  In [Leung et al., Phys. Rev. D 84, 107301 (2011)], we presented our results
on using a general relativistic two-fluid formalism to study the hydrostatic
equilibrium configuration of an admixture of degenerate dark matter and normal
nuclear matter. In this work, we present more analysis to complement our
previous findings. We study the radial oscillation modes of these compact stars
in detail. We find that these stars in general have two classes of oscillation
modes. For a given total mass of the star, the first class of modes is
insensitive to the dark-matter particle mass. They also reduce properly to the
oscillation modes of the corresponding ordinary neutron star, with the same
total mass, when the mass fraction of dark matter tends to zero. On the other
hand, the second class of modes is due mainly to the dark-matter fluid. In the
small dark-matter mass fraction limit, these modes are characterized purely by
the oscillations of dark matter, while the normal matter is essentially at
rest. In the intermediate regime where the mass fractions of the two fluids are
comparable, the normal matter oscillates with the dark matter due to their
coupling through gravity. In contrast to the first class of modes, the
frequencies of these dark-matter dominated modes depend sensitively on the mass
of dark-matter particles.
