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.

• Received 7 May 2022
• Accepted 22 August 2022

DOI:https://doi.org/10.1103/PhysRevD.106.063005