We explore the possibility of phase transitions between different quark matter phases occurring within quark stars, giving rise to the hybrid quark stars (HybQSs). First, we obtain the generic phase diagram of possible mass-radius relation forms for the HybQSs. Then, utilizing a well-established general parametrization of interacting quark matter, we construct quark star models featuring sharp first-order quark-quark phase transitions of various types, in contrast to the hadron-quark transition in conventional hybrid stars. We systematically investigate how recent observations, such as the pulsar mass measurement $M_{\mathrm{TOV}}\gtrsim 2M_{\odot }$ and the GW170817’s tidal deformability bound ${\mathrm{\Lambda }}_{1.4M_{\odot }}<800$, constrain the viable parameter space. We also identified twin stars in some of the HybQS parameter space. Furthermore, we found that the quark-quark phase transitions in hybrid quark stars may also cause the deviation from the approximate universal relation between the dominant postmerger frequency $f_{\mathrm{peak}}$ and tidal deformability ${\mathrm{\Lambda }}_{1.35M_{\odot }}$, which was previously believed to only be caused by the hadron-quark phase transitions in hybrid neutron stars. This work unveils new possibilities of phase transitions and the resulting new types of compact stars in realistic astrophysical scenarios.

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• Gravitational waves
• Neutron stars & pulsars