Entrainment in Superfluid Neutron-Star Crusts: Hydrodynamic Description and Microscopic Origin

Abstract

In spite of the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star cannot flow freely, and is entrained by the nuclear lattice similarly to laboratory superfluid atomic gases in optical lattices. The role of entrainment on the neutron superfluid dynamics is reviewed. For this purpose, a minimal hydrodynamical model of superfluidity in neutron-star crusts is presented. This model relies on a fully four-dimensionally covariant action principle. The equivalence of this formulation with the more traditional approach is demonstrated. In addition, the different treatments of entrainment in terms of dynamical effective masses or superfluid density are clarified. The nuclear energy density functional theory employed for the calculations of all the necessary microscopic inputs is also reviewed, focusing on superfluid properties. In particular, the microscopic origin of entrainment and the different methods to estimate its importance are discussed.

Return of the Big Glitcher: NICER timing and glitches of PSR J0537−6910

“…Subsequently, Ho et al (2015Ho et al ( , 2017 show that, by combining a pulsar's glitch activity with a measurement of true age or surface temperature, one can obtain valuable constraints on properties of the superfluid and even measure the mass of the pulsar; for the A g and estimated age of PSR J0537−6910, the pulsar's mass turns out to be much higher than the canonical 1.4M ⊙ . Very recently, Sauls et al (2020) suggest superfluid entrainment may not be as strong as found by Chamel (2012Chamel ( , 2017. More work is needed to resolve the issue.…”

Superfluidity in nuclear systems and neutron stars

“…The hydrodynamic models of entrainment assume that the coherence length of the neutron superfluid is much smaller than other scales in the problem, in particular, the size of the nucleus. On the other hand, band-structure calculations (analogous to those in the theory of solids) predict a strong entrainment, with the density of superfluid neutrons reduced by an order of magnitude [412][413][414]. While these results were obtained in the limit where the pairing can be neglected compared to other scales, specifically the depth of the lattice potential, a semi-analytical model [415] that includes pairing correlations suggests a rather weak entrainment.…”

“…Of particular interest for the phenomenology of neutron stars is the hydrodynamical limit, in which case a crustal layer can be considered as a two-fluid system consisting of the unbound neutron superfluid and plasma comprising crustal nuclei and electrons [411][412][413][414][415][416][417][418]. The normal fluid is locked into the motion of the star by the magnetic field.…”

Entrainment effects in neutron-proton mixtures within the nuclear energy-density functional theory: Low-temperature limit

“…The neutron superfluid is thus effectively entrained by the crust (see, e.g., Ref. [21] for a recent review). Likewise, neutrons and protons in the core are mutually coupled by nondissipative entrainment effects of the kind originally discussed by Andreev and Bashkin in the context of superfluid 4 He- 3 He mixtures [22]: The mass current ρ q ρ q ρ q of one nucleon species (q = n, p for neutron, proton, respectively) is found to depend on the superfluid velocities V q V q V q of both species, i.e.,…”