A Cellular Automaton Model of Pulsar Glitches

TL;DR

This paper presents a cellular automaton model of pulsar glitches based on vortex unpinning, demonstrating that glitch sizes and timings follow power-law and Poisson distributions, respectively, aligning with observational data and self-organized criticality theory.

Contribution

The study introduces a computationally efficient cellular automaton model capturing vortex dynamics in pulsars, reproducing key statistical features of glitches and exploring parameter effects.

Findings

Glitch sizes follow a power-law distribution with exponents between -4.3 and -2.0.

Waiting times between glitches are Poissonian, indicating independent events.

Model parameters influence glitch statistics, matching observational data.

Abstract

A cellular automaton model of pulsar glitches is described, based on the superfluid vortex unpinning paradigm. Recent analyses of pulsar glitch data suggest that glitches result from scale-invariant avalanches \citep{Melatos07a}, which are consistent with a self-organized critical system (SOCS). A cellular automaton provides a computationally efficient means of modelling the collective behaviour of up to $10^{16}$ vortices in the pulsar interior, whilst ensuring that the dominant aspects of the microphysics are not lost. The automaton generates avalanche distributions that are qualitatively consistent with a SOCS and with glitch data. The probability density functions of glitch sizes and durations are power laws, and the probability density function of waiting times between successive glitches is Poissonian, consistent with statistically independent events. The output of the model depends on the physical and computational paramters used. The fitted power law exponents for the glitch sizes ($a$) and durations ($b$) decreases as the strength of the vortex pinning increases. Similarly the exponents increase as the fraction of vortices that are pinned decreases. For the physical and computational parameters considered, one finds $-4.3\leq a \leq -2.0$ and $-5.5\leq b\leq -2.2$, and mean glitching rates in the range $0.0023\leq\lambda\leq0.13\$ in units of inverse time.