Gravitational wave asteroseismology of neutron stars with unified EOS: On the role of high-order nuclear empirical parameters

We analyze the sensitivity of nonradial fluid oscillation modes and tidal deformations in neutron stars to high-order nuclear empirical parameters (NEPs). In particular, we study the impact of the curvature and skewness of the symmetry energy ${K}_{\mathrm{sym}}$, ${Q}_{\mathrm{sym}}$, and the skewness of the binding energy in symmetric nuclear matter ${Q}_{\mathrm{sat}}$. As we are interested in the possibility of gravitational wave detection by future interferometers, we consider that the tidal interaction is the driving force for the quadrupolar nonradial fluid oscillations. We also study the correlations between those quantities, which will be useful to understand the strong physics of gravitational wave phenomena. Our main results show that ${K}_{\mathrm{sym}}$ impacts the frequencies of the fundamental mode mainly for low-mass neutron stars. The NEPs ${Q}_{\mathrm{sym}}$ and ${Q}_{\mathrm{sat}}$ affect the fundamental modes of intermediate and heavy neutron stars, respectively. In the case of the first pressure mode, ${K}_{\mathrm{sym}}$ shows a small effect, while ${Q}_{\mathrm{sat}}$ shows a considerable decrease in this oscillation mode independent of the neutron star mass. Similarly, for tidal deformability, the NEPs ${Q}_{\mathrm{sat}}$ and ${Q}_{\mathrm{sym}}$ show a more significant impact than ${K}_{\mathrm{sym}}$. Given the impact of the NEPs on gravitational wave phenomena and the currently large uncertainties of these parameters, the prospect of higher sensitivity in future gravitational wave detectors promises a possible new tool to constrain high-order NEPs.