Probing hybrid stars with gravitational waves via interfacial modes

One of the uncertainties in nuclear physics is whether a phase transition between hadronic matter to quark matter exists in supranuclear equations of state. Such a feature can be probed via gravitational-wave signals from binary neutron star inspirals that contain information of the induced tides. The dynamical part of the tides is caused by the resonance of pulsation modes of stars, which causes a shift in the gravitational-wave phase. In this paper, we investigate the dynamical tides of the interfacial mode (i-mode) of spherical degree l = 2, a nonradial mode caused by an interface associated with a quark-hadron phase transition inside a hybrid star. In particular, we focus on hybrid stars with a crystalline quark matter core and a fluid hadronic envelope. We employ a hybrid method which consists of a general relativistic calculation of the stellar structure, together with Newtonian formulations of tidal couplings and mode excitations. We find that the resonant frequency of such i-modes typically ranges from 300 Hz to 1500 Hz, and the frequency increases as the shear modulus of the quark core increases. We next estimate the detectability of such a mode with existing and future gravitational-wave events from the inspiral waveform with a Fisher analysis. We find that GW170817 and GW190425 have the potential to detect the i-mode if the quark-hadron phase transition occurs at a sufficiently low pressure and the shear modulus of the quark matter phase is large enough. We also find that the third-generation gravitational-wave detectors can further probe the i-mode with intermediate transition pressure. Finally, we check our hybrid method against a fully-Newtonian analysis and find that the two results can be off by a factor of a few. Thus, the results presented here should be valid as an order-of-magnitude estimate and provide a new, interesting direction for probing the existence of quark core inside a neutron star using the i-mode. A full general relativistic formalism, however, needs to be pursued for further analysis.