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In the era of gravitational wave astronomy, radial oscillations holdsignificant potential for not only uncovering the microphysics behind theinternal structure but also investigating the stability of neutron stars (NSs).We start by constructing families of static NSs following nucleonic,quarkyonic, and hybrid equations of state and then subject them to radialperturbations in order to explore the stability of these stars. Unlike otherliterature where the fluid elements are assumed to be in chemical equilibrium,we consider the out-of-equilibrium effects on the chemical composition of fluidelements for the calculation of radial modes. Taking these considerations intoaccount, we observe that the sound speed ($c^2_s$) and adiabatic index($\gamma$) avoid singularities and discontinuities over the equilibrium case.We elucidate the response of the fundamental radial modes by examining theout-of-equilibrium matter distribution scenario, offering insights into itsdynamic variations. We also demonstrate that this approach extends the stablebranches of stellar models, enabling stars to sustain stable higher-order massdoublets, shedding some light on observation and existence of PSR J0740+6620.

Exploring Radial Oscillations in Slow Stable and Hybrid Neutron Stars