  We estimate the long-lasting gravitational wave (GW) emission of compact dark
objects following a binary neutron-star (NS) merger. We consider compact dark
objects, which initially reside in the centers of NSs and which may consist of
self-interacting dark matter (DM). By approximating the compact dark objects as
test particles, we model the merging of NS binaries hosting DM components with
three-dimensional relativistic simulations. Our simulation results suggest that
the DM components remain gravitationally bound and orbit inside the merger
remnant with orbital separations of typically a few km. The subsequent orbital
motion of the DM components generates a GW signal with frequencies in the range
of a few kHz. When considering a range of different binary masses and
high-density equations of state (EoS), we find that the GW frequency of the
orbiting DM components scales with the compactness of NSs. Similarly, we find
relations between the DM GW frequency and the dominant postmerger GW frequency
of the stellar fluid or the tidal deformability, which quantifies EoS effects
during the binary inspiral. Hence, a measurement of these quantities can be
used to specify the frequency range of the GW emission by DM. Under the
assumption that GW back reaction is the only relevant dissipative process, the
GW signal may last between seconds and years depending on the mass of the DM
component. We estimate the detectability of the GW signals and find that DM
components in NS mergers may only be detectable with existing and projected GW
instruments if the dark objects are as massive as about 0.01 to 0.1 M_sun. We
emphasize that the GW emission is limited by the lifetime of the remnant. A
forming black hole will immediately swallow the DM objects because their orbits
are smaller than the innermost stable circular orbit of the black hole.
