Abstract

In the limit of short wavelengths, it has been shown that superfluidity significantly affects wave propagation in neutron stars. Here we abandon the short-wavelength restriction and extend these calculations to global oscillation modes. In the present analysis, the solid crust of the neutron star is divided into an outer crust and an inner crust, and a superfluid of neutrons coexists with the solid lattice in the inner crust. We have computed several low-order global spheroidal modes for l = 2 both with and without superfluidity. We find that superfluidity in the inner crust affects the frequency spectra of acoustic (p-) modes, shear (s-) modes, and interfacial (i-) modes, although the surface gravity (g-) modes are not affected at all.

Introduction

Most previous calculations of the non-radial oscillations of neutron stars have completely neglected the effects of superfluidity (cf McDermott, Van Horn, and Hansen 1988 and references therein). Epstein (1988) has previously considered superfluid effects, but only in the short-wavelength limit, where the length scales for variations in equilibrium quantities are all assumed to be much longer than the typical wavelength of an oscillation. In general, global oscillations may be either spheroidal or toroidal in character. Van Horn and Epsetein (1990) extended Epstein's short-wavelength results to include the global toroidal oscillation modes of neutron stars. More recently, Mendell (1991) and his colleagues have also considered the effects of superfluidity, but they employed simple models for neutron stars, and their analysis did not reflect the variety of oscillation modes of realistic, neutron stars.