Superconductivity and Magnetism at Nuclear-matter Densities: An Astronomical Challenge

We report on a study of the evolution of magnetic fields of neutron stars, driven by the expulsion of magnetic flux out of the proton superconducting core of the star. The rate of expulsion, or equivalently the velocity of outward motion of flux-carrying proton-vortices is determined from a solution of their equation of motion. A determination of the effective forces on the fluxoids moving through the quantum liquid interior of neutron stars is however confronted with many ambiguities about the properties of this special case of superconductivity in the nature. Also, the behaviour of the fluxoids at the core boundary, and the subsequent evolution of the expelled flux within the highly conductive surrounding crust, are other related issues that have not been so far explored in any great details.Comment: 8 papegs, 2 figures, accepted at the 1st Regional Conference on Magnetic and Superconducting Materials (MSM-99), Tehran, Sept. 199

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

The loss of angular momentum through gravitational radiation, driven by the excitation of r-modes, is considered in neutron stars having rotation frequencies smaller 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 the 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 behavior observed in the post-glitch relaxations of the Crab.Comment: 9 pages, 4 figures, RevTe

Flux Expulsion - Field Evolution in Neutron Stars

Models for the evolution of magnetic fields of neutron stars are constructed, assuming the field is embedded in the proton superconducting core of the star. The rate of expulsion of the magnetic flux out of the core, or equivalently the velocity of outward motion of flux-carrying proton-vortices is determined from a solution of the Magnus equation of motion for these vortices. A force due to the pinning interaction between the proton-vortices and the neutron-superfluid vortices is also taken into account in addition to the other more conventional forces acting on the proton-vortices. Alternative models for the field evolution are considered based on the different possibilities discussed for the effective values of the various forces. The coupled spin and magnetic evolution of single pulsars as well as those processed in low-mass binary systems are computed, for each of the models. The predicted lifetimes of active pulsars, field strengths of the very old neutron stars, and distribution of the magnetic fields versus orbital periods in low-mass binary pulsars are used to test the adopted field decay models. Contrary to the earlier claims, the buoyancy is argued to be the dominant driving cause of the flux expulsion, for the single as well as the binary neutron stars. However, the pinning is also found to play a crucial role which is necessary to account for the observed low field binary and millisecond pulsars.Comment: 23 pages, + 7 figures, accepted for publication in Ap

Spin-down Rate of Pinned Superfluid

The spinning down (up) of a superfluid is associated with a radial motion of its quantized vortices. In the presence of pinning barriers against the motion of the vortices, a spin-down may be still realized through ``random unpinning'' and ``vortex motion,'' as two physically separate processes, as suggested recently. The spin-down rate of a pinned superfluid is calculated, in this framework, by directly solving the equation of motion applicable to only the unpinned moving vortices, at any given time. The results indicate that the pinned superfluid in the crust of a neutron star may as well spin down at the same steady-state rate as the rest of the star, through random unpinning events, while pinning conditions prevail and the superfluid rotational lag is smaller than the critical lag value.Comment: to appear in ApJ (vol. 649 ?

Magneto-rotational neutron star evolution: the role of core vortex pinning

We consider the pinning of superfluid (neutron) vortices to magnetic fluxtubes associated with a type II (proton) superconductor in neutron star cores. We demonstrate that core pinning affects the spin-down of the system significantly, and discuss implications for regular radio pulsars and magnetars. We find that magnetars are likely to be in the pinning regime, while most radio pulsars are not. This suggests that the currently inferred magnetic field for magnetars may be overestimated. We also obtain a new timescale for the magnetic field evolution which could be associated with the observed activity in magnetars, provided that the field has a strong toroidal component.Comment: 5 pages, no figures, published in ApJ

Superfluid Spin-down, with Random Unpinning of the Vortices

The so-called ``creeping'' motion of the pinned vortices in a rotating superfluid involves ``random unpinning'' and ``vortex motion'' as two physically separate processes. We argue that such a creeping motion of the vortices need not be (biased) in the direction of an existing radial Magnus force, nor should a constant microscopic radial velocity be assigned to the vortex motion, in contradiction with the basic assumptions of the ``vortex creep'' model. We point out internal inconsistencies in the predictions of this model which arise due to this unjustified foundation that ignores the role of the actual torque on the superfluid. The proper spin-down rate of a pinned superfluid is then calculated and turns out to be much less than that suggested in the vortex creep model, hence being of even less observational significance for its possible application in explaining the post-glitch relaxations of the radio pulsars.Comment: To be published in J. Low Temp. Phys., Vol. 139, May 2005 [Eqs 11, 15-17 here, have been revised and, may be substituted for the corresponding ones in that paper

Glitches Induced by the Core Superfluid

The long-term evolution of the relative rotation of the core superfluid in a neutron star with respect to the rest of the star, at different radial distances from the rotation axis, is determined through model calculations. The core superfluid rotates at a different rate (faster, in young pulsars), while spinning down at the same steady-state rate as the rest of the star, because of the assumed pinning between the superfluid vortices and the superconductor fluxoids. We find that the magnitude of this rotational lag changes with time and also depends on the distance from the rotation axis; the core superfluid supports an evolving pattern of differential rotation. We argue that the predicted change of the lag might occur as discrete events which could result in a sudden rise of the spin frequency of the crust of a neutron star, as is observed at glitches in radio pulsars. This new possibility for the triggering cause of glitches in radio pulsars is further supported by an estimate of the total predicted excess angular momentum reservoir of the core superfluid. The model seems to offer also resolutions for some other aspects of the observational data on glitches.Comment: Accepted for publication in MNRA

On the Nature of the Residual Magnetic Fields in Millisecond Pulsars

We consider the expulsion of proton fluxoids along neutron vortices from the superfluid/superconductive core of neutron star with weak ($B<10^{10}$ G) magnetic field. The velocity of fluxoids is calculated from the balance of buoyancy, drag and crustal forces. We show, that the proton fluxoids can leave the superfluid core sliding {\it along} the neutron vortices on a timescale of about $10^7$ years. An alternative possibility is that fluxoids are aligned with the vortices on the same timescale. As the result, non--aligned surface magnetic fields of millisecond pulsars can be sustained for \ga 10^9 years only in case of a comparable dissipation timescale of the currents in the neutron star crust. This defines upper limits of the impurity concentration in the neutron star crust: Q \la 0.1 if a stiff equation of state determines the density profile.Comment: 5 pages, 2 figures; accepted by A&