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$g$ -mode frequencies in cold neutron stars and nuclear saturation parameters

Hajime Sotani ^1,2,3,4,* and Hajime Togashi ⁵

¹Department of Mathematics and Physics, Kochi University, Kochi, 780-8520, Japan
²RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Wako 351-0198, Japan
³Kochi University of Technology, Kochi, 780-8515, Japan
⁴Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
⁵Department of Physics, Kyoto University, Kyoto 606-8502, Japan

^*Contact author: sotani@yukawa.kyoto-u.ac.jp

Phys. Rev. D 114, 043067 – Published 25 August, 2026

DOI: https://doi.org/10.1103/c4yl-hdkm

Abstract

Oscillation frequencies excited in neutron stars are crucial for extracting their interior properties. In addition to the fundamental and pressure modes, the gravity ( $g$ -)modes can be excited even in zero-temperature stellar models due to the composition gradient. In this study, we systematically study the $g$ -mode frequencies, focusing on the nucleonic equation of state. Then, we derive an empirical relation for the first $g$ -mode frequencies as a function of the stellar compactness and the combination of the nuclear saturation parameters, $η_{0} \equiv L / K_{0}$ , where $K_{0}$ and $L$ denote the incompressibility of symmetric nuclear matter and the density dependence of the nuclear symmetry energy, respectively. If an observed first $g$ -mode frequency significantly deviates from our empirical relation, it may indicate the emergence of additional degrees of freedom or new compositions inside the star.

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Article Text

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