### Abstract:

Just as the observations of oscillations of ordinary stars can be used to determine
their composition and structure, the oscillations of neutron stars could potentially be
used to determine the nature of the dense nuclear matter from which they are made.
The superfluidity of the interiors of neutron stars is normally probed by observations of pulsar glitches. It turns out that the superfluidity affects the oscillations in a neutron star core. In particular, it results in a class of oscillation modes specifically
associated with the superfluid core. Although these modes have not been detected
from observations, it is hoped by some that gravitational wave data may be used
to probe the superfluidity of neutron star cores. In this dissertation, a simple
equilibrium model is used in order to calculate the superfluid modes in the context
of newtonian gravity. The equilibrium model that is used is the same combination
of the Serot equation of state and the Harrison-Wheeler equation of state that was
used formerly by Lee and by Lindblom & Mendell. Numerical calculations of the
superfluid modes are done for 20 different neutron star models ranging in mass
between 0.5 and 2 solar masses. The frequencies of the oscillations for the 0.5 and 1.4 solar masses agree fairly well with Lee's results, which strongly validates the
computer code written for numerical calculation in this work. In all the models, the eigenfrequencies of the super
uid or s-modes are found among those of the f and p-modes. For the equation of state that is used, it is shown that the dimensionless
frequencies of the p-modes increase with an increase in mass of the neutron star
while those of the s-modes decrease with an increase in neutron star mass.
The plan of the dissertation is as follows. Chapter 1 gives a short introduction
to stellar oscillations and mentions the oscillations of neutron stars. Chapters 2
and 3 provide the general theoretical background of stellar structure and stellar
oscillations respectively. Chapter 4 is a review of the equations of state of neutron
star matter derived previously in the literature. Chapter 5 provides the method of
calculation as well as the results. Chapter 6 provides a discussion of the results.
Chapter 7 briefly gives a review of a mathematical framework for fluids that could
be used in order to calculate the oscillations in a general relativistic context and then briefly describes the effects of rotation and magnetic fields. Appendix B liststhe source code for the programs used to do the calculations and also explains some of the extra numerical procedures used for the computation.