Measuring the Vortex−Nucleus Pinning Force from Pulsar Glitch Rates

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, Ω ̇ 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 cr = 0.15 − 0.04 + 0.09 rad s − 1 , λ ref = 7.6 − 2.6 + 3.7 × 10 − 8 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.