Vortex Creep Model Research Articles

Chaos in pulsar spin dynamics

In the present paper, a new model describing neutron star dynamics is analysed. The system under consideration can be described as a modified vortex creep model. Two component model and the vortex creep model have been used successfully to describe post glitch relaxation phase. However, glitch behaviour is yet to be explained. There can be a possible stochastic mechanism that trigger glitches in neutron stars. To this aim, we propose a modification in the nonlinear vortex creep model. The significance of the modification is twofold, the dynamics of the system is able to generate intermittency, imitating the glitch behaviour of pulsars, and the system also show chaotic motion when the system parameters are set accordingly. The chaotic dynamics is verified by using nonlinear tools such as numerical phase portraits, Lyapunov exponents and bifurcation diagrams.

Finite superconducting square wire-network based on two-dimensional crystalline Mo2C

Superconducting wire-networks are paradigms to study Cooper pairing issues, vortex dynamics and arrangements. Recently, emergent low-dimensional crystalline superconductors were reported in the minimal-disorder limit, providing novel platforms to reveal vortices-related physics. Study on superconducting loops with high-crystallinity is thus currently demanded. Here, we report fabrication and transport measurement of finite square-network based on two-dimensional crystalline superconductor Mo2C. We observe oscillations in the resistance as a function of the magnetic flux through the loops. Resistance dips at both matching field and fractional fillings are revealed. Temperature and current evolutions are carried out in magnetoresistance to study vortex dynamics. The amplitude of oscillation is enhanced due to the interaction between thermally activated vortices and the currents induced in the loops. The driving current reduces the effective activation energy for vortex, giving rise to stronger vortex interaction. Moreover, by the thermally activated vortex creep model, we derive the effective potential barrier for vortex dissipation, which shows well-defined correspondence with structures in magnetoresistance. Our work shows that low-dimensional crystalline superconducting network based on Mo2C possesses pronounced potential in studying the modulation of vortex arrangements and dynamics, paving the way for further investigations on crystalline superconducting network with various configurations.

Glitches in four gamma-ray pulsars and inferences on the neutron star structure

ABSTRACT We present timing solutions from the Fermi-LAT observations of gamma-ray pulsars PSR J0835 − 4510 (Vela), PSR J1023−5746, PSR J2111+4606, and PSR J2229+6114. Data ranges for each pulsar extend over a decade. From data analysis, we have identified a total of 20 glitches, 11 of which are new discoveries. Among them, 15 glitches are large ones with Δν/ν ≳ 10−6. PSR J1023−5746 is the most active pulsar with glitch activity parameter being Ag = 14.5 × 10−7 yr−1 in the considered data span and should be a target for frequently glitching Vela-like pulsars in future observations. We have done fits within the framework of the vortex creep model for 16 glitches with Δν/ν ≳ 10−7. By theoretical analysis of these glitches, we are able to obtain important information on the structure of neutron star, including moments of inertia of the superfluid regions participated in glitches and coupling time-scales between various stellar components. The theoretical prediction for the time to the next glitch from the parameters of the previous one is found to be in qualitative agreement with the observed inter-glitch time-scales for the considered sample. Recoupling time-scales of the crustal superfluid are within the range of theoretical expectations and scale inversely with the spin-down rate of a pulsar. We also determined a braking index n = 2.63(30) for PSR J2229+6114 after glitch-induced contributions have been removed.

The 2016 Vela glitch: a key to neutron star internal structure and dynamics

ABSTRACT High-resolution, pulse-to-pulse observation of the 2016 Vela glitch and its relaxation provided an opportunity to probe the neutron star internal structure and dynamics with unprecedented detail. We use the observations of this glitch to infer superfluid characteristics in the framework of the vortex creep model. The glitch rise time constraint of 12.6 s put stringent limits on the angular momentum exchange between the crustal superfluid and the observed crust. Together with the observed excess acceleration in the rotation rate as compared to the post-glitch equilibrium value, this discriminates crustal superfluid-crust lattice and core superfluid-crustal normal matter coupling time-scales. An evident decrease in the crustal rotation rate immediately before the glitch is consistent with the formation of a new vortex trap zone that initiates the large-scale vortex unpinning avalanche. Formation of vortex trap by a crust breaking quake induces short-lived magnetospheric changes. The long-term post-glitch spin-down rate evolution reveals the moments of inertia and recoupling time-scales of the superfluid layers participating in the glitch and leads to an estimation of the time to the next glitch that agrees with the time interval between the 2016 and 2019 glitches. Our results are consistent with theoretical estimates of effective neutron and proton masses in the superfluid. We also constrain the vortex line-flux tube pinning energy per intersection as 2 MeV.

Neutron star dynamics under time dependent external torques

The two component model of neutron star dynamics describing the behaviour of the observed crust coupled to the superfluid interior has so far been applied to radio pulsars for which the external torques are constant on dynamical timescales. We recently solved this problem under arbitrary time dependent external torques. Our solutions pertain to internal torques that are linear in the rotation rates, as well as to the extremely non-linear internal torques of the vortex creep model. Two-component models with linear or nonlinear internal torques can now be applied to magnetars and to neutron stars in binary systems, with strong variability and timing noise. Time dependent external torques can be obtained from the observed spin-down (or spin-up) time series, .

