A layered model for non-thermal radio emission from single O stars
  We present a model for the non-thermal radio emission from bright O stars, in terms of synchrotron emission from wind-embedded shocks. The model is an extension of an earlier one, with an improved treatment of the cooling of relativistic electrons. This improvement limits the synchrotron-emitting volume to a series of fairly narrow layers behind the shocks. We show that the width of these layers increases with increasing wavelength, which has important consequences for the shape of the spectrum. We also show that the strongest shocks produce the bulk of the emission, so that the emergent radio flux can be adequately described as coming from a small number of shocks, or even from a single shock.   A single shock model is completely determined by four parameters: the position of the shock, the compression ratio and velocity jump of the shock, and the surface magnetic field. Applying a single shock model to the O5 If star Cyg OB2 No. 9 allows a good determination of the compression ratio and shock position and, to a lesser extent, the magnetic field and velocity jump.   Our main conclusion is that strong shocks need to survive out to distances of a few hundred stellar radii. Even with multiple shocks, the shocks needed to explain the observed emission are stronger than predictions from time-dependent hydrodynamical simulations. 
S. Van Loo, M. C. Runacres and R. Blomme