Imprints of high-density nuclear symmetry energy on the crustal fraction of neutron star moment of inertia

The density dependence of nuclear symmetry energy $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ remains the most uncertain aspect of the equation of state (EOS) of supradense neutron-rich nucleonic matter. Implications of observational crustal fraction of neutron star (NS) moment of inertia $\mathrm{\Delta }I\mathrm{/}I$ on the $E_{\mathrm{s}\mathrm{y}\mathrm{m}}(\rho )$ are examined in the present work, utilizing an isospin-dependent parameterization of NS EOS. We find that symmetry energy parameters significantly influence the $\mathrm{\Delta }I\mathrm{/}I$, while the EOS of symmetric nuclear matter has a negligible effect. An increase in the slope $L$ and skewness $J_{\mathrm{s}\mathrm{y}\mathrm{m}}$ of symmetry energy results in a larger $\mathrm{\Delta }I\mathrm{/}I$, whereas an increase in the curvature $K_{\mathrm{s}\mathrm{y}\mathrm{m}}$ leads to a reduction in $\mathrm{\Delta }I\mathrm{/}I$. Additionally, we discuss the imprints of observational $\mathrm{\Delta }I\mathrm{/}I$ on the symmetry energy for NSs with masses of 1.0 M${}_{\odot }$ or 1.4 M${}_{\odot }$. Our results indicate that the $\mathrm{\Delta }I\mathrm{/}I$ has the potential to set a lower limit of symmetry energy at densities exceeding $3{\rho }_0$, particularly when $L$ is constrained to values less than $60$ MeV, thereby enhancing our understanding of supradense NS matter.