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.     

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.     

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.     

Positions of sunspot groups and solar rotation

The question is studied whether the one-year solar oscillation found by V. F. Chistyakov for the years 1965–1973 can be traced in the observations of sunspots of 1874–1971 published by Greenwich Observatory. The result is negative. But the study leads to the following two conclusions: (1) The average observable centres of gravity of spot groups are variably displaced towards the central meridian or towards the limb, the time scale of this variability being of the order of 70 years. Thus the angular velocity should be determined from recurrent groups in transit of the central meridian only. (2) The angular velocity will be smaller when determined from older spots.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

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.     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

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.     

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.     

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.     

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.     

Properties of New Coordinates for the General Three-Body Problem

This is an analysis of the features of the new coordinate system given by the principal axes of inertia, as determined by Euler angles, and twodistances related to the inertia principal moments and an auxiliar angleas coordinates, for studying the general three-body problem, interactingthrough gravitational forces.The reduction of order is performed in these new coordinates by using the angular velocity vector or the Euler angles.The Eulerian case of collinear motion is revisited from our own perspective.The value of the auxiliar angle is computed for the Sun–Earth–Moon system.     

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.     

Quasi-sinusoidal oscillations of the angular velocity of pulsars

We study the oscillations of the angular velocity of pulsars, obtaining an equation for the angular velocity and its derivative taking account of the curvature of vortices. We show that this equation has a quasisinusoidal solution and find the period of these oscillations. We show that the estimates for the value of the periods for various models of neutron stars give quantities of the order of tens of days, which is in agreement with the observations of the quasi-periodic oscillations and fluctuations of the angular velocity of pulsars.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

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.     

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.     

On the latitude drift of sunspot groups and solar rotation

The N-S drift of sunspot groups has been studied in a different way than previously, using positions of recurrent groups of the years 1874–1976. The existence of the meridional motions, the general shape of the drift curves, and the dissimilarity between these curves around sunspot maxima and minima, are all confirmed. In addition, also for the angular velocity of the Sun the same material gives differences around the times of sunspot maxima and minima.     

On changes of the rotation velocities of stable,recurrent sunspots and their interpretation with a flux tube model

The angular rotation velocities of stable, recurrent sunspots were investigated using data from the Greenwich Photoheliographic Results 1940 until 1968. We found constant rotation velocities during the passages on the solar disk with errors of about ±4 m s^–1. During their lifetime these spots show a decreasing braking of their rotation velocities from 0.8 to 0.3 m s^–1 per day. A plausible interpretation is found by assuming the spots to be coupled to a slowly rising subsurface flux tube and a rotation velocity which increases with depth.Mitteilungen aus dem Kiepenheuer-Institut Nr. 201.     

Rotating superdense configurations: pulsars and their astrophysical manifestations

This paper is a discussion of some results from papers by followers of V. A. Ambartsumyan, whose fundamental articles serve as the beginning of research on superdense stars: white dwarfs and neutron stars. Solutions of the Einstein equations are given for the case of axial symmetry and are used to determine the integral parameters of rotating neutron stars and white dwarfs. A theory of magnetic field generation in neutron stars has been developed and is consistent with the existence of high, nonuniform magnetic fields on the order of 10¹⁴ G in pulsars. A theory has been proposed for the dynamics of neutron vortices and used to explain the observed relaxation of the angular velocity of pulsars following glitches.     

Progressive dipole waves as the constituents of the 22-year magnetic cycle

A pair of dipole waves propagating with constant phase velocity forward and backward relative to the solar rotation is suggested to explain the characteristic features of the field variation of the 22-year cycles. The interference of these waves results in a single dipole moving with varying phase velocity over the photosphere. The heliographic coordinates of the dipole axis are derived from the harmonic coefficients published for the Mount Wilson observational period 1959–1973. It is found that the dipole axis moves very slowly near the equator at the time of sunspot maximum whereas during the minimum it changes by 180° along a great circle in the direction of the rotation. During minimum the angular velocity of the axis is about ten times larger than during maximum and the poleward elongation of the axis is about 50°.     

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).