Effects of inner crusts on $g$-mode oscillations in neutron stars

TL;DR

This study explores how neutron star crusts influence $g$-mode oscillations, revealing correlations with nuclear matter properties and potential for gravitational wave-based measurements of nuclear symmetry energy slope.

Contribution

It provides the first detailed analysis of crust and core $g$-mode interactions and their dependence on nuclear symmetry energy slope $L$, including the avoid-crossing phenomenon.

Findings

Crust $g$-mode frequencies are insensitive to density functional at densities above neutron drip.

Core $g$-mode frequencies increase with the slope of nuclear symmetry energy $L$.

Correlation between $g_1$ mode and $L$ enables potential gravitational wave measurements.

Abstract

In this work we investigate the influence of neutron stars' crusts on the non-radial $g$-mode oscillations and examine their correlations with nuclear matter properties fixed by adopting 10 different relativistic density functionals. At subsaturation densities, neutron star matter takes non-uniform structures and form the crusts. We find that the Brunt-V\"{a}is\"{a}l\"{a} (BV) frequency increases significantly at densities slightly above the neutron drip density (i.e., neutron stars' inner crusts), which leads to crust $g$-mode oscillations with their frequencies insensitive to the adopted density functional. At larger densities, BV frequency increases as well due to the core-crust transitions and emergence of muons, which lead to core $g$-mode oscillations. It is found that the obtained core $g$-mode frequencies generally increase with the slope of nuclear symmetry energy $L$, which eventually intersect with that of the crust $g$ modes adopting large enough $L$. This leads to the avoid-crossing phenomenon for the global $g$ modes that encompass contributions from both the crust and core. The correlation between the global $g_1$ mode and $L$ is identified for neutron stars with masses $M\gtrsim 1.4\ M_{\odot}$, which enables the measurements of $L$ based on gravitational wave observations. In our future study, the effects of the discontinuities in density or shear modulus should be considered, while the temperature, rotation, magnetic field, and superfluid neutron gas in neutron stars could also play important roles.