We calculate the $f$-mode frequency of quark stars using the full general relativity method, and evaluate the tidal overlap with an analogy method incorporating effective general relativistic corrections. We verify the universal relations obtained from conventional neutron stars in the case of quark stars, including the $f{M}_{1.4}–\mathrm{\Lambda }$ and $Q_{f}R/M–\mathrm{\Lambda }$ relations, and explore the cases with different values of parameters of the quark star equation of state. Since quark stars have significantly smaller radii compared to neutron stars in the low-mass range, the ${\omega }_{f}R–\mathrm{\Lambda }$ relation differs between neutron stars and quark stars. This difference has an impact on the dynamical tide, which is the lowest-order effect we know of that can distinguish quark stars and neutron stars from the gravitational wave during the inspiral phase. We calculate the tidal dephasing caused by this effect using the post-Newtonian method and estimate that ${34}_{-16}^{+12}$ events for the Einstein Telescope and ${10}_{-6}^{+5}$ events for Cosmic Explorer are required to distinguish between quark stars and neutron stars at the population level.

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• Gravitational waves
• Neutron stars & pulsars