Impact of the equation of state on $f$- and $p$- mode oscillations of neutron stars

TL;DR

This study explores how different equations of state for neutron-star matter influence the oscillation modes, frequencies, and damping times, revealing strong correlations with matter pressure and symmetry energy parameters.

Contribution

It provides a detailed analysis of the impact of the equation of state on neutron star oscillations using representative models, highlighting correlations and approximation accuracies.

Findings

Strong correlation between oscillation frequencies and matter pressure.

Frequency of the $p_1$-mode correlates with symmetry energy slope $L_0$.

Cowling approximation accuracy varies with star mass and mode.

Abstract

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_\odot$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $\beta$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density $\rho_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1.4M_\odot$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $\beta$-equilibrated pressure at density $\rho_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30\% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15\% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.