  Matter in compact stars is dense enough that transient events within the star
could have sufficiently high energies to produce detectable gravitational waves
(GWs). These GWs could be used to constrain the equation of state (EoS) for
matter in the star and could reveal that there is more than one type of EoS at
play in the population, implying that multiple types of compact stars exist.
One of these types could be quark stars, composed almost entirely of stable
quark matter, and observing GWs is a way to test for the strange matter EoS.
Here we explore the possibility that, if fundamental (f-) mode oscillations in
pulsars are induced by a pulsar glitch, then these oscillations might produce
detectable GWs. We use the existing population of pulsars and their glitches,
as well as a much larger synthesized population, along with 15 EoSs (8 for
neutron stars and 7 for quark stars) to generate frequencies, damping times,
and GW strengths for each. We find that of the EoSs examined, all quark star
EoSs produce narrower distributions of f-mode frequency than neutron star EoSs.
This result, along with other elements of the data, could be used to
differentiate between GWs (or other signals from f-modes) originating from
neutron stars and quark stars and thus could confirm the existence of quark
stars. We also find that GW astronomy is a potentially viable method for
detecting a larger population of pulsars which are not observable
electromagnetically and that future GW observatories have the possibility to
greatly expand this capability.
