68 research outputs found
Oscillatory superfluid Ekman pumping in Helium II and neutron stars
The linear response of a superfluid, rotating uniformly in a cylindrical
container and threaded with a large number of vortex lines, to an impulsive
increase in the angular velocity of the container is investigated. At zero
temperature and with perfect pinning of vortices to the top and bottom of the
container, we demonstrate that the system oscillates persistently with a
frequency proportional to the vortex line tension parameter to the quarter
power. This low-frequency mode is generated by a secondary flow analogous to
classical Ekman pumping that is periodically reversed by the vortex tension in
the boundary layers. We compare analytic solutions to the two-fluid equations
of Chandler & Baym (1986) with the spin-up experiments of Tsakadze & Tsakadze
(1980) in helium II and find the frequency agrees within a factor of four,
although the experiment is not perfectly suited to the application of the
linear theory. We argue that this oscillatory Ekman pumping mode, and not
Tkachenko modes provide a natural explanation for the observed oscillation. In
neutron stars, the oscillation period depends on the pinning interaction
between neutron vortices and flux tubes in the outer core. Using a simplified
pinning model, we demonstrate that strong pinning can accommodate modes with
periods of days to years, which are only weakly damped by mutual friction over
longer timescales.Comment: 25 pages, 6 figures, submitted to Journal of Fluid Mechanic
Spin down of superfluid-filled vessels: theory versus experiment
The spin up of helium II is studied by calculating the spin-down recovery of
a superfluid-filled container after an impulsive acceleration and comparing
with experiments. The calculation takes advantage of a recently published
analytic solution for the spin up of a Hall-Vinen-Bekharevich-Khalatnikov
superfluid that treats the back-reaction torque exerted by the viscous
component self-consistently in arbitrary geometry for the first time. Excellent
agreement at the 0.5% level is obtained for experiments at ,
after correcting for the non-uniform rotation in the initial state, confirming
that vortex tension and pinning (which are omitted from the theory) play a
minimal role under certain conditions (small Rossby number, smooth walls). The
dependence of the spin-down time on temperature and the mass fraction of the
viscous component are also investigated. Closer to the lambda point, the
predicted onset of turbulence invalidates the linear Ekman theory.Comment: 5 figures, 1 tabl
Continuous-wave gravitational radiation from pulsar glitch recovery
Nonaxisymmetric, meridional circulation inside a neutron star, excited by a
glitch and persisting throughout the post-glitch relaxation phase, emits
gravitational radiation. Here, it is shown that the current quadrupole
contributes more strongly to the gravitational wave signal than the mass
quadrupole evaluated in previous work. We calculate the signal-to-noise ratio
for a coherent search and conclude that a large glitch may be detectable by
second-generation interferometers like the Laser Interferometer
Gravitational-Wave Observatory. It is shown that the viscosity and
compressibility of bulk nuclear matter, as well as the stratification
length-scale and inclination angle of the star, can be inferred from a
gravitational wave detection in principle.Comment: 19 pages, 4 figures, accepted for publication in MNRA
Gravitational radiation from pulsar glitches
The nonaxisymmetric Ekman flow excited inside a neutron star following a
rotational glitch is calculated analytically including stratification and
compressibility. For the largest glitches, the gravitational wave strain
produced by the hydrodynamic mass quadrupole moment approaches the sensitivity
range of advanced long-baseline interferometers. It is shown that the
viscosity, compressibility, and orientation of the star can be inferred in
principle from the width and amplitude ratios of the Fourier peaks (at the spin
frequency and its first harmonic) observed in the gravitational wave spectrum
in the plus and cross polarizations. These transport coefficients constrain the
equation of state of bulk nuclear matter, because they depend sensitively on
the degree of superfluidity.Comment: 28 page
Pulsar glitch recovery and the superfluidity coefficients of bulk nuclear matter
A two-component hydrodynamic model is constructed of the global superfluid
flow induced by two-component Ekman pumping during the recovery stage of a
glitch. The model successfully accounts for the quasi-exponential recovery
observed in pulsars like Vela and the "overshoot" observed in pulsars like the
Crab. By fitting the model to high-resolution timing data, three important
constitutive coefficients in bulk nuclear matter can be extracted: the shear
viscosity, the mutual friction parameter, and the charged fluid fraction. The
fitted coefficients for the Crab and Vela are compared with theoretical
predictions for several equations of state, including the color-flavor locked
and two-flavor color superconductor phases of quark matter.Comment: 19 pages, 12 figure
Gravitational-wave spin-down and stalling lower limits on the electrical resistivity of the accreted mountain in a millisecond pulsar
The electrical resistivity of the accreted mountain in a millisecond pulsar
is limited by the observed spin-down rate of binary radio millisecond pulsars
(BRMSPs) and the spins and X-ray fluxes of accreting millisecond pulsars
(AMSPs). We find (where is the
spin-down age) for BRMSPs and (where
and are the actual and Eddington
accretion rates) for AMSPs. These limits are inferred assuming that the
mountain attains a steady state, where matter diffuses resistively across
magnetic flux surfaces but is replenished at an equal rate by infalling
material. The mountain then relaxes further resistively after accretion ceases.
The BRMSP spin-down limit approaches the theoretical electron-impurity
resistivity at temperatures \ga 10^5 K for an impurity concentration of , while the AMSP stalling limit falls two orders of magnitude below the
theoretical electron-phonon resistivity for temperatures above K. Hence
BRMSP observations are already challenging theoretical resistivity calculations
in a useful way. Next-generation gravitational-wave interferometers will
constrain at a level that will be competitive with electromagnetic
observations.Comment: accepted for publication in ApJ
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