Probing phase transitions in neutron stars via the crust-core interfacial mode

Gravitational waves emitted from the binary neutron star (BNS) systems can carry information about the dense matter phase in these compact stars. The crust-core interfacial mode is an oscillation mode in a neutron star, and it depends mostly on the equation of state of the matter in the crust-core transition region. This mode can be resonantly excited by the tidal field of an inspiraling-in BNS system, thereby affecting the emitted gravitational waves and hence could be used to probe the equation of state in the crust-core transition region. In this work, we investigate, in detail, how the first-order phase transition inside the neutron star, if it exists, affects the properties of the crust-core interfacial mode using a Newtonian fluid perturbation theory on a general relativistic background solution of the stellar structure. Two possible types of phase transitions are considered: (1) the phase transitions happen in the fluid core but near the crust-core interface, which results in density discontinuities, and (2) the strong interaction phase transitions in the dense core (as in the conventional hybrid star case). We study how these phase transitions affect the properties of the neutron star oscillation mode excited at the interface, where there exists a shear modulus discontinuity (interfacial mode). In particular, the former phase transition has a minor effect on the mass-radius relation, and the adiabatic tidal deformability, but has the potential to significantly affect the interfacial mode frequency and thereby could be probed using gravitational waves. For the BNS systems, we discuss the possible observational signatures of these phase transitions in the gravitational waveforms and their detectability. Our work enriches the exploration of the physical properties of the crust-core interfacial mode and provides a promising method for probing the phase transition using the seismology of a compact star.