Vortex pinning and the elastic response of neutron-star crusts - I. Axisymmetric loading

Abstract

Vortex pinning is central to the standard interpretation of pulsar glitches, but the mechanical load exerted by a pinned vortex array on the solid crust has received less attention than the angular-momentum reservoir itself. We calculate the axisymmetric elastic response of a continuously stratified neutron-star crust to this load using realistic SLy4 and BSk21 stellar backgrounds and composition-dependent Coulomb shear moduli. The superfluid-crust lag sets the Magnus force, while the mesoscopic pinning force of Seveso et al. (2016) provides a local upper bound. At low lag the response is linear; progressive local saturation then produces a broad transition and a finite high-lag envelope. The stress maximum is robustly located at the deep crustal boundary towards the rotation axis, although the local Magnus force vanishes on-axis, showing that the localization is produced by global elastic-gravitational redistribution. Realistic elasticity changes the stress amplitude by 10-20 per cent relative to the common mu=10^-2 P prescription and reverses the SLy4-BSk21 ordering. At a Vela-motivated lag of 10^-2 rad s^-1, the maximum strain is only 3.1 x 10^-5 (SLy4) and 4.7 x 10^-5 (BSk21), remaining below 1.4 x 10^-4 on the formal plateau. A 1.2-2.0 solar-mass scan changes the stress amplitude by only about 20 per cent and leaves the deep-polar localization unchanged. Pinning therefore supplies a structured and astrophysically relevant crustal pre-stress, but cannot by itself break an initially relaxed crust.