D. Dey, Jeet Amrit Pattnaik, R. N. Panda, S. K. Patra

The gravitational wave $ω$ mode spectrum presents a unique window into the dense interior of neutron stars, probing physics inaccessible to electromagnetic observations. This work investigates the $ω$ modes of compact stars composed of quarkyonic matter. The quarkyonic model, which describes a cross-over transition between nucleonic and quark matter treated as quasi-particles, is formulated within the Relativistic Mean-Field (RMF) theory using the G3 and IOPB-I parameterizations. This core is surrounded by a mantle of hadronic matter, creating a multicomponent stellar interior. The overall Equation of State (EOS) is governed by two key parameters: the transition density ($n_t$), the QCD confinement scale ($Λ_{\rm cs}$), which are varied to construct models consistent with current astrophysical constraints on mass and radius. We compute the complex eigenfrequencies (damped oscillations) of the fundamental and first excited $ω$ modes using the phase-amplitude method within a full general relativistic framework. Our simulations reveal that the admixed quarkyonic structure produces a unique $ω$ mode signature, distinctly different from pure hadronic or hybrid stars. The spectrum exhibits a strong, degenerate dependence on the EOS, where the stiffening effect of the quarkyonic matter influences oscillation frequencies and damping times in a characteristic manner. We also demonstrate that $ω$ mode frequencies for quarkyonic stars follow approximate universal relations, largely independent of the EOS.