Breaking of universal relationships of axial wI-modes in hybrid stars: rapid and slow hadron-quark conversion scenarios

Multi-messenger astronomy with gravitational waves is a blooming area whose limits are not clear. After the first detection of binary black hole merger and the famous event GW170817 and its electromagnetic counterpart, the compact-object astrophysical community is starting to grasp the physical implications of such event and trying to improve numerical models to compare with future observations. Moreover, recent detections made by the NICER collaboration increased the tension between several theoretical models used to describe matter in the inner core of compact objects. In this paper, we focus on quadrupolar purely spacetime wI-modes of oscillating compact objects described using a wide range of hybrid equations of state able to include several theoretical possibilities of exotic matter in the inner core of such stars. We study the case in which a sharp first order hadron-quark phase transition occurs and explore the scenarios of rapid and slow phase conversions at the interface. We put special attention on the validity of universal relationships for the oscillation frequency and damping time that might help unravel the mysteries hidden at the inner cores of compact objects. We show that, within the slow conversion regime where extended branches of hybrid stars appear, universal relationships for wI-modes proposed in the literature do not hold.