Probing hadron-quark phase transition in twin stars using $f$-modes

Abstract

Although it is conjectured that a phase transition from hadronic to deconfined quark matter in the ultrahigh-density environment of Neutron Stars (NS), the nature of phase transition remains an unresolved mystery. Furthermore, recent efforts reveal that the finite surface tension effects can lead to a mixed phase with different geometric shapes (so-called "pasta" phases), leading to a smooth phase transition from hadronic to quark matter in the NS interior. Depending on whether there is a strong or a pasta-induced smooth first-order phase transition, one may expect a third family of stable, compact stars or "twin stars" to appear, with the same mass but different radii compared to NSs. The possibility of identifying twin stars using astrophysical observations has been a subject of interest. This study investigates the potential of probing the nature of the hadron-quark phase transition through future gravitational wave (GW) detections from fundamental ($f$-) mode oscillations in Neutron Stars. Using a newly developed model that parametrizes the hadron-quark phase transition with ``pasta phases," we calculate $f$-mode characteristics within a full general relativistic framework. We then use Universal Relations in GW asteroseismology to derive stellar properties from the detected mode parameters. Our findings suggest that detecting GWs from $f$-modes with third-generation GW detectors offers a promising scenario for the existence of twin stars. However, we also estimate various uncertainties in determining the mode parameters and conclude that these uncertainties make it more challenging to identify the nature of the hadron-quark phase transition.