Relaxation of the Angular Velocity of the Vela Pulsar within the Framework of General Relativity. Quark Model of a Neutron Star

A previously developed theory of the relaxation of a pulsar's angular velocity within the framework of general relativity is compared with observational data for the Vela pulsar on the basis of a quark model of a neutron star. The relative moments of inertia and the positions of relaxation regions are found. It is shown that the model of a neutron star containing normal quark matter is inconsistent with observations of the relaxation of pulsar angular velocity.     

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.     

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.     

Statistical studies of pulsar glitches

Shemar & Lyne have previously presented observations and an analysis of 32 glitches and their subsequent relaxations observed in a total of 15 pulsars. These data are brought together in this paper with those published by other authors. We show quantitatively how glitch activity decreases linearly with decreasing rate of slow-down. As indicated previously from studies of the Vela pulsar, the analysis suggests that 1.7 per cent of the moment of inertia of a typical neutron star is normally contained in pinned superfluid which releases its excess angular momentum at the time of a glitch. There is a broad range of glitch amplitude and there is a strong indication that pulsars with large magnetic fields suffer many small glitches while others show a smaller number of large glitches. Transient effects following glitches are very marked in young pulsars and decrease linearly with decreasing rate of slow-down, suggesting that the amount of loosely pinned superfluid decreases with age. We suggest that the low braking index of the Vela and Crab pulsars cannot be caused by a decreasing moment of inertia and should be attributed to step increases in the effective magnetic moment of the neutron star at the glitches.     

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.     

Inverse compton emission of gamma rays near the pulsar surface

The physical conditions near pulsar surface that might give rise to gamma ray emission from Crab and Vela pulsars are not yet well understood. Here I suggest that, in the context of the vacuum discharge mechanism proposed by Ruderman and Sutherland (1975), gamma rays are produced by inverse Compton scattering of secondary electrons with the thermal radiation of the star surface as well as for curvature and synchrotron radiation. It is found that inverse Compton scattering is relevant if the neutron star surface temperature is greater than 10⁶K or if the polar cap temperature is of the order of 5×10⁶K. Inverse Compton scattering in anisotropic photon fields and Klein-Nishina regime is here carefully considered.     

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.     

Angular velocity glitches of the Vela pulsar in a model with “centrifugal buoyancy” of vortices

The forces acting on the solid crust of a differentially rotating neutron star are examined when a nonuniform excess of chemical potential exists. The resultant of the external forces, a stress force, is expressed in terms of a centrifugal buoyancy force and the deformation of the star’s crust under the action of this force is calculated. It is shown that there is a region within the star where the resulting stresses lead to fracture of the crust when the difference in the angular velocities of the superfluid and normal components reaches a critical value. The “centrifugal buoyancy” mechanism for generating a glitch is used to estimate the parameters of glitches in the Vela pulsar. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 183–197 (May 2007).     

Radio-silent isolated neutron stars as a new astronomical reality

Summary. As of today, seven X-ray sources have been tentatively identified as radio-quiet, isolated neutron stars. The family appears to be a rapidly growing one, although not all the objects have been identified with the same degree of certainty. The most convincing example of radio quiet pulsar is certainly Geminga, the neutron star nature of which, proposed in 1983 on the basis of its similarity with the Vela pulsar, has been firmly established with the discovery of its X and pulsation. Four more neutron star candidates, originally found in the Einstein data, have been confirmed by ROSAT, which has added to the list two more entries. All this is not the result of an unbiased search. The seven sources were not selected at random: four are inside supernova remnants, an obvious place to search for isolated neutron stars, while the remaining three were singled out because of some peculiarity. Intense -ray emission in the case of Geminga, very high X-ray counting rate for RXJ185635-3754, or being the brightest unidentified source in the Einstein medium sensitivity survey, MS 0317-6647. In spite of the limited number of objects and of the observational biases, these seven radio quiet neutron star candidates add valuable pieces of information to the observational panorama of known pulsars. Their properties, inferred from the X-ray emission, offer a coherent picture, pointing towards thermally emitting, cooling neutron stars. Received: April 1, 1996     

Impact of neutron star oscillations on the accelerating electric field in the polar cap of pulsar

Pulsar “standard model”, that considers a pulsar as a rotating magnetized conducting sphere surrounded by plasma, is generalized to the case of oscillating star. We developed an algorithm for calculation of the Goldreich-Julian charge density for this case. We consider distortion of the accelerating zone in the polar cap of pulsar by neutron star oscillations. It is shown that for oscillation modes with high harmonic numbers (l,m) changes in the Goldreich-Julian charge density caused by pulsations of neutron star could lead to significant altering of an accelerating electric field in the polar cap of pulsar. In the moderately optimistic scenario, that assumes excitation of the neutron star oscillations by glitches, it could be possible to detect altering of the pulsar radioemission due to modulation of the accelerating field. This work was partially supported by RFBR grant 04-02-16720, and by the grants N.Sh.-5218.2006.2 and RNP-2.1.1.5940.     

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.     

