scholarly journals Superfluid vortex-mediated mutual friction in non-homogeneous neutron star interiors

2020 ◽  
Vol 499 (3) ◽  
pp. 3690-3705
Author(s):  
M Antonelli ◽  
B Haskell
Keyword(s):  
Neutron Star ◽  
Normal Component ◽  
Homogeneous Medium ◽  
Outer Core ◽  
Two Dimensions ◽  
Pinning Force ◽  
Mutual Friction ◽  
Momentum Exchange ◽  
Drag Forces ◽  
Vortex Lines

ABSTRACT Understanding the average motion of a multitude of superfluid vortices in the interior of a neutron star is a key ingredient for most theories of pulsar glitches. In this paper, we propose a kinetic approach to compute the mutual friction force that is responsible for the momentum exchange between the normal and superfluid components in a neutron star, where the mutual friction is extracted from a suitable average over the motion of many vortex lines. As a first step towards a better modelling of the repinning and depinning processes of many vortex lines in a neutron star, we consider here only straight and non-interacting vortices: we adopt a minimal model for the dynamics of an ensemble of point vortices in two dimensions immersed in a non-homogeneous medium that acts as a pinning landscape. Since the degree of disorder in the inner crust or outer core of a neutron star is unknown, we compare the two possible scenarios of periodic and disordered pinscapes. This approach allows us to extract the mutual friction between the superfluid and the normal component in the star when, in addition to the usual Magnus and drag forces acting on vortex lines, also a pinning force is at work. The effect of disorder on the depinning transition is also discussed.

scholarly journals A universal formula for the relativistic correction to the mutual friction coupling time-scale in neutron stars

2020 ◽  
Vol 494 (3) ◽  
pp. 3562-3580 ◽  
Author(s):  
L Gavassino ◽  
M Antonelli ◽  
P M Pizzochero ◽  
B Haskell
Keyword(s):  
General Relativity ◽  
Neutron Star ◽  
Time Scale ◽  
Outer Core ◽  
Relativistic Correction ◽  
Quantized Vortices ◽  
Universal Relation ◽  
Mutual Friction ◽  
Universal Formula ◽  
Coupling Time

ABSTRACT Vortex-mediated mutual friction governs the coupling between the superfluid and normal components in neutron star interiors. By, for example, comparing precise timing observations of pulsar glitches with theoretical predictions it is possible to constrain the physics in the interior of the star, but to do so an accurate model of the mutual friction coupling in general relativity is needed. We derive such a model directly from Carter’s multifluid formalism, and study the vortex structure and coupling time-scale between the components in a relativistic star. We calculate how general relativity modifies the shape and the density of the quantized vortices and show that, in the quasi-Schwarzschild coordinates, they can be approximated as straight lines for realistic neutron star configurations. Finally, we present a simple universal formula (given as a function of the stellar compactness alone) for the relativistic correction to the glitch rise-time, which is valid under the assumption that the superfluid reservoir is in a thin shell in the crust or in the outer core. This universal relation can be easily employed to correct, a posteriori, any Newtonian estimate for the coupling time-scale, without any additional computational expense.

scholarly journals 1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 470
Author(s):  
Valentin Allard ◽  
Nicolas Chamel
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Neutron Stars ◽  
Physical Meaning ◽  
Outer Core ◽  
Time Dependent ◽  
Hartree Fock ◽  
Chemical Potentials ◽  
Bogoliubov Equations ◽  
Flow Velocities

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

scholarly journals Two-fluid simulations of the magnetic field evolution in neutron star cores in the weak-coupling regime

2020 ◽  
Vol 498 (2) ◽  
pp. 3000-3012 ◽  
Author(s):  
F Castillo ◽  
A Reisenegger ◽  
J A Valdivia
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Charged Particles ◽  
Stable Stratification ◽  
Composition Gradient ◽  
Axially Symmetric ◽  
Drag Forces ◽  
Degeneracy Pressure ◽  
The Magnetic Field ◽  
Two Fluid

