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, $\dot{\Omega}_{\rm c}$, and two phenomenological parameters quantifying the vortex-nucleus pinning force: a crust-superfluid angular velocity lag threshold, $X_{\rm cr}$, and a reference unpinning rate, $\lambda_0$. A Bayesian analysis of 541 glitches in 177 pulsars, with $N_{\rm g} \geq 1$ events per pulsar, yields $X_{\rm cr} = 0.15^{+0.09}_{-0.04} \, {\rm rad \, s^{-1}}$, $\lambda_{\rm ref} = 7.6^{+3.7}_{-2.6} \times 10^{-8} \, {\rm s^{-1}}$, and $a = -0.27^{+0.04}_{-0.03}$ assuming the phenomenological rate law $\lambda_0 = \lambda_{\rm ref} [\tau/(1 \, {\rm yr})]^a$, where $\tau$ denotes the characteristic spin-down age. The results are broadly similar, whether one includes or excludes quasiperiodic glitch activity, giant glitches, or pulsars with $N_{\rm g}=0$, up to uncertainties about the completeness of the sample and the total observation time per pulsar. The $X_{\rm cr}$ and $\lambda_0$ estimates are consistent with first-principles calculations based on nuclear theory, e.g. in the semiclassical local density approximation.