Global Three-dimensional Flow of a Neutron Superfluid in a Spherical Shell in a Neutron Star
Abstract
We integrate for the first time the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a 1S0-paired neutron superfluid in a rotating spherical shell, using a pseudo-spectral 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. (1) When the inner and outer spheres are put into steady differential rotation, the viscous torque exerted on the spheres oscillates quasi-periodically and persistently (after an initial transient). The fractional oscillation amplitude (~10-2) increases with the angular shear and decreases with the gap width. (2) 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 (1). The relaxation timescale is determined principally by the angular velocity jump, whereas the oscillation amplitude is determined principally by the gap width. (3) 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 timescale is reduced by a factor of ~3 compared to (2), and the system reaches a stationary state in which the torque oscillates with fractional amplitude ~10-3 about a constant mean value. Preliminary scalings are computed for observable quantities such as angular velocity and acceleration as functions of the 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.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- December 2005
- DOI:
- 10.1086/497899
- arXiv:
- arXiv:astro-ph/0509416
- Bibcode:
- 2005ApJ...635.1224P
- Keywords:
-
- Dense Matter;
- Hydrodynamics;
- Stars: Interiors;
- Stars: Neutron;
- Stars: Rotation;
- Astrophysics
- E-Print:
- 6 figures, 23 pages. Accepted for publication in Astrophysical Journal