Building on results from the Magnetism in Massive Stars (MiMeS) project, this paper shows how a two-parameter classification of massive-star magnetospheres in terms of the magnetic wind confinement (which sets the Alfvén radius R A ) and stellar rotation (which sets the Kepler co-rotation radius R K ) provides a useful organisation of both observational signatures and theoretical predictions. We compile the first comprehensive study of inferred and observed values for relevant stellar and magnetic parameters of 64 confirmed magnetic OB stars with T eff 16 kK. Using these parameters, we locate the stars in the magnetic confinement-rotation diagram, a log-log plot of R K vs. R A . This diagram can be subdivided into regimes of centrifugal magnetospheres (CM), with R A > R K , vs. dynamical magnetospheres (DM), with R K > R A . We show how key observational diagnostics, like the presence and characteristics of Hα emission, depend on a star's position within the diagram, as well as other parameters, especially the expected wind mass-loss rates. In particular, we identify two distinct populations of magnetic stars with Hα emission: namely, slowly rotating O-type stars with narrow emission consistent with a DM, and more rapidly rotating B-type stars with broader emission associated with a CM. For O-type stars, the high mass-loss rates are sufficient to accumulate enough material for line emission even within the relatively short free-fall timescale associated with a DM: this high mass-loss rate also leads to a rapid magnetic spindown of the stellar rotation. For the B-type stars, the longer confinement of a CM is required to accumulate sufficient emitting material from their relatively weak winds, which also lead to much longer spindown timescales. Finally, we discuss how other observational diagnostics, e.g. variability of UV wind lines or X-ray emission, relate to the inferred magnetic properties of these stars, and summarise prospects for future developments in our understanding of massive-star magnetospheres.

We present the analysis performed on spectropolarimetric data of 97 O-type targets included in the framework of the MiMeS (Magnetism in Massive Stars) Survey. Mean Least-Squares Deconvolved Stokes I and V line profiles were extracted for each observation, from which we measured the radial velocity, rotational and nonrotational broadening velocities, and longitudinal magnetic field B ℓ . The investigation of the Stokes I profiles led to the discovery of 2 new multi-line spectroscopic systems (HD 46106, HD 204827) and confirmed the presence of a suspected companion in HD 37041. We present a modified strategy of the Least-Squares Deconvolution technique aimed at optimising the detection of magnetic signatures while minimising the detection of spurious signatures in Stokes V . Using this analysis, we confirm the detection of a magnetic field in 6 targets previously reported as magnetic by the MiMeS collaboration (HD 108, HD 47129A2, HD 57682, HD 148937, CPD-28 2561, and NGC 1624-2), as well as report the presence of signal in Stokes V in 3 new magnetic candidates (HD 36486, HD 162978, HD 199579). Overall, we find a magnetic incidence rate of 7 ± 3%, for 108 individual O stars (including all O-type components part of multi-line systems), with a median uncertainty of the B ℓ measurements of about 50 G. An inspection of the data reveals no obvious biases affecting the incidence rate or the preference for detecting magnetic signatures in the magnetic stars. Similar to A-and B-type stars, we find no link between the stars' physical properties (e.g. T eff , mass, age) and the presence of a magnetic field. However, the Of?p stars represent a distinct class of magnetic O-type stars.

In this paper, we use the very recent spectropolarimetric observations of β Cep collected by Henrichs et al. and propose for this star a consistent model of the large‐scale magnetic field and of the associated magnetically confined wind and circumstellar environment. A re‐examination of the fundamental parameters of β Cep in the light of the Hipparcos parallax indicates that this star is most likely a 12‐M⊙ star with a radius of 7 R⊙, effective temperature of 26 000 K and age of 12 Myr, viewed with an inclination of the rotation axis of about 60°. Using two different modelling strategies, we obtain that the magnetic field of β Cep can be approximately described as a dipole with a polar strength of , the axis of symmetry of which is tilted with respect to the rotation axis by about . Although one of the weakest detected to date, this magnetic field is strong enough to magnetically confine the wind of β Cep up to a distance of about 8 to 9 R∗. We find that both the X‐ray luminosity and variability of β Cep can be explained within the framework of the magnetically confined wind‐shock model of Babel & Montmerle, in which the stellar‐wind streams from both magnetic hemispheres collide with each other in the magnetic equatorial plane, producing a strong shock, an extended post‐shock region and a high‐density cooling disc. By studying the stability of the cooling disc, we obtain that field lines can support the increasing disc weight for no more than a month before they become significantly elongated in an effort to equilibrate the gravitational plus centrifugal force, thereby generating strong field gradients across the disc. The associated current sheet eventually tears, forcing the field to reconnect through resistive diffusion and the disc plasma to collapse towards the star. We propose that this collapse is the cause for the recurrent Be episodes of β Cep, and finally discuss the applicability of this model to He peculiar, classical Be and normal non‐supergiant B stars.