39 research outputs found
Dynamics of Quantum Vorticity in a Random Potential
I study the dynamics of a superfluid vortex in a random potential, as in the
inner crust of a neutron star. Below a critical flow velocity of the ambient
superfluid, a vortex is effectively immobilized by lattice forces even in the
limit of zero dissipation. Low-velocity, translatory motion is not dynamically
possible, a result with important implications for understanding neutron star
precession and the dynamical properties of superfluid nuclear matter.Comment: Physical Review Letters, final versio
Global three-dimensional flow of a neutron superfluid in a spherical shell in a neutron star
We integrate for the first time the hydrodynamic
Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a -paired
neutron superfluid in a rotating spherical shell, using a pseudospectral
collocation algorithm coupled with a time-split fractional scheme. Numerical
instabilities are smoothed by spectral filtering. Three numerical experiments
are conducted, with the following results. (i) When the inner and outer spheres
are put into steady differential rotation, the viscous torque exerted on the
spheres oscillates quasiperiodically and persistently (after an initial
transient). The fractional oscillation amplitude () increases
with the angular shear and decreases with the gap width. (ii) When the outer
sphere is accelerated impulsively after an interval of steady differential
rotation, the torque increases suddenly, relaxes exponentially, then oscillates
persistently as in (i). The relaxation time-scale is determined principally by
the angular velocity jump, whereas the oscillation amplitude is determined
principally by the gap width. (iii) When the mutual friction force changes
suddenly from Hall-Vinen to Gorter-Mellink form, as happens when a rectilinear
array of quantized Feynman-Onsager vortices is destabilized by a counterflow to
form a reconnecting vortex tangle, the relaxation time-scale is reduced by a
factor of compared to (ii), and the system reaches a stationary state
where the torque oscillates with fractional amplitude about a
constant mean value. Preliminary scalings are computed for observable
quantities like angular velocity and acceleration as functions of Reynolds
number, angular shear, and gap width. The results are applied to the timing
irregularities (e.g., glitches and timing noise) observed in radio pulsars.Comment: 6 figures, 23 pages. Accepted for publication in Astrophysical
Journa
Quantum turbulence at finite temperature: the two-fluids cascade
To model isotropic homogeneous quantum turbulence in superfluid helium, we
have performed Direct Numerical Simulations (DNS) of two fluids (the normal
fluid and the superfluid) coupled by mutual friction. We have found evidence of
strong locking of superfluid and normal fluid along the turbulent cascade, from
the large scale structures where only one fluid is forced down to the vorticity
structures at small scales. We have determined the residual slip velocity
between the two fluids, and, for each fluid, the relative balance of inertial,
viscous and friction forces along the scales. Our calculations show that the
classical relation between energy injection and dissipation scale is not valid
in quantum turbulence, but we have been able to derive a temperature--dependent
superfluid analogous relation. Finally, we discuss our DNS results in terms of
the current understanding of quantum turbulence, including the value of the
effective kinematic viscosity
General-Relativistic Curvature of Pulsar Vortex Structure
The motion of a neutron superfluid condensate in a pulsar is studied. Several
theorems of general-relativistic hydrodynamics are proved for a superfluid. The
average density distribution of vortex lines in pulsars and their
general-relativistic curvature are derived.Comment: 18 pages, 1 figure
Vortex dynamics in rotating counterflow and plane Couette and Poiseuille turbulence in superfluid Helium
An equation previously proposed to describe the evolution of vortex line
density in rotating counterflow turbulent tangles in superfluid helium is
generalized to incorporate nonvanishing barycentric velocity and velocity
gradients. Our generalization is compared with an analogous approach proposed
by Lipniacki, and with experimental results by Swanson et al. in rotating
counterflow, and it is used to evaluate the vortex density in plane Couette and
Poiseuille flows of superfluid helium.Comment: 18 pages, 2 figure
Transitions between turbulent and laminar superfluid vorticity states in the outer core of a neutron star
We investigate the global transition from a turbulent state of superfluid
vorticity to a laminar state, and vice versa, in the outer core of a neutron
star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov
equations for a rotating superfluid in a differentially rotating spherical
shell, we find that the meridional counterflow driven by Ekman pumping exceeds
the Donnelly-Glaberson threshold throughout most of the outer core, exciting
unstable Kelvin waves which disrupt the rectilinear vortex array, creating a
vortex tangle. In the turbulent state, the torque exerted on the crust
oscillates, and the crust-core coupling is weaker than in the laminar state.
This leads to a new scenario for the rotational glitches observed in radio
pulsars: a vortex tangle is sustained in the differentially rotating outer core
by the meridional counterflow, a sudden spin-up event brings the crust and core
into corotation, the vortex tangle relaxes back to a rectilinear vortex array,
then the crust spins down electromagnetically until enough meridional
counterflow builds up to reform a vortex tangle. The turbulent-laminar
transition can occur uniformly or in patches; the associated time-scales are
estimated from vortex filament theory. We calculate numerically the global
structure of the flow with and without an inviscid superfluid component, for
Hall-Vinen and Gorter-Mellink forms of the mutual friction. We also calculate
the post-glitch evolution of the angular velocity of the crust and its time
derivative, and compare the results with radio pulse timing data, predicting a
correlation between glitch activity and Reynolds number.Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010,
Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de
Oriente, Cumana, Venezuela, (3) Department of Mechanical and Manufacturing
Engineering, University of Melbourne, Parkville, VIC 3010, Australia.
