Comparing models of the periodic variations in spin-down and beam-width for PSR B1828-11

TL;DR

This study uses Bayesian analysis to compare two models explaining periodic variations in PSR B1828-11, finding that a precession model with flexible beam geometry better fits the data than a simple switching model.

Contribution

It introduces a Bayesian framework for model comparison of pulsar variability, evaluating phenomenological switching and precession models with improved statistical rigor.

Findings

Precession model with general beam geometry fits data well.

Simple circular beam precession model fails to describe the data.

Bayesian odds favor precession over switching model by approximately 10^2.7.

Abstract

We build a framework using tools from Bayesian data analysis to evaluate models explaining the periodic variations in spin-down and beam-width of PSR B1828-11. The available data consists of the time averaged spin-down rate, which displays a distinctive double-peaked modulation, and measurements of the beam-width. Two concepts exist in the literature that are capable of explaining these variations; we formulate predictive models from these and quantitatively compare them. The first concept is phenomenological and stipulates that the magnetosphere undergoes periodic switching between two meta-stable states as first suggested by Lyne et al. The second concept, precession, was first considered as a candidate for the modulation of B1828-11 by Stairs et al.. We quantitatively compare models built from these concepts using a Bayesian odds-ratio. Because the phenomenological switching model itself was informed by this data in the first place, it is difficult to specify appropriate parameter-space priors that can be trusted for an unbiased model comparison. Therefore we first perform a parameter estimation using the spin-down data, and then use the resulting posterior distributions as priors for model comparison on the beam-width data. We find that a precession model with a simple circular Gaussian beam geometry fails to appropriately describe the data, while allowing for a more general beam geometry provides a good fit to the data. The resulting odds between the precession model (with a general beam geometry) and the switching model are estimated as $10^{2.7 \pm 0.5}$ in favour of the precession model.