Radial Oscillations in Neutron Stars from Unified Hadronic and Quarkyonic Equation of States

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M-circle dot star criterion. We solve the Sturm-Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron star modeled with eight selected unified EoSs from distinct Skyrme-Hartree-Fock, relativistic mean field and quarkyonic models. We compare the behavior of the computed eigenfrequency for an NS modeled with hadronic to one with quarkyonic EoSs while varying the central densities. The lowestorder f-mode frequency varies substantially between the two classes of the EoS at 1.4M(circle dot) but vanishes at their respective maximum masses, consistent with the stability criterion partial derivative M/partial derivative rho c > 0. Moreover, we also compute large frequency separation and discover that higher-order mode frequencies are significantly reduced by incorporating a crust in the EoS.