Band structure effects for dripped neutrons in neutron star crust

Abstract

Abstract. The outer layers of a neutron star are supposed to be formed of a solid Coulomb lattice of neutron rich nuclei. At densities above neutron drip density (about one thousandth of nuclear saturation density), this lattice is immersed in a neutron fluid. Bragg scattering of those dripped neutrons by the nuclei which has been usually neglected is investigated, within a simple mean field model with Bloch type boundary conditions. The main purpose of this work is to provide some estimates for the entrainment coefficients, as required for hydrodynamical two fluid simulations of neutron star crust [1,2], which relate the momentum of one fluid to the particle currents of the other two fluids [3]. The implications for the equilibrium neutron star crust structure are also briefly discussed.

Effect of BCS pairing on entrainment in neutron superfluid current in neutron star crust

“…This prediction has now been confirmed by an analysis [7] based on the phenomenological model of Oyamatsu et al [26] where values as large as m ⋆ /m ∼ 15 has been found at a baryon density n b = 0.03 fm −3 . Our present analysis indicates that this conclusion will not be significantly affected by taking the relevant pairing gap ∆ into account.…”

“…Recent numerical work [7] has shown that this treatment implies an enormous enhancement by the entrainment of the effective mass of the free neutrons in the middle layers of the inner crust (a result that contrasts with the rather moderate diminution predicted for the effective neutron mass in the deeper core layers). The purpose of the present work is to evaluate the adjustments -which turn out to be small -that will result from allowance for the superfluid pairing of the neutrons.…”

“…Since (particularly for the middle layers of a neutron star crust, where the effective mass enhancement is likely [6,7] to be most important) we are still far from having a sufficient knowledge of the solutions ϕ kα {r} for the independent particle model, it will evidently take some time before we can hope to obtain a complete evaluation of the solutions for the coupled equations for ϕ 0 kα {r} and ϕ 1 kα {r} using an accurate estimate of the coupling coefficient ∆{r} . In the meanwhile, as an immediately available approximation, offering the best that can be hoped for as a provisional estimate in the short run, we can use an ansatz of the standard BCS kind, which means adopting the prescription U kα,lβ = cos θ kα δ kl δ αβ , V kα,lβ = sin θ kα δ −k,l δ αβ .…”

“…The salient conclusion to be drawn from all this work is that in these homogeneous fluid layers the effective mass of the neutron will be significantly but not enormously reduced (by several tens of percent) below its ordinary bare mass value. The present article is part of a newer program of work [6,7] concerned with the previously unstudied problem of evaluating what turns out to be a much more substantial effective mass modification that is obtained from the corresponding entrainment coefficients in the crust at subnuclear densities, above the neutron drip threshold (at about 10 11 g/cm 3 ). In these layers, relativistic corrections are insignificant but the issue is complicated by the microscopic inhomogeneity of the medium, in which some neutrons can still flow freely but protons are confined to atomic nuclei.…”

“…The use of appropriate Bloch type periodicity conditions is routine in terrestrial solid state physics [17], but has so far been applied to neutron star matter only in a simplified zero temperature independent particle treatment [6,7] (of the kind applicable well below the Fermi temperature, but most appropriate for a young neutrons star that has not yet fallen below the critical temperature for the onset of superfluidity) for which the neutrons are considered to move as independent particles without allowance for the pairing interactions responsible for the superfluid energy gap that (in cool mature neutron stars) allows the currents to persist.…”