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Spin symmetry energy and equation of state of spin-polarized neutron star matter

Equation of states (EOS) of the spin-polarized nuclear matter (NM) is studied within the Hartree-Fock (HF) formalism using the realistic density dependent nucleon-nucleon interaction. With a nonzero fraction $Δ$ of spin-polarized baryons in NM, the spin- and spin-isospin dependent parts of the HF energy density give rise to the \emph{spin symmetry} energy that behaves in about the same manner as the \emph{isospin symmetry} energy, widely discussed in literature as the nuclear symmetry energy. The present HF study shows a strong correlation between the spin symmetry energy and nuclear symmetry energy over the whole range of baryon densities. The important contribution of the spin symmetry energy to the EOS of the spin-polarized NM is found to be comparable with that of the nuclear symmetry energy to the EOS of the isospin-polarized or asymmetric (neutron-rich) NM. Based on the HF energy density, the EOS of the spin-polarized ($β$-stable) np$eμ$ matter is obtained for the determination of the macroscopic properties of neutron star (NS). A realistic density dependence of the spin-polarized fraction $Δ$ have been suggested to explore the impact of the spin symmetry energy to the gravitational mass $M$ and radius $R$, as well as the tidal deformability of NS. Given the empirical constrains inferred from a coherent Bayesian analysis of gravitational wave signals of the NS merger GW170817 and the observed masses of the heaviest pulsars, the strong impacts of the spin symmetry energy $W$, nuclear symmetry energy $S$, and nuclear incompressibility $K$ to the EOS of nucleonic matter in magnetar were revealed.