Accepted for publication in The Astrophysical Journal. 30 pages, 9 figures
(in jpg format
Entropy entrainment and dissipation in superfluid Helium
Building on a general variational framework for multi-fluid dynamics, we
discuss finite temperature effects in superfluids. The main aim is to provide
insight into the modelling of more complex finite temperature superfluid
systems, like the mixed neutron superfluid/proton superconductor that is
expected in the outer core of a neutron star. Our final results can also (to a
certain extent) be used to describe colour-flavour locked quark superconductors
that may be present at the extreme densities in the deep neutron star core. As
a demonstration of the validity of the model, which is based on treating the
excitations in the system as a massless ``entropy'' fluid, we show that it is
formally equivalent to the traditional two-fluid approach for superfluid
Helium. In particular, we highlight the fact that the entropy entrainment
encodes the ``normal fluid density'' of the traditional approach. We also show
how the superfluid constraint of irrotationality reduces the number of
dissipation coefficients in the system. This analysis provides insight into the
more general problem when vortices are present in the superfluid, and we
discuss how the so-called mutual friction force can be accounted for in our
framework. The end product is a hydrodynamic formalism for finite temperature
effects in a single superfluid condensate. This framework can readily be
extended to more complex situations.Comment: revised version, clarifies points regarding entrainment in different
context
R-Modes in Superfluid Neutron Stars
The analogs of r-modes in superfluid neutron stars are studied here. These
modes, which are governed primarily by the Coriolis force, are identical to
their ordinary-fluid counterparts at the lowest order in the small
angular-velocity expansion used here. The equations that determine the next
order terms are derived and solved numerically for fairly realistic superfluid
neutron-star models. The damping of these modes by superfluid ``mutual
friction'' (which vanishes at the lowest order in this expansion) is found to
have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a
``typical'' superfluid neutron-star model. This time-scale is far too long to
allow mutual friction to suppress the recently discovered gravitational
radiation driven instability in the r-modes. However, the strength of the
mutual friction damping depends very sensitively on the details of the
neutron-star core superfluid. A small fraction of the presently acceptable
range of superfluid models have characteristic mutual friction damping times
that are short enough (i.e. shorter than about 5 s) to suppress the
gravitational radiation driven instability completely.Comment: 15 pages, 8 figure
The r-modes in accreting neutron stars with magneto-viscous boundary layers
We explore the dynamics of the r-modes in accreting neutron stars in two
ways. First, we explore how dissipation in the magneto-viscous boundary layer
(MVBL) at the crust-core interface governs the damping of r-mode perturbations
in the fluid interior. Two models are considered: one assuming an
ordinary-fluid interior, the other taking the core to consist of superfluid
neutrons, type II superconducting protons, and normal electrons. We show,
within our approximations, that no solution to the magnetohydrodynamic
equations exists in the superfluid model when both the neutron and proton
vortices are pinned. However, if just one species of vortex is pinned, we can
find solutions. When the neutron vortices are pinned and the proton vortices
are unpinned there is much more dissipation than in the ordinary-fluid model,
unless the pinning is weak. When the proton vortices are pinned and the neutron
vortices are unpinned the dissipation is comparable or slightly less than that
for the ordinary-fluid model, even when the pinning is strong. We also find in
the superfluid model that relatively weak radial magnetic fields ~ 10^9 G (10^8
K / T)^2 greatly affect the MVBL, though the effects of mutual friction tend to
counteract the magnetic effects. Second, we evolve our two models in time,
accounting for accretion, and explore how the magnetic field strength, the
r-mode saturation amplitude, and the accretion rate affect the cyclic evolution
of these stars. If the r-modes control the spin cycles of accreting neutron
stars we find that magnetic fields can affect the clustering of the spin
frequencies of low mass x-ray binaries (LMXBs) and the fraction of these that
are currently emitting gravitational waves.Comment: 19 pages, 8 eps figures, RevTeX; corrected minor typos and added a
referenc
Reconnection dynamics and mutual friction in quantum turbulence
We investigate the behaviour of the mutual friction force in finite temperature quantum turbulence in 4He, paying particular attention to the role of quantized vortex reconnections. Through the use of the vortex filament model, we produce three experimentally relevant types of vortex tangles in steady-state conditions, and examine through statistical analysis, how local properties of the tangle influence the mutual friction force. Finally, by monitoring reconnection events, we present evidence to indicate that vortex reconnections are the dominant mechanism for producing areas of high curvature and velocity leading to regions of high mutual friction, particularly for homogeneous and isotropic vortex tangles