Nuclear constraints on properties of neutron star crusts

The transition density $ρ_{t}$ and pressure $P_{t}$ at the inner edge separating the liquid core from the solid crust of neutron stars are systematically studied using a modified Gogny (MDI) and 47 popular Skyrme interactions within well established dynamical and thermodynamical methods. It is shown that the widely used parabolic approximation to the full Equation of State (EOS) of isospin asymmetric nuclear matter may lead to huge errors in estimating the ρ_{t} and P_{t}, especially for stiffer symmetry energy functionals $E_{sym}(ρ)$. The ρ_{t} and P_{t} decrease roughly linearly with the increasing slope parameter $L$ of the $E_{sym}(ρ)$ using the full EOS within both methods. It is also shown that the thickness, fractional mass and moment of inertia of neutron star crust are all very sensitive to the parameter $L$ through the $ρ_{t}$. Moreover, it is shown that the $E_{sym}(ρ)$ constrained in the same sub-saturation density range as the neutron star crust by the isospin diffusion data in heavy-ion collisions at intermediate energies limits the transition density and pressure to 0.040$ fm^-3}< ρ_{t} < 0.065$ fm^-3 and 0.01 MeV/fm^3 < P_{t} < 0.26$MeV/fm^3, respectively. These constrained values for the transition density and pressure are significantly lower than their fiducial values currently used in the literature. Furthermore, the mass-radius relation and several other properties closely related to the neutron star crust are studied by using the MDI interaction. It is found that the newly constrained$ρ_t$and$P_t$together with the earlier estimate of$ΔI/I>0.014$for the crustal fraction of the moment of inertia of the Vela pulsar impose a stringent constraint of R>= 4.7+4.0M/M_sun km for the radius$R$and mass$M$ of neutron stars.

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