Measuring the Vortex−Nucleus Pinning Force from Pulsar Glitch Rates

Abstract

Superfluid vortex avalanches are one plausible cause of pulsar glitch activity. If they occur according to a state-dependent Poisson process, the measured long-term glitch rate is determined by the spin-down rate of the stellar crust, ${\dot{{\rm{\Omega }}}}_{c}$ , and two phenomenological parameters quantifying the vortex−nucleus pinning force: a crust−superfluid angular velocity lag threshold, X _cr , and a reference unpinning rate, λ _0 . A Bayesian analysis of 541 glitches in 177 pulsars, with N _g ≥ 1 events per pulsar, yields ${X}_{\mathrm{cr}}={0.15}_{-0.04}^{+0.09}\,\mathrm{rad}\,{{\rm{s}}}^{-1}$ , ${\lambda }_{\mathrm{ref}}={7.6}_{-2.6}^{+3.7}\times {10}^{-8}\,{{\rm{s}}}^{-1}$ , and $a=-{0.27}_{-0.03}^{+0.04}$ assuming the phenomenological rate law λ _0 = λ _ref [ τ /(1 yr)] ^a , where τ denotes the characteristic spin-down age. The results are broadly similar, whether one includes or excludes quasiperiodic glitch activity, giant glitches, or pulsars with N _g = 0, up to uncertainties about the completeness of the sample and the total observation time per pulsar. The X _cr and λ _0 estimates are consistent with first-principles calculations based on nuclear theory, e.g., in the semiclassical local density approximation.

Keywords

• Pulsars
• Neutron stars
• Stellar rotation
• Nuclear astrophysics