized to be normal neutron stars, but sometimes have been argued to be quark stars. Submillisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars. We focus on the formation of such submillisecond pulsars in this paper. A new approach to the formation of a submillisecond pulsar (quark star) by means of the accretion-induced collapse (AIC) of a white dwarf is investigated. Under this AIC process, we found that: (i) almost all newborn quark stars could have an initial spin period of ∼0.1 ms; (ii) nascent quark stars (even with a low mass) have a sufficiently high spin-down luminosity and satisfy the conditions for pair production and sparking process and appear as submillisecond radio pulsars; (iii) in most cases, the times of newborn quark stars in the phase with spin period <1 (or <0.5) ms are long enough for the stars to be detected.
As a comparison, an accretion spin-up process (for both neutron and quark stars) is also investigated. It is found that quark stars formed through the AIC process can have shorter periods (≤0.5 ms), whereas the periods of neutron stars formed in accretion spin-up processes must be longer than 0.5 ms. Thus, if a pulsar with a period shorter than 0.5 ms is identified in the future, it could be a quark star.     

The structure of polar caps and the equatorial belt of pulsars

The self-consistent balanced pulsar magnetosphere of a magnetic neutron star with aligned magnetic and rotational axes is considered. It is shown that the magnetosphere consists of electron polar caps separated by empty space from a positron equatorial belt. The shape of the cold polar caps at a large distance from the star is calculated. It is shown that the cap shape at a large distance is independent of the magnetospheric structure near the neutron star. The shape of the equatorial belt is calculated. It is shown that a part of the equatorial belt rotates differentially, and its angular velocity is larger than that of the star (superrotation). It is shown that under certain conditions the space charge density of the belt can be very large. In principle, the formation of a surface charge placed in vacuum on a magnetic surface is possible. Magnetospheric vibrations are considered. A connection is established between drifting subpulses and the equatorial belt superrotation and also between drifting subpulses and cap vibrations. The characteristic frequency of vibrations and the angular velocity of superrotation are estimated.     

混杂星的r-模不稳定性窗口

考虑到混杂星既具有奇异夸克物质核,又具有中子星固体壳层的特殊结构,运用完全自洽的二级修正方法,研究了在低温极限下(T<109K)混杂星的体粘滞耗散时标,并利用该时标计算了混杂星的临界旋转频率,发现其最小值为704.42 Hz(对应1.42 ms脉冲周期).与中子星和奇异星比较,更好地解释了观测数据.     

Rotation of superfluid liquids in the framework of the general theory of relativity

Equations for the dynamics of a rotating two-component neutron star are derived in the framework of the general theory of relativity. The density of neutron vortex filaments is expressed in terms of the angular momentum density of the superfluid neutrons in the “npe” phase of the neutron star. It is shown that a theory of the relaxation of the angular velocity of pulsars must include corrections associated with the deviation of g₀₀ from unity, which is a consequence of the curvature of space.     

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).     

On the role of the current loss in radio pulsar evolution

The aim of this article is to draw attention to the importance of the electric current loss in the energy output of radio pulsars. We remind that even the losses attributed to the magneto-dipole radiation of a pulsar in vacuum can be written as a result of an Ampere force action of the electric currents flowing over the neutron star surface (see the books of Michel (Theory of Neutron Star Magnetosphere. University of Chicago Press (1991)) and of Beskin, Gurevich and Istomin (Physics of the Pulsar Magnetosphere. Cambridge Univ. Press (1993)). It is this force that is responsible for the transfer of angular momentum of a neutron star to an outgoing magneto-dipole wave. If a pulsar is surrounded by plasma, and there is no longitudinal current in its magnetosphere, there is no energy loss. It is the longitudinal current closing within the pulsar polar cap that exerts the retardation torque acting on the neutron star. This torque can be determined if the structure of longitudinal current is known. Here we remind of the solution by Beskin, Gurevich and Istomin (ed. cit.) and discuss the validity of such an assumption. The behavior of the recently observed “part-time job” pulsar B1931+24 can be naturally explained within the model of current loss while the magneto-dipole model faces difficulties. This work was partially supported by the Russian Foundation for Basic Research (Grant no. 05-02-17700) and Dynasty fund. Elena Nokhrina thanks the Conference Organizing Committee for the PPARC/Padova University Grant, and the RFFR for the travel grant (no. 06-02-26645).     

