The MiMeS survey of Magnetism in Massive Stars: Magnetic properties of the O-type star population

In this paper, we describe an analysis of the MiMeS Survey of O-type stars to explore the range of dipolar field strengths permitted by the polarisation spectra that do not yield a magnetic detection. We directly model the Stokes V profiles with a dipolar topology model using Bayesian inference. The noise statistics of the Stokes V profiles are in excellent agreement with those of the null profiles. Using a Monte-Carlo approach we conclude that a model in which all the stars in our sample were to host a 100\,G, dipolar magnetic field can be ruled out by the MiMeS data. Furthermore, if all the stars with no detection were to host a magnetic field just below their detection limit, the inferred distribution in strength of these undetected fields would be distinct from the known distribution in strength of the known magnetic O-type stars. This indicates that the Initial magnetic (B-)field Function (IBF) is likely bimodal -- young O-type stars are expected to either have weak/absent magnetic fields, or strong magnetic fields. We also find that better upper limits, by at least a factor of 10, would have been necessary to rule out a detection bias as an explanation for the apparent lack of evolved main-sequence magnetic O-type stars reported in the literature, and we conclude that the MiMeS survey cannot confirm or refute a magnetic flux decay in O-type stars.