Pinning and Binding Energies for Vortices in Neutron Stars: Comments on Recent Results

TL;DR

This paper analyzes the conditions under which vortex pinning energies in neutron star crusts can be approximated by binding energies, highlighting that current quantum calculations are only valid in very dilute, outer regions and are not predictive for glitch theories.

Contribution

The study clarifies the limitations of quantum calculations of vortex energies, emphasizing the need for more accurate models in denser regions of neutron star crusts.

Findings

Dilute limit for pinning energy approximation is only achieved at large Wigner-Seitz cell radii (>55 fm).

Current quantum calculations are only applicable to the outermost low-density crust regions.

Results suggest existing calculations are not predictive for neutron star glitch models.

Abstract

We investigate when the energy that pins a superfluid vortex to the lattice of nuclei in the inner crust of neutron stars can be approximated by the energy that binds the vortex to a single nucleus. Indeed, although the pinning energy is the quantity relevant to the theory of pulsar glitches, so far full quantum calculations have been possible only for the binding energy. Physically, the presence of nearby nuclei can be neglected if the lattice is dilute, namely with nuclei sufficiently distant from each other. We find that the dilute limit is reached only for quite large Wigner-Seitz cells, with radii > 55 fm; these are found only in the outermost low-density regions of the inner crust. We conclude that present quantum calculations do not correspond to the pinning energies in almost the entire inner crust and thus their results are not predictive for the theory of glitches.