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

TL;DR

This study estimates the crust-superfluid coupling time-scale in 105 pulsars using Kalman filtering and Bayesian analysis, revealing population-level scaling laws and stochastic torque variances relevant to neutron star physics.

Contribution

It introduces a novel application of Kalman filtering to pulsar timing data for estimating crust-superfluid coupling timescales and performs hierarchical Bayesian analysis to uncover population-level scaling relations.

Findings

Median coupling time-scale ranges from 10^{4.6} to 10^{7.7} seconds.

Population-level scaling laws for u and torque variances are derived.

Hierarchical Bayesian analysis reveals correlations with spin-down rate and angular velocity.

Abstract

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.