Hyperfast pulsars as the remnants of massive stars ejected from young star clusters

Recent proper motion and parallax measurements for the pulsar PSR B1508+55 indicate a transverse velocity of  ∼1100 km s⁻¹  , which exceeds earlier measurements for any neutron star. The spin-down characteristics of PSR B1508+55 are typical for a non-recycled pulsar, which implies that the velocity of the pulsar cannot have originated from the second supernova disruption of a massive binary system. The high velocity of PSR B1508+55 can be accounted for by assuming that it received a kick at birth or that the neutron star was accelerated after its formation in the supernova explosion. We propose an explanation for the origin of hyperfast neutron stars based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star which attained its peculiar velocity (similar to that of the pulsar) in the course of a strong dynamical three- or four-body encounter in the core of dense young star cluster. To check this hypothesis, we investigated three dynamical processes involving close encounters between: (i) two hard massive binaries, (ii) a hard binary and an intermediate-mass black hole (IMBH) and (iii) a single stars and a hard binary IMBH. We find that main-sequence O-type stars cannot be ejected from young massive star clusters with peculiar velocities high enough to explain the origin of hyperfast neutron stars, but lower mass main-sequence stars or the stripped helium cores of massive stars could be accelerated to hypervelocities. Our explanation for the origin of hyperfast pulsars requires a very dense stellar environment of the order of  10⁶– 10⁷ stars pc⁻³  . Although such high densities may exist during the core collapse of young massive star clusters, we caution that they have never been observed.     

脉冲星的非共转模型

本文讨论了脉冲星的磁层运动和能量状态。对于满足一定条件的脉冲星系统,证明了在极轴处的等离子体的角速度和电荷密度趋于零。提出了一个磁层与星体非共转的简单模型以及边界条件。利用变分原理,求得参数值,从而,得出了与参数相关的各个物理量,例如:等离子体的漂移速度v_D,等离子体与星体的相对滑动速度v_s,脉冲星的输出功率等。结果表明:功率值比较接近观测值,非共转的模型相对通常采用的共转模型而言是比较合理的。     

Influence of electron-positron pair production on a pulsar magnetospheric structure

A self-consistent pulsar magnetospheric model with electron-positron pair production is considered. Unlike conventional models, the primary particles (electrons) are accelerated towards the neutron star and their curvature radiation towards a star generates electron-positron plasma near the neutron star. Inside an outflow channel, the generated plasma flows away from the pulsar magnetosphere. A part of the plasma electrons returns and, being accelerated towards the star, regenerate the plasma by their curvature radiation. It is shown that plasma production near the star causes an appearance of positron and electron equatorial belts. The plasma concentration and the flux of the returning electrons are estimated. The portion of the energy entering into the pulsar magnetosphere and its dependence on pulsar parameters are estimated.     

Maximum mass of a hot neutron star with a quark core

We have considered a hot neutron star with a quark core,a mixed phase of quark-hadron matter,and a hadronic matter crust and have determined the equation of state of the hadronic phase and the quark phase.We have then found the equation of state of the mixed phase under the Gibbs conditions.Finally,we have computed the structure of a hot neutron star with a quark core and compared our results with those of the neutron star without a quark core.For the quark matter calculations,we have used the MIT bag model...     

On the formation of pulsar radiation diagrmas

A model of pulsars is discussed in which formation of a polar diagram of the radiation is influenced by the motion of the source around a neutron star with a velocity close to that of light. For a power-law frequency-spectrum of the radiation and isotropy of the diagram in a system of coordinates rotating with the source, the width of the observed pulse is shown to be independent of frequency.The proposed explanation of the second period characteristics of type CP 1919 pulsars is based on the effect of relativistic motion of the radiation source. The positions are established (relative to the axis of rotation of the star) of the local sources of radiation in the optical and in the radio ranges for the pulsar NP 0532. It is shown how the polarization characteristics of the optical radiation of this pulsar may be connected with the effects of relativistic orbiting of the source of radiation about the star.     

Open cluster ASCC21 as a probable birthplace of the neutron star Geminga

We analyze the encounters of the neutron star (pulsar) Geminga with open star clusters in the OB association Ori OB1a through the integration of epicyclic orbits into the past by taking into account the errors in the data. The open cluster ASCC21 is shown to be the most probable birthplace of either a single progenitor star for the Geminga pulsar or a binary progenitor system that subsequently broke up. Monte Carlo simulations of Geminga-ASCC21 encounters with the pulsar radial velocity V _r = ?100±50 km s^?1 have shown that close encounters could occur between them within ≤10 pc at about t = ?0.52 Myr. In addition, the trajectory of the neutron star Geminga passes at a distance of ≈25 pc from the center of the compact OB association λ Ori at about t = ?0.39 Myr, which is close to the age of the pulsar estimated from its timing.