Tkachenko modes as sources of quasiperiodic pulsar spin variations

Abstract

We study the long wavelength shear modes (Tkachenko waves) of triangular lattices of singly quantized vortices in neutron star interiors taking into account the mutual friction between the superfluid and the normal fluid as well as the shear viscosity of the normal fluid. The set of Tkachenko modes that propagate in the plane orthogonal to the spin vector are weakly damped if the coupling between the superfluid and the normal fluid is small. In strong coupling, their oscillation frequencies are lower and are undamped for small and moderate shear viscosities. The periods of these modes are consistent with the observed $\ensuremath{\sim}100--1000\text{ }\text{ }\mathrm{day}$ variations of spin for PSR 1828-11.