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 ?

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

Star Formation in the Interacting Pair NGC7733/34

The problem of star formation within the interacting pair NGC7733/34 has been studied, based on the UBVRI photometry of the source. The distribution of the colors of selected regions within the galaxies is used to infer an estimate for the age distribution of the star forming regions. The results seem to indicate the presence of numerous extended young star-forming regions in the disk of one of the two galaxies, NGC 7733, with ages in the range of $10^6$--$10^8$ yr. However, there exist no evidence for any violent star formation activity, in the past $10^8$ yr, in the nuclei of the two galaxies. The pair seems to be a merger bound system with the brightest, youngest, site of star forming activity lying at the disk interface.Comment: Accepted for publication in Astronomical Journa

Improved estimate of the detectability of gravitational radiation from a magnetically confined mountain on an accreting neutron star

We give an improved estimate of the detectability of gravitational waves from magnetically confined mountains on accreting neutron stars. The improved estimate includes the following effects for the first time: three-dimensional hydromagnetic ("fast") relaxation, three-dimensional resistive ("slow") relaxation, realistic accreted masses M_a \la 2 \times 10^{-3} M_\odot, (where the mountain is grown ab initio by injection), and verification of the curvature rescaling transformation employed in previous work. Typically, a mountain does not relax appreciably over the lifetime of a low-mass X-ray binary. The ellipticity reaches $\epsilon \approx 2 \times 10^{-5}$ for $M_a=2\times 10^{-3} M_\odot$. The gravitational wave spectrum for triaxial equilibria contains an additional line, which, although weak, provides valuable information about the mountain shape. We evaluate the detectability of magnetic mountains with Initial and Advanced LIGO. For a standard, coherent matched filter search, we find a signal-to-noise ratio of $d = 28 (M_a/10^{-4} M_\odot) (1+5.5 M_a/10^{-4} M_\odot)^{-1} (D/10 \mathrm{kpc})^{-1} (T_0/14 \mathrm{d})^{1/2}$ for Initial LIGO, where $D$ is the distance and $T_0$ is the observation time. From the nondetection of gravitational waves from low-mass X-ray binaries to date, and the wave strain limits implied by the spin frequency distribution of these objects (due to gravitational wave braking), we conclude that there are other, as yet unmodelled, physical effects that further reduce he quadrupole moment of a magnetic mountain, most notably sinking into the crust.Comment: accepted by MNRA