Measuring the crust-superfluid coupling time-scale for 105 UTMOST pulsars with a Kalman filter

Crust-superfluid coupling plays an important role in neutron star rotation, particularly with respect to timing noise and glitches. Here, we present new timing-noise-based estimates of the crust-superfluid coupling time-scale $\tau$ for 105 radio pulsars in the UTMOST dataset, by Kalman filtering the pulse times of arrival. The 105 objects are selected because they favor a two-component, crust-superfluid model over a one-component model with log Bayes factor $\ln \mathfrak{B}_{\rm BF} \geq 5$. The median estimate of $\tau$ ranges from $10^{4.6\pm0.4}$\,s for PSR J2241$-$5236 to $10^{7.7^{+0.7}_{-0.4}}$\,s for PSR J1644$-$4559 among 28 out of 105 objects with sharply peaked $\tau$ posteriors. A hierarchical Bayesian analysis is performed on 101 out of 105 objects that are canonical (i.e.\ neither recycled nor magnetars) and reside in the populous core of the $\Omega_{\rm c}$-$\dot{\Omega}_{\rm c}$ plane. It returns the population-level scaling $\tau \propto \Omega_{\rm c}^{0.19^{+0.50}_{-0.52}} |\dot{\Omega}_{\rm c}|^{0.18^{+0.18}_{-0.19}}$, where $\Omega_{\rm c}$ and $\dot{\Omega}_{\rm c}$ are the angular velocity and spin-down rate of the crust respectively. The variances of the stochastic crust and superfluid torques are also estimated hierarchically, with $Q_{\rm c} \propto \Omega_{\rm c}^{1.23^{+0.80}_{-0.75}} |\dot{\Omega}_{\rm c}|^{0.49^{+0.27}_{-0.32}}$ and $Q_{\rm s} \propto \Omega_{\rm c}^{0.71^{+0.76}_{-0.78}} |\dot{\Omega}_{\rm c}|^{1.27^{+0.30}_{-0.28}}$ respectively. Implications for the physical origin of crust-superfluid coupling, e.g.\ through mutual friction, are discussed briefly.