ABSTRACT In a previous paper, we reported simulations of the evolution of the magnetic field in neutron star (NS) cores through ambipolar diffusion, taking the neutrons as a motionless uniform background. However, in real NSs, neutrons are free to move, and a strong composition gradient leads to stable stratification (stability against convective motions) both of which might impact on the time-scales of evolution. Here, we address these issues by providing the first long-term two-fluid simulations of the evolution of an axially symmetric magnetic field in a neutron star core composed of neutrons, protons, and electrons with density and composition gradients. Again, we find that the magnetic field evolves towards barotropic ‘Grad–Shafranov equillibria’, in which the magnetic force is balanced by the degeneracy pressure gradient and gravitational force of the charged particles. However, the evolution is found to be faster than in the case of motionless neutrons, as the movement of charged particles (which are coupled to the magnetic field, but are also limited by the collisional drag forces exerted by neutrons) is less constrained, since neutrons are now allowed to move. The possible impact of non-axisymmetric instabilities on these equilibria, as well as beta decays, proton superconductivity, and neutron superfluidity, are left for future work.

scholarly journals Spin rotation, Chandler wobble and free core nutation of isolated multi-layer pulsars

2012 ◽  
Vol 8 (S291) ◽  
pp. 392-392
Author(s):  
Alexander Gusev ◽  
Irina Kitiashvili
Keyword(s):  
Neutron Star ◽  
Differential Rotation ◽  
Heat Dissipation ◽  
Inner Core ◽  
Outer Core ◽  
Chandler Wobble ◽  
Time Of Arrival ◽  
Layer Model ◽  
Free Core Nutation ◽  
Rotation Pole

AbstractAt present time there are investigations of precession and nutation for very different celestial multi-layer bodies: the Earth (Getino 1995), Moon (Gusev 2010), planets of Solar system (Gusev 2010) and pulsars (Link et al. 2007). The long-periodic precession phenomenon was detected for few pulsars: PSR B1828-11, PSR B1557-50, PSR 2217+47, PSR 0531+21, PSR B0833-45, and PSR B1642-03. Stairs, Lyne & Shemar (2000) have found that the arrival-time residuals from PSR B1828-11 vary periodically with a different periods. According to our model, the neutron star has the rigid crust (RC), the fluid outer core (FOC) and the solid inner core (SIC). The model explains generation of four modes in the rotation of the pulsar: two modes of Chandler wobble (CW, ICW) and two modes connecting with free core nutation (FCN, FICN) (Gusev & Kitiashvili 2008). We are propose the explanation for all harmonics of Time of Arrival (TOA) pulses variations as precession of a neutron star owing to differential rotation of RC, FOC and crystal SIC of the pulsar PSR B1828-11: 250, 500, 1000 days. We used canonical method for interpretation TOA variations by Chandler Wobble (CW) and Free Core Nutation (FCN) of pulsar.The two - layer model can explain occurrence twin additional fashions in rotation pole motion of a NS: CW and FCN. In the frame of the three-layer model we investigate the free rotation of dynamically-symmetrical PSR by Hamilton methods. Correctly extending theory of SIC-FOC-RC differential rotation for neutron star, we investigated dependence CW, ICW, FCN and FICN periods from flatness of different layers of pulsar.Our investigation showed that interaction between rigid crust, RIC and LOC can be characterized by four modes of periodic variations of rotation pole: CW, retrograde Free Core Nutation (FCN), prograde Free Inner Core Nutation (FICN) and Inner Core Wobble (ICW). In the frame of the three-layer model we proposed the explanation for all pulse fluctuations by differential rotation crust, outer core and inner core of the neutron star and received estimations of dynamical flattening of the pulsar inner and outer cores, including the heat dissipation. We have offered the realistic model of the dynamical pulsar structure and two explanations of the feature of flattened of the crust, the outer core and the inner core of the pulsar.

Kinetic theory of mutual friction force in superfluid 4He with vortex lines

1990 ◽  
Vol 165-166 ◽  
pp. 773-774
Author(s):  
Kazuo Yamada ◽  
Kazumasa Miyake ◽  
Shohei Kashiwamura
Keyword(s):  
Kinetic Theory ◽  
Friction Force ◽  
Superfluid 4He ◽  
Mutual Friction ◽  
Vortex Lines

scholarly journals Modal approximation for plasmonic resonators in the time domain: the scalar case

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Lorenzo Baldassari ◽  
Pierre Millien ◽  
Alice L. Vanel
Keyword(s):  
Time Domain ◽  
Homogeneous Medium ◽  
Low Frequency ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Scalar Case ◽  
Singular Boundary ◽  
Metallic Nanoparticle ◽  
The Time Domain ◽  
Modal Approximation

