Exploring Radial Oscillations in Slow Stable and Hybrid Neutron Stars

In the era of gravitational wave astronomy, radial oscillations hold significant potential for not only uncovering the microphysics behind the internal 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 radial perturbations in order to explore the stability of these stars. Unlike other literature where the fluid elements are assumed to be in chemical equilibrium, we consider the out-of-equilibrium effects on the chemical composition of fluid elements for the calculation of radial modes. Taking these considerations into account, 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 the out-of-equilibrium matter distribution scenario, offering insights into its dynamic variations. We also demonstrate that this approach extends the stable branches of stellar models, enabling stars to sustain stable higher-order mass doublets, shedding some light on observation and existence of PSR J0740+6620.