Nonlinear interglitch dynamics, the braking index of the Vela pulsar and the time to the next glitch

The interglitch timing of the Vela pulsar is characterized by a constant second derivative of the rotation rate. This takes over after the post-glitch exponential relaxation and is completed at about the time of the next glitch. The vortex creep model explains the second derivatives in terms of nonlinear response to the glitch. We present interglitch timing fits to the present sample covering 16 large glitches, taking into account the possibility that in some glitches part of the step in the spin-down rate may involve a ‘persistent shift’, as observed in the Crab pulsar. Modifying the expression for the time between glitches with this hypothesis leads to better agreement with the observed interglitch time intervals. We extrapolate the interglitch model fits to obtain spin-down rates just prior to each glitch and use these to calculate the braking index n = 2.81 ± 0.12. The next glitch should occur around 2017 December 22, ±197 d if no persistent shift is involved, but could occur as early as 2016 July 27, ±152 d if the 2013 glitch gave rise to a typical Vela persistent shift. Note added: Literally while we were submitting the first version of this paper on 2016 December 12, we saw ATel |$\#$| 9847 announcing a Vela pulsar glitch which has arrived 138 d after our prediction with a persistent shift, within the 1σ uncertainty of 152 d.

Peculiar glitch of PSR J1119−6127 and extension of the vortex creep model

Glitches are sudden changes in rotation frequency and spin-down rate, observed from pulsars of all ages. Standard glitches are characterized by a positive step in angular velocity ($\Delta\Omega$ $ > $ $0$) and a negative step in the spin-down rate ($\Delta \dot \Omega$ $ < $ $0$) of the pulsar. There are no glitch-associated changes in the electromagnetic signature of rotation-powered pulsars in all cases so far. For the first time, in the last glitch of PSR J1119-6127, there is clear evidence for changing emission properties coincident with the glitch. This glitch is also unusual in its signature. Further, the absolute value of the spin-down rate actually decreases in the long term. This is in contrast to usual glitch behaviour. In this paper we extend the vortex creep model in order to take into account these peculiarities. We propose that a starquake with crustal plate movement towards the rotational poles of the star induces inward vortex motion which causes the unusual glitch signature. The component of the magnetic field perpendicular to the rotation axis will decrease, giving rise to a permanent change in the pulsar external torque.

Statistical Study of Neutron Star Glitches

Neutron star glitches; spanning a period of 42 years of pulsar timing were studied. These glitches are from Radio, X-ray, Anomalous X-ray and Milliseconds Pulsars. Radio Pulsars dominates the glitch events, contributing 87% of the glitches. Pulsars of characteristic age bracket 103 to 105 yrs dominated the glitch events, at a rate of 5.2 glitches per year per pulsar. Pulsar of the above age bracket exhibits large size glitches compared to others. A large frequency spin-up (△v) is generally associated with large frequency derivative jump (△v ̇). The distribution of the glitch magnitude (△v/v) is bimodal reaffirming dual glitch mechanism, but that of spin-up (△v) is tending towards multi-modal. Moreover, glitches in Vela pulsar and PSR J0537-6910 showed strong elasticity of the objects, suggesting that the interiors of these objects are in thermal equilibrium. Glitches from PSR J1740-3015 and PSR J1341-6220 appeared to occur in groups, suggesting that their interior fluid is switching between two phases. We discussed the glitch activity of young pulsars in terms of vortex creep model.

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.

Single vortex creep in Tl2Ba2CaCu2O8 epitaxial thin films.

By measuring the magnetization hysteresis loops and the remanent magnetization relaxation for an epitaxial ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ thin film, we determined the temperature dependence of the experimental critical current density j(T) and the normalized relaxation rate S(T) at ${\mathit{B}}_{\mathit{e}}$=0.4 T. It is shown that the data j(T) and S(T) can be well fitted to the single vortex creep model with only one fitting parameter in each fitting process. The data j(T) and S(T) were then used as the input for the generalized inversion scheme (GIS); the output of the GIS, i.e., the temperature dependence of the true (unrelaxed) critical current density ${\mathit{j}}_{\mathit{c}}$(T) and the pinning potential ${\mathit{U}}_{\mathit{c}}$(T), follows the theoretical expressions predicted by the single-vortex collective pinning model. Finally, the magnetization (and thus the current) dependence of the activation energy U(${\mathit{M}}_{\mathit{T}=0}$, T=0) was determined by using the magnetization relaxation data. Again, the single vortex creep model explains the resulting U(${\mathit{M}}_{\mathit{T}=0}$, T=0 K) relation very well. \textcopyright{} 1996 The American Physical Society.

