Impact of Fermi-surface distortion in a relativistic mean-field model on the moment of inertia and tidal deformability of neutron stars

We have previously shown [R. Rizaldy, A. R. Alfarasyi, A. Sulaksono, and T. Sumaryada, Phys. Rev. C 100, 055804 (2019)] that Fermi-surface distortion can affect nuclear matter and neutron star (NS) properties within the relativistic mean-field formalism. However, our previous results had the caveat that the $k_f/M^{*}<1$ approximation was used. This approximation needs revision for high-density NS cases. This work proposes a more refined approximation in calculating the Fermi-surface distortion correction. We reinvestigate the consequences in nuclear and NS matter. The new expressions of the corresponding nucleon densities, energy density, and pressures are shown. The behavior of the predictions in high-density regions is studied. We found a better convergence of results for higher $\delta$ values than in the previous work. We also found that all recent experimental observations and other calculations constrain the acceptable value of $\delta$ to $\lesssim 0.1$. We also study the impact of Fermi-surface distortion on NS mass, radius, moment of inertia, and tidal deformability. The results are compared to the recent observation data. The impact of the anisotropy of acceptable $\delta$ values still does not profoundly impact a NS's mass and moment of inertia. However, we also observed a substantial effect in tidal deformation properties, such as $\Lambda$ and $k_2$ parameters. Therefore, the signature of Fermi-surface distortion might be detected in observations of gravitational waves.