Exploring the internal structure of a neutron star and the associated magnetic fields aided by the mass-radius relationship

Abstract

Neutron stars exhibit magnetic fields and densities far beyond those achievable in terrestrial laboratories, offering a natural probe of strongly interacting matter under extreme conditions. Using observationally anchored mass-radius relations and a density profile consistent with established equations of state, we construct a piecewise model that explicitly integrates the neutron-drip line, nuclear-saturation, the electron-dominated halo, and core-crust interfaces. The resulting structure reproduces the stiffness and curvature behavior across the nuclear-pasta regime reported in the literature, validating our treatment of the crust-core transition. From this model, we derive updated moments of inertia, crustal mass fractions, and the effective number of neutrons contributing to the star's magnetic moment. Comparing these quantities with spin-down inferred magnetic dipole moments indicates that the observed magnetic fields of particularly millisecond pulsars can be sustained entirely by the crustal neutron polarization, requiring alignment of only about $\lesssim5.5\%$ ($99\%$ C.L.) of the neutrons in the crust. This finding supports a crust-confined magnetic-field origin for non-magnetar neutron stars, consistent with magneto-thermal evolution studies, and provides a quantitative framework for connecting neutron-star observables to its underlying structure.