The role of adiabatic sound speeds in neutron star radial oscillations and stability

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Abstract
We investigate the impact of adiabatic sound speed on the radial oscillations and stability of neutron stars (NSs), using five representative equations of state (EOSs): three hadronic (FSU2R, HPUC, SINPA) and two hybrid (Gibbs 40, KW 55). The adiabatic case, which assumes fixed particle composition during compression, corresponds to slow reaction scenarios and leads to an extension of the stable branch toward smaller radii and higher compactness, even beyond the maximum mass configuration. This extended regime, known as the “slow stable” branch, remains dynamically stable only when reactions are sufficiently slow. To assess stability, we subject the NSs to radial perturbations and examine their fundamental radial (f-mode) oscillations, identifying the transition point where the mode frequency vanishes. The adiabatic sound speed, compared to the equilibrium sound speed, delays the onset of instability, allowing NSs to sustain stability at higher compactness and thus exhibit smaller radii — a more physically realistic outcome for slow reaction rates. Notably, the delays in the onset of instability are more pronounced for hybrid EOSs than for hadronic ones.

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