Knock-on processes in superfluid vortex avalanches and pulsar glitch statistics

TL;DR

This paper develops a statistical framework for neutron star glitches, demonstrating that vortex unpinning must involve knock-on processes to reproduce observed broad glitch size distributions, and introduces a formalism for future research.

Contribution

It introduces a new statistical model incorporating knock-on processes to explain pulsar glitch size distributions, moving beyond independent vortex unpinning assumptions.

Findings

Independent vortex unpinning yields narrow Gaussian size distributions.

Knock-on processes produce scale-invariant vortex avalanches with power-law distributions.

Fine-tuning between temperature and spin-down torque affects avalanche behavior.

Abstract

A framework is presented for a statistical theory of neutron star glitches, motivated by the results emerging from recent Gross-Pitaevskii simulations of pinned, decelerating quantum condensates. It is shown that the observed glitch size distributions cannot be reproduced if superfluid vortices unpin independently via a Poisson process; the central limit theorem yields a narrow Gaussian for the size distribution, instead of the broad, power-law tail observed. This conclusion is not altered fundamentally when a range of pinning potentials is included, which leads to excavation of the potential distribution of occupied sites, vortex accumulation at strong pinning sites, and hence the occasional, abnormally large glitch. Knock-on processes are therefore needed to make the unpinning rate of a vortex conditional on the pinning state of its near and/or remote neighbours, so that the Gaussian size distributions resulting generically from the central limit theorem are avoided. At least two knock-on processes, nearest- neighbour proximity knock-on and remote acoustic knock-on, are clearly evident in the Gross-Pitaevskii simulation output. It is shown that scale-invariant (i.e. power-law) vortex avalanches occur when knock-on is included, provided that two specific relations hold between the temperature and spin-down torque. This fine tuning is unlikely in an astronomical setting, leaving the overall problem partly unsolved. A state-dependent Poisson formalism is presented which will form the basis of future studies in this area.