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, $\dot{\hat{I}}{\text{c◯}}_{\mathrm{c}}$, and two phenomenological parameters quantifying the vortex-nucleus pinning force: a crust-superfluid angular velocity lag threshold, $X_{\mathrm{cr}}$, and a reference unpinning rate, $\hat{I}{»}_0$. A Bayesian analysis of 541 glitches in 177 pulsars, with $N_{\mathrm{g}}\ge 1$ events per pulsar, yields $X_{\mathrm{cr}}=0.15_{-0.04}^{+0.09}\mathrm{rad}{\mathrm{s}}^{-1}$, $\hat{I}{»}_{\mathrm{ref}}=7.6_{-2.6}^{+3.7}\times 10^{-8}{\mathrm{s}}^{-1}$, and $a=-0.27_{-0.03}^{+0.04}$ assuming the phenomenological rate law $\hat{I}{»}_0=\hat{I}{»}_{\mathrm{ref}}[\ddot{I}„/(1\mathrm{yr}){]}^a$, where $\ddot{I}„$ denotes the characteristic spin-down age. The results are broadly similar, whether one includes or excludes quasiperiodic glitch activity, giant glitches, or pulsars with $N_{\mathrm{g}}=0$, up to uncertainties about the completeness of the sample and the total observation time per pulsar. The $X_{\mathrm{cr}}$ and $\hat{I}{»}_0$ estimates are consistent with first-principles calculations based on nuclear theory, e.g. in the semiclassical local density approximation.

34 pages, 6 figures, accepted for publication in the Astrophysical Journal