Stellar magnetic field parameters from a Bayesian analysis of high-resolution spectropolarimetric observations

In this paper we describe a Bayesian statistical method designed to infer the magnetic properties of stars observed using high-resolution circular spectropolarimetry in the context of large surveys. This approach is well suited for analysing stars for which the stellar rotation period is not known, and therefore the rotational phases of the observations are ambiguous. The model assumes that the magnetic observations correspond to a dipole oblique rotator, a situation commonly encountered in intermediate- and high-mass stars. Using reasonable assumptions regarding the model parameter prior probability density distributions, the Bayesian algorithm determines the posterior probability densities corresponding to the surface magnetic field geometry and strength by performing a comparison between the observed and computed Stokes V profiles. Based on the results of numerical simulations, we conclude that this method yields a useful estimate of the surface dipole field strength based on a small number (i.e. one or two) of observations. On the other hand, the method provides only weak constraints on the dipole geometry. The odds ratio, a parameter computed by the algorithm that quantifies the relative appropriateness of the magnetic dipole model versus the non-magnetic model, provides a more sensitive diagnostic of the presence of weak magnetic signals embedded in noise than traditional techniques. To illustrate the application of the technique to real data, we analyse seven ESPaDOnS and Narval observations of the early B-type magnetic star LP Ori. Insufficient information is available to determine the rotational period of the star and therefore the phase of the data; hence traditional modelling techniques fail to infer the dipole strength. In contrast, the Bayesian method allows a robust determination of the dipole polar strength, G.