Entrainment Coefficient and Effective Mass for Conduction Neutrons in Neutron Star Crust: Macroscopic Treatment

Abstract

Phenomena such as pulsar frequency glitches are believed to be attributable to differential rotation of a current of "free" superfluid neutrons at densities above the "drip" threshold in the ionic crust of a neutron star. Such relative flow is shown to be locally describable by adaption of a canonical two fluid treatment that emphasizes the role of the momentum covectors constructed by differentiation of action with respect to the currents, with allowance for stratification whereby the ionic number current may be conserved even when the ionic charge number Z is altered by beta processes. It is demonstrated that the gauge freedom to make different choices of the chemical basis determining which neutrons are counted as "free" does not affect their "superfluid" momentum covector, which must locally have the form of a gradient (though it does affect the "normal" momentum covector characterising the protons and those neutrons that are considered to be "confined" in the nuclei). It is shown how the effect of "entrainment" (whereby the momentum directions deviate from those of the currents) is controlled by the (gauge independent) mobility coefficient K , estimated in recent microscopical quantum mechanical investigations, which suggest that the corresponding (gauge dependent) "effective mass" m ⋆ of the free neutrons can become very large in some layers. The relation between this treatment of the crust layers and related work (using different definitions of "effective mass") intended for the deeper core layers is discussed.

Band structure effects for dripped neutrons in neutron star crust

“…Introducing the dripped or free neutron density n , the effective mass (from which the entrainment coefficients can be obtained [2]) is defined [1] by the simple formula…”

“…In a preceeding work [1,2] we have introduced a macroscopic effective mass m ⋆ relevant for hydrodynamical simulations, such that the momentum of the neutron superfluid is given by the mean neutron velocity times this effective mass in the crust rest frame. In a (super)fluid mixture, in general the momentum of one species is a linear combination of the particle currents of the other components.…”

“…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.…”

Low-energy collective excitations in the neutron star inner crust

“…[5]). Despite the absence of viscous drag, the neutron superfluid can still be coupled to the crust due to non-dissipative entrainment effects arising from elastic Bragg scattering of dripped neutrons by the crystal lattice [6,7]. Recent calculations have shown that in some regions of the inner crust only a very small fraction of dripped neutrons participate in the superfluid dynamics [8,9].…”

Density Functional Calculations for the Neutron Star Matter at Subnormal Density

“…These structures resemble images of various kinds of pasta; gnocchi, spaghetti, lasagna, bucatini or antispaghetti, and Swiss cheese. The nuclear pasta phases consist of periodic Coulomb lattices whose static and dynamical properties could influence the oscillations of neutron star crusts, the cooling process, and the glitch phenomena [4][5][6].…”