  Neutron stars could contain a mixture of ordinary nuclear matter and dark
matter, such that dark matter could influence observable properties of the
star, such as its mass and radius. We study these dark matter admixed neutron
stars for two choices of dark matter: a free Fermi gas and mirror dark matter.
In addition to solving the multi-fluid Tolman-Oppenheimer-Volkoff equations for
static solutions and presenting mass-radius diagrams, we focus on two
computations that are lacking in the literature. The first is a rigorous
determination of stability over the whole of parameter space, which we do using
two different methods. The first method is based on harmonic time-dependent
perturbations to the static solutions and on solving for the radial oscillation
frequency. The second method, which is less well-known, conveniently makes use
of unperturbed, static solutions only. The second computation is of the radial
oscillation frequency, for fundamental modes, over large swaths of parameter
space.
