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

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 will 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. (2010). The second concept, precession, was first considered as a candidate for the modulation of B1828-11 by Stairs et al. (2000). 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 results in a model that seems strongly preferred by the data over a switching model.