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We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ 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 lowest-order f-mode frequency varies substantially between the two classes of the EoS at 1.4 M⊙ but vanishes at their respective maximum masses, consistent with the stability criterion ∂M/∂ρc>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.

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which is consistent with finite nuclei and nuclear matter properties and supports the ≥ 2M star criterion. We solve the Sturm-Liouville problem to compute oscillation of f -mode frequency and their eigenfunction for neutron star modelled with six selected unified EoSs from two distinct Skyrme-Hartree Fock and Relativistic Mean-Field models. The calculated eigenfunction reveals the damped harmonic motion varying with the frequencies corresponding to EoS and with different central densities. We check the variation of f -mode frequency of oscillation with different quantities like central density, mass, average density and compactness of the neutron star. In particular, we derived an empirical relation for the frequency of f -mode scaled with central density as a function of the square of the average density and discovered a linear trend.