Magnetic flux penetration and creep in a ceramic superconductor

A magnetic study has been carried out on a ceramic sample, which showed a high intergrain connectivity. A.C. susceptibility, d.c. magnetization and low-field hysteresis loop measurements have been performed with the aim of determining the characteristic superconducting parameters involved in a ceramic superconductor: lower critical fields ( and ), penetration depths ( and ), penetration fields ( and ), critical currents () and irreversibility fields ( and ). We experimentally confirm the validity of the two-level critical state analysis for the interpretation of the intergranular and intragranular magnetic flux effects in ceramic samples and we propose a methodology to define the magnetic phase diagram of the sample. A consistent picture of all the magnetic flux effects is obtained by analysing the intergranular flux effects in terms of an array of Josephson junctions. Flux creep associated with the Josephson vortices is detected and the effective activation energy is found to be consistent with a Josephson vortex creep model.

Accretion on to strange-matter pulsars

We study the effects of the accretion of normal matter on to strange-matter pulsar models. It is assumed that, because of the high strangeness barrier, normal matter is inert in contact with |${\rm Q}_\alpha$| matter. For this reason, normal matter accretion is able to form a thick outer layer with densities far above neutron drip. Accretion can make the superfluid quark-alpha |${\rm Q}_\alpha$| layer disappear by solidification but, for the same reason, a superfluid neutron layer is formed. The fractional moment of inertia of the latter is large enough to fulfil the vortex-creep glitch model requirements. The high rotational stability of millisecond pulsars is discussed in the framework of the strange-matter hypothesis. If the validity of the vortex-creep model is assumed, it is shown that, for the case of accreted strange-pulsar models, this stability cannot be interpreted as due to the solidification of the superfluid |${\rm Q}_\alpha$| layer. Nevertheless, ‘standard’ homogeneous strange stars remain as interesting candidates for the internal composition of these objects. The main conclusions of this work should be unaltered if |${\rm Q}_\alpha$| is not preferred to strange matter at low pressures, but some other strange complex plays a similar role.

Postglitch relaxation of the VELA pulsar after its first eight large glitches - A reevaluation with the vortex creep model

We present a comprehensive reevaluation of eight of the nine glitches observed to date from the Vela pulsar, and the postglitch relaxation following each glitch. All glitch data sets can be described in terms of three distinct components of short and intermediate time scale exponential relaxation, followed by a long-term recovery of the glitch-induced change in the spin-down rate that is linear in t, ΔΩ˙ c (t)∞t. We interpret the short and the intermediate time scale exponential relaxation, characterized by relaxation times of 10 hr, 3 d .2, and 32 d as the linear response of vortex creep in those regions of the pinned superfluid in the neutron star crust through which no sudden vortex motion occurred at the time of the glitch

Correlated creep rate of a vortex line under the effect of vortex tension and its relation to the glitches of pulsars.

In our earlier works, we have calculated the correlated creep velocity of a vortex line with line tension, which is pinned to a perfect simple-cubic lattice, and creeps out under the action of a biased potential by thermal activation. In this paper, we extend the result to cases in which the biased potential, the line tension, and the pinning energy of the line are all functions of position. Although an evaluation of the exact correlated creep velocity is difficult, a good approximate form can be found. We show that the Anderson-Kim thermal-activation formula in the vortex-creep model is still valid after suitable modification even though their uncorrelated-creeping assumption is incorrect. We apply our formalism to study the motion of vortex lines in the crustal region of neutron stars. The model results suggests that the steady-state configuration of vortex lines should form a set of hyperbolic-like curves because the stronger-pinning regions (which also have higher tension) are located in the inner regions of the crust. Perturbations, like a star quake, can cause a large number of vortex lines to unpin from the stronger-pinning region and the tension forces the vortex lines to move by a macroscopic distance. Such a mechanism may be responsible for the glitches of pulsars.

A second giant glitch in PSR 1641 - 45

Eight years of timing observations of PSR 1641-45 are presented. During this time, two sudden increases in rotation rate were observed. One of these flitches is of similar size to those observed regularly in the Vela pulsar, and is the second such event observed in PSR1641-45. Some features of this ditch are not easily explained within the context of the vortex creep model of glitches. Timing noise similar to that seen in other pulsars is evident, particularly after the glitch

Implications of 3P2 superfluidity in the interior of neutron stars

The magnetized vortex lines of the 3 P 2 paired neutron superfluid are effectively pinned by the magnetic energy barriers produced by the flux tubes of the 1 S 0 paired proton superconducting fluid. The stellar crust and the core superfluid can be coupled primarily via thermal vortex creep against the barriers. The postglitch relaxation of the core superfluid is studied by using the thermal vortex creep model in the limit where the motion of flux tubes is slow compared with that of the vortex lines

Outer magnetospheric fluctuations and pulsar timing noise

The Cheng, Ho, and Ruderman (1986) outer-magnetosphere gap model was used to investigate the stability of Crab-type outer magnetosphere gaps for pulsars having the parameter (Omega-square B) similar to that of the Crab pulsar. The Lamb, Pines, and Shaham (1978) fluctuating magnetosphere noise model was applied to the Crab pulsar to examine the type of the equation of state that best describes the structure of the neutron star. The noise model was also applied to other pulsars, and the theoretical results were compared with observational data. The results of the comparison are consistent with the stiff equation of state, as suggested by the vortex creep model of the neutron star interior. The timing-noise observations also contribute to the evidence for the existence of superfluid in the core of the neutron star.