Oscillatory superfluid Ekman pumping in Helium II and neutron stars

TL;DR

This paper investigates oscillatory superfluid Ekman pumping in Helium II and neutron stars, revealing a persistent oscillation mode driven by vortex tension and boundary layer dynamics, with implications for observed stellar oscillations.

Contribution

It introduces a new understanding of oscillatory Ekman pumping driven by vortex tension, connecting superfluid dynamics in Helium II and neutron stars with experimental and astrophysical observations.

Findings

Analytic solutions match helium II experiments within a factor of four.

Oscillation periods in neutron stars can range from days to years with strong pinning.

The mode is weakly damped and explains observed stellar oscillations.

Abstract

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.