Reaction-constrained composition $g$-modes in neutron stars with antikaon condensates, hyperons, and $\Delta(1232)$ resonances

Prashant Thakur; Ishfaq Ahmad Rather

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arXiv · 2607.20693

Reaction-constrained composition $g$-modes in neutron stars with antikaon condensates, hyperons, and $\Delta(1232)$ resonances

Prashant Thakur·Ishfaq Ahmad Rather

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Abstract

We study core composition $g_1$ modes of cold, nonrotating neutron stars containing antikaon condensates, hyperons, and $\Delta(1232)$ baryons and present, to our knowledge, the first calculation in full general relativity of the continuous-composition $g_1$-mode frequency and gravitational-wave damping time for stars with a $K^-$ condensate. Using the BigApple relativistic mean-field equation of state, we compute frequencies, damping times, and frozen-composition tidal overlaps, and identify the buoyancy channels with a species-resolved Ledoux decomposition validated by mode-frequency sensitivities. We compare fully frozen matter with a fast-$K$ limit for $n\leftrightarrow p+K^-$ and a strong-equilibrium limit for the $\Delta$ quartet. Fast-$K$ equilibration retains $36\%$--$44\%$ of the peak local kaon buoyancy and $65.7\%$--$73.4\%$ of the frozen terminal-configuration frequencies, while increasing the damping times by factors of $14.4$--$31.8$; the mode remains above the nucleonic band. Strong $\Delta$ equilibration removes most of the direct $\Delta$-induced enhancement, returning the $N\Delta$ mode toward the nucleonic band, whereas the high-frequency $NY\Delta$ branch survives through the frozen $\Lambda$ gradient. Eigenfunction tracking confirms a continuous $g_1$ branch, and representative DD-ME2 calculations reproduce this hierarchy. The direct full-GR frozen-composition phase shifts satisfy $|\Delta\Phi_{g_1}|\leq1.410\times10^{-3}$ rad, a factor of 21 below the $0.03$-rad favorable-event scale for the Einstein Telescope. An exotic species therefore produces a distinct composition mode only if its composition gradient, or a coupled slowly equilibrating gradient, survives over the oscillation period.

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Prashant Thakur, Ishfaq Ahmad Rather. 2026-07-22. Reaction-constrained composition $g$-modes in neutron stars with antikaon condensates, hyperons, and $\Delta(1232)$ resonances. https://arxiv.org/abs/2607.20693

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