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 $T=1.57\,{\rm K}$, 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

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

Gross-Pitaevskii model of pulsar glitches

The first large-scale quantum mechanical simulations of pulsar glitches are presented, using a Gross-Pitaevskii model of the crust-superfluid system in the presence of pinning. Power-law distributions of simulated glitch sizes are obtained, in accord with astronomical observations, with exponents ranging from -0.55 to -1.26. Examples of large-scale simulations, containing $\sim 200$ vortices, reveal that these statistics persist in the many-vortex limit. Waiting-time distributions are also constructed. These and other statistics support the hypothesis that catastrophic unpinning mediated by collective vortex motion produces glitches; indeed, such collective events are seen in time-lapse movies of superfluid density. Three principal trends are observed. (1) The glitch rate scales proportional to the electromagnetic spin-down torque. (2) A strong positive correlation is found between the strength of vortex pinning and mean glitch size. (3) The spin-down dynamics depend less on the pinning site abundance once the latter exceeds one site per vortex, suggesting that unpinned vortices travel a distance comparable to the inter-vortex spacing before repinning.Comment: 24 pages, 19 figures, accepted for publication in MNRA

The effect of realistic equations of state and general relativity on the "snowplow" model for pulsar glitches

Many pulsars are observed to "glitch", i.e. show sudden jumps in their rotational frequency $\nu$, some of which can be as large as $\Delta \nu/\nu\approx 10^{-6}-10^{-5}$ in a subset of pulsars known as giant glitchers. Recently Pizzochero (2011) has shown that an analytic model based on realistic values for the pinning forces in the crust and for the angular momentum transfer in the star can describe the average properties of giant glitches, such as the inter-glitch waiting time, the step in frequency and that in frequency derivative. In this paper we extend the model (originally developed in Newtonian gravity and for a polytropic equation of state) to realistic backgrounds obtained by integrating the relativistic equations of stellar structure and using physically motivated equations of state to describe matter in the neutron star. We find that this more detailed treatment still reproduces the main features of giant glitches in the Vela pulsar and allows us to set constraints on the equation of state. In particular we find that stiffer equations of state are favoured and that it is unlikely that the Vela pulsar has a high mass (larger than $M\approx 1.5 M_\odot$).Comment: 15 pages, 8 figures, submitted to MNRA