AbstractWe study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non-Hermitian problem as perturbations of electro-static modes, and obtain a modal approximation of the scattered field in the frequency domain. The poles of the expansion correspond to the eigenvalues of a singular boundary integral operator and are shown to lie in a bounded region near the origin of the lower-half complex plane. Finally, we show that this modal representation gives a very good approximation of the field in the time domain. We present numerical simulations in two dimensions to corroborate our results.

scholarly journals Vortex pinning in the superfluid core of relativistic neutron stars

2021 ◽  
Vol 503 (1) ◽  
pp. 1407-1417
Author(s):  
Aurélien Sourie ◽  
Nicolas Chamel
Keyword(s):  
Neutron Stars ◽  
Outer Core ◽  
Vortex Pinning ◽  
Global Dynamics ◽  
Mutual Friction ◽  
Dynamical Equations ◽  
General Relativistic ◽  
Superfluid Core ◽  
Relativistic Framework

ABSTRACT Our recent Newtonian treatment of the smooth-averaged mutual-friction force acting on the neutron superfluid and locally induced by the pinning of quantized neutron vortices to proton fluxoids in the outer core of superfluid neutron stars is here adapted to the general-relativistic framework. We show how the local non-relativistic motion of individual vortices can be matched to the global dynamics of the star using the fully 4D covariant Newtonian formalism of Carter & Chamel. We derive all the necessary dynamical equations for carrying out realistic simulations of superfluid rotating neutron stars in full general relativity, as required for the interpretation of pulsar frequency glitches. The role of vortex pinning on the global dynamics appears to be non-trivial.

On the boundary conditions in estimating ∇ω by div ω and curl ω

2018 ◽  
Vol 149 (03) ◽  
pp. 739-760
Author(s):  
Gyula Csató ◽  
Olivier Kneuss ◽  
Dhanya Rajendran
Keyword(s):  
Boundary Conditions ◽  
Normal Component ◽  
Tangential Component ◽  
Two Dimensions ◽  
Classical Boundary ◽  
Image Position ◽  
Special Case ◽  
Interpolation Result

AbstractIn this paper, we study under what boundary conditions the inequality$${\rm \Vert }\nabla \omega {\rm \Vert }_{L^2(\Omega )}^2 \les C({\rm \Vert }{\rm curl}\omega {\rm \Vert }_{L^2(\Omega )}^2 + {\rm \Vert }{\rm div}\omega {\rm \Vert }_{L^2(\Omega )}^2 + {\rm \Vert }\omega {\rm \Vert }_{L^2(\Omega )}^2 )$$holds true. It is known that such an estimate holds if either the tangential or normal component ofωvanishes on the boundary ∂Ω. We show that the vanishing tangential component condition is a special case of a more general one. In two dimensions, we give an interpolation result between these two classical boundary conditions.

scholarly journals Turbulent, pinned superfluids in neutron stars and pulsar glitch recoveries

2020 ◽  
Vol 499 (1) ◽  
pp. 161-170
Author(s):  
B Haskell ◽  
D Antonopoulou ◽  
C Barenghi
Keyword(s):  
Neutron Star ◽  
Second Derivative ◽  
Mutual Friction ◽  
Turbulent Model ◽  
Turbulent Region ◽  
Rotational Evolution ◽  
Vela Pulsar ◽  
Superfluid Vortices ◽  
Insight Into ◽  
Better Than

ABSTRACT Pulsar glitches offer an insight into the dynamics of superfluids in the high-density interior of a neutron star. To model these phenomena, however, one needs to have an understanding of the dynamics of a turbulent array of superfluid vortices moving through a pinning lattice. In this paper, we develop a theoretical approach to describe vortex-mediated mutual friction in a pinned, turbulent and rotating superfluid. Our model is then applied to the study of the post-glitch rotational evolution in the Vela pulsar and in PSR J0537-6910. We show that in both cases a turbulent model fits the evolution of the spin frequency derivative better than a laminar one. We also predict that the second derivative of the frequency after a glitch should be correlated with the waiting time since the previous glitch, which we find to be consistent with observational data for these pulsars. The main conclusion of this paper is that in the post-glitch rotational evolution of these two pulsars we are most likely observing the response to the glitch of a pinned turbulent region of the star (possibly the crust) and not the laminar response of a regular straight vortex array.

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