Radial and Non-Radial Oscillations of Protoneutron Stars with Hyperonic Composition

TL;DR

This study analyzes the oscillation modes of protoneutron stars with hyperonic matter, developing a universal relation for mode frequencies that aids in understanding their internal composition and evolution.

Contribution

It introduces a robust, temperature-sensitive universal relation involving the moment of inertia and a new parameter, improving asteroseismology of PNSs across all evolutionary stages.

Findings

Hyperonic composition raises oscillation frequencies.

The new universal relation shows strong agreement across phases.

Differences in frequency separation serve as observational diagnostics.

Abstract

This paper explores radial and non-radial oscillations of protoneutron stars (PNSs) as they evolve from hot, neutrino-rich configurations through deleptonization to cold, catalyzed states. The equation of state (EoS) is modeled using a density-dependent relativistic mean-field framework, with stellar evolution characterized by changes in entropy and lepton fraction. Both nucleonic and hyperonic compositions are considered. Non-radial $f$- and $p_1$-mode oscillations are computed using both the Cowling approximation and the full General Relativistic framework. Trapped neutrinos initially increase the error in the Cowling approximation for $f$-modes, which decreases during deleptonization and rises again in the cold phase. In contrast, $p_1$-mode errors peak during intermediate stages due to evolving pressure and density gradients. The emergence of hyperons modestly raises oscillation frequencies in both modes. Existing universal relations for $f$-mode frequency and damping time lack model independence for PNSs, motivating a more robust relation. In particular, our proposed universal relation involving the moment of inertia and $\tilde{\eta}$ shows strong agreement across all evolutionary phases, offering a temperature-sensitive, model-independent scaling for asteroseismology. Radial oscillations of a $1.4\,M_\odot$ PNS are also studied for different EoSs. Our results show that displacement ($\xi$) and pressure perturbation ($\eta$) profiles are highly sensitive to thermal state, composition, and compactness. Hyperonic stars show higher frequencies, altered node structures, and stronger pressure perturbations due to EoS softening. Differences in frequency separation $\Delta \nu_n$ and fundamental frequency $\nu_0$ between nucleonic and hyperonic models provide clear observational diagnostics for probing the interiors of PNSs and constraining the EoS of dense matter.