Ruderman's Theory of Vortex–Lattice Vibrations in Pulsars

Abstract

RUDERMAN¹ has suggested that the observed modulation with a period ≈4 months of the rotation frequency of the Crab pulsar (0.03 s period) arises from waves in the triangular lattice of quantized vortex lines, which are expected to occur in pulsars (rotating superfluid neutron stars) as well as in rotating He II. If the wavelength is comparable with the pulsar radius and the wave vector is perpendicular to the vortices, then these oscillations may have a period of about four months. This calculation¹ neglected mutual friction between the vortices and the normal component (essentially electrons and protons); we here estimate the fractional effects, which seem to be considerable. We also point out a difficulty associated with the three-dimensional nature of the pulsar.