Simulations of glitches in isolated pulsars

Many radio pulsars exhibit glitches wherein the star's spin rate increases fractionally by ∼10⁻¹⁰–10⁻⁶. Glitches are ascribed to variable coupling between the neutron star crust and its superfluid interior. With the aim of distinguishing among different theoretical explanations for the glitch phenomenon, we study the response of a neutron star to two types of perturbations to the vortex array that exists in the superfluid interior: (1) thermal motion of vortices pinned to inner crust nuclei, initiated by sudden heating of the crust, (e.g., a starquake), and (2) mechanical motion of vortices (e.g., from crust cracking by superfluid stresses). Both mechanisms produce acceptable fits to glitch observations in four pulsars, with the exception of the 1989 glitch in the Crab pulsar, which is best fitted by the thermal excitation model. The two models make different predictions for the generation of internal heat and subsequent enhancement of surface emission. The mechanical glitch model predicts a negligible temperature increase. For a pure and highly conductive crust, the thermal glitch model predicts a surface temperature increase of as much as ∼2 per cent, occurring several weeks after the glitch. If the thermal conductivity of the crust is lowered by a high concentration of impurities, however, the surface temperature increases by ∼10 per cent about a decade after a thermal glitch. A thermal glitch in an impure crust is consistent with the surface emission limits following the 2000 January glitch in the Vela pulsar. Future surface emission measurements coordinated with radio observations will constrain glitch mechanisms and the conductivity of the crust.     

Spin evolution of neutron stars in binary systems

I review our understanding of the evolution of the spin periods of neutron stars in binary stellar systems, from their birth as fast, spin-powered pulsars, through their middle life as accretion-powered pulsars, upto their recycling or “rebirth” as spin-powered pulsars with relatively low magnetic fields and fast rotation. I discuss how the new-born neutron star is spun down by electromagnetic and “propeller” torques, until accretion of matter from the companion star begins, and the neutron star becomes an accretion-powered X-ray pulsar. Detailed observations of massive radio pulsar binaries like PSR 1259-63 will yield valuable information about this phase of initial spindown. I indicate how the spin of the neutron star then evolves under accretion torques during the subsequent phase as an accretion-powered pulsar. Finally, I describe how the neutron star is spun up to short periods again during the subsequent phase of recycling, with the accompanying reduction in the stellar magnetic field, the origins of which are still not completely understood.     

On the creation of magnetic monopoles in pulsars

The production of pairs of magnetic monopoles-antimonopoles should be expected in the interactions of the high energy particles accelerated by pulsars. In the frame of the Sturrock model, the interactions of the very high energy protons emitted from the polar caps with the secondary electrons can be a source of magnetic monopoles. It may be the dominating process in very young pulsars such as the Crab pulsar. In the polar gap model of Ruderman and Sutherland, magnetic monopoles can be created by the electrons accelerated across the cap and interacting with the neutron star crust or by the negatons and positrons interacting head-on inside the sparks.Half of these monopoles are accelerated towards the interstellar medium by the pulsar magnetic field and the others are likely to be trapped inside the neutron star crust. This leads to a decrease in the pulsar magnetic field which would imply that the characteristic age may not give the true age of the pulsar This can be related to the discrepancy between and the real age of the Crab pulsar and the kinematical ages obtained from the measurement of the proper motion of some pulsars. Furthermore, the trapping of magnetic monopoles close under the surface of the neutron star perturbates the pulsar electrodynamics. To have such observable effects, it is shown that the cross-sections for the magnetic monopoles production can be several orders of magnitude smaller than the upper limits so far derived from cosmic rays or accelerator data.The possibility that the magnetic monopoles, accelerated outwards, are responsible for the highest energy extensive air showers, is considered.The production of an avalanche of secondary monopoles, due to acceleration by the magnetic field in the neutron star crust, is possible and the consequences of this process are considered.     

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).     

Evidence for the free precession of a neutron star

Although the free precession of a neutron star has been put forward as the cause of long-period variations in some X-ray pulsar emissions, no corroborating evidence has been found. The recent observation of a pulsar in Cygnus X-3, a system with a well measured long-period variation, provides an opportunity to examine the possibility of free precession. The properties of the pulsar which have been observed so far are consistent with the neutron star having a small free precession amplitude.     

Evolution of Pulsars with Energy Release in the Superfluid Core of a Neutron Star

The effect of a neutron-proton vortex system on the rotation dynamics of neutron stars is examined. The dynamics of the motion of a two component superfluid system in the core of a neutron star yields an equation for the evolution of the pulsar's rotation period. The spin down of the star owing to energy release at the core boundary, which is associated with a contraction of the length of the neutron vortex as it moves radially and magnetic energy of the vortical cluster is released, is taken into account. Evolutionary curves are constructed for pulsars with different magnetic fields and stellar radii. For certain values of the coefficient of friction between the superfluid and normal components in the core of the neutron star, at the end of its evolution a radio pulsar may become an anomalous x-ray pulsar or a source of soft gamma radiation with a period on the order of 10 seconds.