Neutron Star Stability beyond the Mass Peak: Assessing the Role of Out-of-equilibrium Perturbations

We investigate the radial stability of neutron stars under conditions where their composition may or may not remain in chemical equilibrium during oscillations. Using different equations of state that include nucleons, hyperons, and/or $Delta$ resonances, we compute stellar configurations and examine their fundamental mode frequencies in two limiting scenarios. In one limit, nuclear reactions are fast enough to maintain chemical equilibrium throughout the pulsation, resulting in a lower adiabatic index, $Gamma_{mathrmÉQ}}$, and softer stellar responses. In the opposite limit, nuclear reactions are too slow to adjust particle abundances during oscillations, yielding a higher index, $Gamma_{mathrm{FR}}$, and stiffer stellar responses. We find that the equilibrium scenario triggers dynamic instability at the maximum mass configuration, whereas the frozen composition scenario allows stable solutions to persist beyond this mass, extending the stable branch. This effect is modest for simpler equations of state, but becomes increasingly pronounced for more complex compositions, where a complex interplay between available degrees of freedom due to the emergence of new particle species and the values of the coupling constants leads to a significant disparity between $Gamma_{mathrmÉQ}}$ and $Gamma_{mathrm{FR}}$. Realistic conditions, in which different nuclear reactions have distinct timescales, will place the effective $Gamma$ between these two extreme values, thereby limiting the length of the extended branch relative to the fully frozen limit studied here. We also explore the astrophysical scenarios in which the extended branch may be populated and outline the multimessenger observations that could reveal its presence. Fil: Canullan Pascual, Martin Oscar. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina Fil: Lugones, Germán. Universidad Federal do Abc; Brasil