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 (Magnetism in Massive Stars) survey of O-type stars to explore the range of dipolar field strengths permitted by the polarization 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 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 field function' (IBF) is likely bimodal - young O-type stars are expected to have either 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.